arXiv CSopen access

An Ontology for Machine Learning Interatomic Potentials

arXiv:2607.23219v1 [cs.AI] 25 Jul 2026

An Ontology for Machine Learning Interatomic Potentials DANIEL HERNÁNDEZ , Institute for Artificial Intelligence, University of Stuttgart, Germany JONG HYUN JUNG , Institute for Materials Science, University of Stuttgart, Germany YUJI IKEDA , Institute for Materials Science, University of Stuttgart, Germany YONGLIANG OU , Institute for Materials Science, University of Stuttgart, Germany PRANAV KUMAR , Institute for Materials Science, University of Stuttgart, Germany TOM SCHÄCHTEL , Institute for Materials Science, University of Stuttgart, Germany WENCHUAN LIU , Institute for Materials Science, University of Stuttgart, Germany XIN LI , Institute for Materials Science, University of Stuttgart, Germany XI ZHANG , Institute for Materials Science, University of Stuttgart, Germany XIANG XU , Institute for Materials Science, University of Stuttgart, Germany LIFANG ZHU , Institute for Materials Science, University of Stuttgart, Germany FRITZ KÖRMANN , Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), RuhrUniversität Bochum, Germany and Department for Computational Materials Design, Max-Planck-Institut for Sustainable Materials, Germany STEFFEN STAAB , Institute for Artificial Intelligence, University of Stuttgart, Germany BLAZEJ GRABOWSKI , Institute for Materials Science, University of Stuttgart, Germany Machine learning interatomic potentials (MLIPs) approximate quantum-mechanical energies and forces— conventionally computed by density functional theory (DFT) or wave-function methods—at a fraction of the cost. The field encompasses a growing ecosystem of algorithms, training datasets, hyperparameters, and target materials, yet the metadata needed to systematically compare, reproduce, and build upon MLIP studies remains scattered across papers, scripts, and ad-hoc file formats. We present the MLIPs ontology, an OWL 2 DL ontology that captures the concepts needed to describe MLIP methods, their hyperparameters, training datasets with DFT provenance, and published benchmarks. The ontology is organized into three modules—Method, Training Data, and Benchmark—and connects existing ontologies in materials science (MDO, CMSO/ASMO) and machine learning (ML-Schema), complementing dataset-side schemas such as Croissant. It declares 27 formal axioms enforcing data completeness and consistency, including property chains that link trained models to their methods and training data. We demonstrate the ontology through a running example based on Moment Tensor Potentials and evaluate it through competency-question execution on a 20-paper seeded knowledge graph, OWL reasoning, and comparison with existing ontologies. Additional Key Words and Phrases: Ontology, Machine learning interatomic potentials, Materials science, OWL, FAIR data Authors’ Contact Information: Daniel Hernández , [email protected], Institute for Artificial Intelligence, University of Stuttgart, Stuttgart, Germany; Jong Hyun Jung , [email protected], Institute for Materials Science, University of Stuttgart, Stuttgart, Germany; Yuji Ikeda , [email protected], Institute for Materials Science, University of Stuttgart, Stuttgart, Germany; Yongliang Ou , [email protected], Institute for Materials Science, University of Stuttgart, Stuttgart, Germany; Pranav Kumar , [email protected], Institute for Materials Science, University of Stuttgart, Stuttgart, Germany; Tom Schächtel , Institute for Materials Science, University of Stuttgart, Stuttgart, Germany; Wenchuan Liu , Institute for Materials Science, University of Stuttgart, Stuttgart, Germany; Xin Li , Institute for Materials Science, University of Stuttgart, Stuttgart, Germany; Xi Zhang , [email protected], Institute for Materials Science, University of Stuttgart, Stuttgart, Germany; Xiang Xu , Institute for Materials Science, University of Stuttgart, Stuttgart, Germany; Lifang Zhu , [email protected], Institute for Materials Science, University of Stuttgart, Stuttgart, Germany; Fritz Körmann , [email protected], Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universität Bochum, Bochum, Germany and Department for Computational Materials Design, Max-Planck-Institut for Sustainable Materials, Düsseldorf, Germany; Steffen Staab , [email protected], Institute for Artificial Intelligence, University of Stuttgart, Stuttgart, Germany; Blazej Grabowski , [email protected], Institute for Materials Science, University of Stuttgart, Stuttgart, Germany.

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Introduction

The MLIP community is sizable and growing: VASP, LAMMPS, and DeePMD-kit drew 13,200, 4,190, and 1,510 citations in 2025 [51], and MLIP-related publications rose from ∼50/year in 2015 to over 1,500 in 2024 [16, 34]. Machine learning interatomic potentials (MLIPs) [6, 10] predict atomic energies and forces at near the accuracy of their quantum-mechanical reference method— conventionally density functional theory (DFT) [35], increasingly also wave-function methods—at a fraction of its cost, enabling atomistic simulations at scale. MLIP families have proliferated over the past decade—HDNNP, GAP, ACE, MACE, NequIP, M3GNet, MTP, and others [7, 8, 14, 17, 49]—each with its own architecture, hyperparameter space, and application domain. This diversity makes routine tasks—selecting an algorithm for a given material, building a training set, comparing results across papers—hard [24]. Study metadata (algorithm, training set, material, DFT settings, accuracy) is scattered across papers, supplements, scripts, and library-specific formats. Existing ontologies do not close the gap: ML-Schema [46], DMOP [33], MEX [19], and CMO [20] model generic ML workflows; EMMO [28], MDO [37], PMDco [9], and CMSO/ASMO [38] model the physical domain—neither captures the MLIP-specific concepts: physics-aware hyperparameters, training-dataset construction strategies, algorithm-aligned DFT reference settings, and benchmark accuracy across method/material pairs. We present the MLIPs ontology, an OWL 2 DL ontology [55] organized into three modules (Method, Training Data, Benchmark) that connects existing schemas rather than displacing them, reusing established vocabularies wherever an existing class or property already names the concept at hand: 22 formal alignment axioms plus 14 rdfs:subClassOf/subPropertyOf edges thread its terms through ML-Schema, PROV-O, MDO, CMSO/ASMO, schema.org, and QUDT (§5.2); 27 additional axioms enforce the MLIP-specific structure that no single existing ontology supplies, and SHACL shapes validate instance data. Its conceptual contributions are three MLIP-specific design decisions: hyperparameters are first-class type-level entities with units, defaults, and ranges (not literal values on runs); a DFT / wave-function reference-calculation hierarchy uses rdfs:subPropertyOf so legacy DFT data validates against family-agnostic super-properties; and an mlips:metaSort annotation per class carries the OntoClean classification. The schema is exercised on a 20-paper knowledge graph (all nine competency questions return non-empty rows), populated via an agenticAI extraction protocol whose output was returned to the domain experts for review—an extensional validation cycle that extends LOT’s intensional CQ-agreement loop (§4)—and is served at https://w3id.org/mlips with content negotiation. For consumers, cross-paper questions—which method reaches a target accuracy on a material class, which training data exists with compatible DFT settings—reduce to single SPARQL queries instead of a manual literature survey, for human researchers and autonomous agents alike; for producers, an encoded study is one that those selection queries can find, and the encoding protocol doubles as a reporting checklist that surfaces unreported metadata before reviewers do. A concrete usage plan sustains the resource beyond this paper (§7): the META-LEARN project (2026–2030) commits the two Stuttgart institutes to maintenance and feeds the knowledge graph from its own MLIP studies; practitioners extend the controlled vocabulary through the candidate-vocabulary workflow without ontology-engineering skills; and we are in contact with the maintainers of complementary materials-science vocabularies toward federated semantic services, with our service contributing the MLIP metadata. 2

Running Example: Moment Tensor Potentials for TiCr2 Laves Phases

We introduce the MLIPs ontology (presented in Section 5) through a concrete published study: training a Moment Tensor Potential (MTP) [42, 49] for hydrogen absorption in the TiCr2 –H system by Kumar et al. [36]. TiCr2 is an intermetallic compound which absorbes hydrogen (𝐻 ). It crystallizes

An Ontology for Machine Learning Interatomic Potentials

3 Ti

N𝑖

Cr H

𝑅cut 𝑅min

(a)

(b)

Fig. 1. (a) A TiCr2 H𝑥 simulation cell. (b) Neighborhood set N𝑖 of atom 𝑖 (calligraphic N , not nickel): atoms within 𝑅cut contribute to 𝑉 (N𝑖 ); greyed atoms (outside 𝑅cut ) are excluded; 𝑅min bounds the radial domain. Table 1. Namespace prefixes used by the MLIPs ontology. Prefix Namespace

Prefix

Namespace

schema: https://schema.org/

entity:

https://w3id.org/mlips/entity/

mlips:

https://w3id.org/mlips/

wd:

http://www.wikidata.org/entity/

mls:

http://www.w3.org/ns/mls#

mdo-calc:

https://w3id.org/mdo/calculation/

prov:

http://www.w3.org/ns/prov#

cmso:

https://purls.helmholtz-metadaten.de/cmso/

mdo:

https://w3id.org/mdo/core/

asmo:

https://purls.helmholtz-metadaten.de/asmo/

qudt:

http://qudt.org/schema/qudt/

in two close-packed forms (a cubic one and a hexagonal one), and Kumar et al. train one MTP per form over the hydrogen-content range 0 < 𝑥 ≤ 6 for TiCr2 H𝑥 (the stoichiometric ratio of H atoms per TiCr2 formula unit). We use the cubic form (called C15 in the materials literature) as the running example. The example illustrates how the ontology captures the full lifecycle of an MLIP study—from the underlying physics, through the method’s hyperparameters and training data, to the evaluation of the trained model. A simulation cell is a finite region of space with periodic boundary conditions containing 𝑛 atoms at positions r1, . . . , r𝑛 with atomic types 𝑧 1, . . . , 𝑧𝑛 (𝑧𝑖 ∈ {Ti, Cr, H} for our TiCr2 H𝑥 running example). An interatomic potential predicts the total energy 𝐸 and forces F𝑖 = −∇r𝑖 𝐸 acting on each atom given only the atomic positions and types (Fig. 1a). In quantum mechanics, the total energy can be computed accurately (within the approximations of density functional theory) by solving the Kohn–Sham equations [35]. However, this is computationally expensive—scaling as 𝑂 (𝑛 3 ) with the number of atoms—limiting DFT to systems of a few hundred atoms. Machine learning interatomic potentials approximate the DFT energy surface at a fraction of the cost—scaling linearly in 𝑛 for strictly local short-ranged potentials—enabling simulations of millions of atoms. The MTP method. In the MTP framework [49], theÍtotal energy of an atomic configuration cfg is decomposed into local contributions 𝐸 mtp (cfg) = 𝑛𝑖=1 𝑉 (N𝑖 ), where N𝑖 is the neighborhood of atom 𝑖, defined as the set of all atoms within the cutoff radius 𝑅cut . The neighborhood consists of the atomic type 𝑧𝑖 of the central atom, and for each neighbor 𝑗 within 𝑅cut : the atomic type 𝑧 𝑗 and the relative position vector r𝑖 𝑗 = r 𝑗 − r𝑖 . Atoms beyond 𝑅cut do not contribute to 𝑉 (N Í𝑖 )—this locality assumption keeps the energy computation tractable. The local energy 𝑉 (N𝑖 ) = 𝛼 𝜉𝛼 𝐵𝛼 (N𝑖 ) is a linear combination of basis functions, where the 𝐵𝛼 are moment tensor descriptors—invariant

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functions of the neighborhood that capture the local atomic environment—and 𝝃 = {𝜉𝛼 } are the parameters to be learned by fitting to DFT reference data. The basis functions 𝐵𝛼 are contractions of moment tensors 𝑀𝜇,𝜈 involving radial functions 𝑄 𝜇 (|r𝑖 𝑗 |, 𝑧𝑖 , 𝑧 𝑗 ) that vanish smoothly at 𝑅cut and are evaluated above a minimum interatomic distance 𝑅min (a numerical lower bound; physical interactions are not truncated). MTP thus has four hyperparameters: two geometric (the cutoff radius 𝑅cut and minimum interatomic distance 𝑅min , illustrated in Fig. 1b) and two algorithmic that control basis size (the number of radial basis functions 𝑁𝑄 and the maximum polynomial level levmax of the moment-tensor descriptors, both systematically increasable for higher accuracy). The MLIP workflow—and the ontology—separate three levels of parameterization: hyperparameter definitions (a parameter’s name, data type, valid range, default; declared once in the controlled vocabulary or paper-locally with a candidateForVocabulary marker), hyperparameter settings (concrete values chosen for a specific MLIP run, e.g., 𝑅cut = 5.0 Å, levmax = 16), and the learned parameters 𝝃 that define the trained model. To enable queries such as “which physically motivated hyperparameters does this method accept?”, we classify hyperparameters into three non-disjoint subclasses of Hyperparameter: physical (parameters set by reference to a physical scale, such as an interaction range—strictly speaking, every hyperparameter is a parameter of the mathematical approximation rather than of the physics, and this subclass marks those whose values domain scientists choose on physical grounds), architectural (model-architecture choice), and training (training-procedure parameter). The non-disjointness is a modelling choice informed by domain expertise: 𝑅cut and 𝑅min are physically motivated (they tie to interaction-range and short-distance scales), the optimizer’s learning rate is purely training, but 𝑁𝑄 and levmax are both architectural and physically motivated—they control the model size and also determine how finely the radial and angular expansions are resolved. A strict partition would misrepresent how materials scientists think about these parameters. Encoding: run, settings, model. The example is expository, not the design method: the schema’s decisions were elicited from the competency questions of Section 4, their rationale is given in Section 5 and Appendix G, and their validation is extensional—competency-question execution over the 20-paper corpus of Section 6, of which this study is one entry. The listings below show what the finished vocabulary looks like in use. Throughout the section, prefix entity: is bound to https://w3id.org/mlips/entity/. An MLIPRun applies a method to a training dataset under concrete hyperparameter settings—each an instance of HyperparameterSetting linking to a definition—and produces the trained model. A TrainedModel holds the fitted coefficients 𝝃 : Listing 1. MLIP run, a hyperparameter setting, and the trained model. entity : run - mtp - TiCr2H - c15 a mlips : MLIPRun ; mlips : appliesMethod entity : MTP ; mlips : runsOn entity : ds - TiCr2H - c15 ; mlips : produces entity : model - mtp - TiCr2H - c15 ; mlips : hasHyperparameterSetting entity : setting - rcut . entity : setting - rcut a mlips : HyperparameterSetting ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : settingValue " 5.0 " ^^ xsd : double ; mlips : hasUnit unit : ANGSTROM . entity : model - mtp - TiCr2H - c15 a mlips : TrainedModel ; rdfs : label " C15 - MTP ␣ for ␣ TiCr2 - H ␣ ( lev16 , ␣ rcut5 ) " .

Hyperparameter definitions are attached to the method, whereas the settings of Listing 1 belong to the run. The method also names its three components (functional form, loss function, training algorithm), supported simulation types, and implementations (Listing 2): Listing 2. MTP method: functional form, loss function, training algorithm, hyperparameter definitions, and implementation.

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entity : MTP a mlips : MLIPMethod ; rdfs : label " Moment ␣ Tensor ␣ Potential " ; mlips : hasFunctionalForm entity : mtp - functional - form ; mlips : hasLossFunction entity : mtp - loss ; mlips : hasTrainingAlgorithm entity : bfgs ; mlips : hasHyperparameter mlips : cutoffRadius , mlips : minInteratomicDistance , entity :hp -nq , mlips : momentLevel ; mlips : hasImplementation entity : mlip - package - v2 ; mlips : supportsSimulation entity : sim - md , entity : sim - geopt . entity : mtp - functional - form a mlips : FunctionalForm ; rdfs : label " MTP ␣ moment - tensor ␣ polynomial " . entity : mtp - loss a mlips : LossFunction ; rdfs : label " Weighted ␣ MSE ␣ ( energy ␣ 1 , ␣ force ␣ 0.01 , ␣ stress *V␣ 0.001) " . entity : bfgs a mls : Algorithm ; rdfs : label " BFGS " . entity :hp - nq a mlips : Hyperparameter ; mlips : hyperparameterName " N_Q " ; mlips : hyperparameterDatatype xsd : integer ; mlips : candidateForVocabulary mlips : Hyperparameter . entity : mlip - package - v2 a mlips : Implementation ; mlips : implementedIn mlips : MLIP ; mlips : version " 2 " . entity : sim - md a mlips : SimulationType ; rdfs : label " molecular ␣ dynamics " . entity : sim - geopt a mlips : SimulationType ; rdfs : label " geometry ␣ optimization " .

Training data. Ground truth comes from DFT calculations of total energy, forces, and (optionally) stresses for each configuration; configurations are drawn from MD trajectories, random perturbations, or active learning [42]. The initial low-hydrogen enumeration in Kumar et al. [36] yields 1,019 configurations on 2×2×2 C15 supercells, computed with PBE/PAW and a 400 eV plane-wave cutoff in VASP: Listing 3. Training dataset and DFT settings. entity :ds - TiCr2H - c15 a mlips : TrainingDataset ; rdfs : label " TiCr2 - H ␣ DFT ␣ dataset ␣ ( C15 , ␣ step ␣ 1) " ; mlips : coversMaterial entity : mat - TiCr2 ; mlips : coversProperty mlips : Energy , mlips : Forces , mlips : Stresses ; mlips : datasetProvenance mlips : Published ; mlips : numConfigurations " 1019 " ^^ xsd : integer ; mlips : hasDFTCalculation entity : dft - TiCr2H . entity : mat - TiCr2 a mlips : MaterialSystem ; mlips : chemicalFormula " TiCr2 " ; mlips : materialClass " Laves ␣ phase , ␣ C15 ␣ cubic ␣ ( Fd -3 m ) " . entity : dft - TiCr2H a mlips : DFTCalculation ; mlips : hasDFTSettings entity : dft - settings - TiCr2H . entity : dft - settings - TiCr2H a mlips : DFTSettings ; mlips : usedDFTCode mlips : VASP ; mlips : xcFunctional mlips : PBE ; mlips : pseudopotentialType mlips : PAW ; mlips : energyCutoff " 400 " ^^ xsd : double ; mlips : kPointMesh " 4 x4x4 ␣ Gamma - centered " .

Evaluation. Each evaluation produces a BenchmarkResult within a BenchmarkStudy: Listing 4. Benchmark study and evaluation result. entity : study - kumar2025 a mlips : BenchmarkStudy ; rdfs : label " Kumar ␣ et ␣ al . ␣ (2025) ␣ -␣ MTP ␣ for ␣ TiCr2 - H ␣ Laves ␣ phases " ; mlips : hasResult entity : result -01 . entity : result -01 a mlips : BenchmarkResult ; mlips : evaluatesModel entity : model - mtp - TiCr2H - c15 ; mlips : targetMaterial entity : mat - TiCr2 ; mlips : hasAccuracyMetric entity : metric - rmse - energy . entity : metric - rmse - energy a mlips : AccuracyMetric ; mlips : metricType mlips : RMSE ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricValue " 3.17 " ^^ xsd : double ; mlips : hasUnit mlips : MilliEV - PER - ATOM .

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Related Work

We organize the related work into three streams: ontologies for machine learning, ontologies for materials science, and cross-domain metadata templates and FAIR [56, 57]-data consortia. The MLIPs Ontology is a domain-specific schema; for cross-domain terminology covering scientificworkflow systems generally we refer to Suter et al. [50]. Section 6.4 returns to the ontologies surveyed here: Table 6 assesses, term by term, which of them can answer the competency questions of Section 4. Ontologies for Machine Learning. ML-Schema [46], from a W3C community group, provides top-level classes for ML algorithms, datasets, and experiments. DMOP [33] supports ontologydriven algorithm selection and hyperparameter optimization for data mining workflows. The MEX vocabulary [19] provides a lightweight RDF vocabulary for ML experiment metadata, built on PROV-O. The Common Metadata Ontology (CMO) [20] integrates pipeline metadata from multiple ML platforms. These efforts cover generic ML workflows but miss MLIP-specific concepts: algorithm families with physics-specific hyperparameters (cutoff radii, angular/radial basis functions), trainingset construction strategies, and DFT reference settings. Ontologies for Materials Science. The European Materials Modelling Ontology (EMMO) provides a top-level ontology grounded in mereocausality theory [28]. The Materials Design Ontology (MDO) [37] is an OWL 2 DL ontology with four modules (Core, Structure, Calculation, Provenance); it has been used for SPARQL-based integrated querying over the Materials Project [32] and OQMD [47]. PMDco [9] provides a mid-level ontology aligned with BFO. CMSO and ASMO [38] describe atomic structures and simulation methods, and a recent survey by Norouzi et al. [41] analyzes 60 ontologies in the field. These ontologies cover the physical domain but miss MLIP-training concepts: per-algorithm hyperparameters, training-dataset construction and DFT settings, and benchmark comparisons across algorithms, materials, and properties. Concurrent work by Ravari et al. [5] pursues LLM-assisted extraction of DFT workflows aligned to CMSO/ASMO via atomRDF, addressing workflow reproducibility rather than benchmark-comparison knowledge graphs. Metadata schemas and platforms in computational materials science. Major computationalmaterials-science platforms define rich metadata schemas for simulation data, often in platform-specific formats but increasingly with Semantic Web surfaces. NOMAD [22]’s NOMAD Metainfo normalizes outputs from diverse simulation codes and is progressively aligning with EMMO. The Materials Project [32], AFLOW [15], and OQMD [47] expose data through custom REST APIs with their own JSON schemas; OPTIMADE [2] standardizes cross-database queries via a JSON:API spec. AiiDA [29] automatically tracks full data provenance as a directed acyclic graph and, with Materials Cloud [52], provides data-dissemination infrastructure. Kadi4Mat [13] is a virtual research environment for FAIR data management with hierarchical collections, access control, and metadata records (e.g., the file repository in Circular Factory CRC 1574 [53]); recent versions add RDF export and SPARQL endpoints. Recent work by Azocár Guzmán et al. [3] demonstrates FAIR-compliant RDF workflows using CMSO, ASMO, and PROV-O within pyiron, and a follow-on infrastructure paper from the same group [4] generalizes the approach to a knowledge graph of ∼750 K triples across ∼8 K samples covering grain-boundary, cross-dataset, and thermodynamic queries beyond pyiron-specific workflows. These schemas, platforms, and workflow graphs focus on DFT calculations, material structures, and simulation provenance, but lack descriptions of specific MLIP algorithms and workflows—hyperparameters, training-set construction, and cross-paper benchmarks. Concretely, a user of these platforms today cannot ask: which trained models were fitted to PBE reference data with a 5 Å cutoff, and how do they rank on

An Ontology for Machine Learning Interatomic Potentials

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phonon benchmarks?—the platforms store MLIP runs as opaque files, so selection and comparison queries over method, training-data, and benchmark metadata have nothing to bind to. The MLIPs ontology offers these platforms an MLIP-specific shared vocabulary they can adopt to expose their metadata with explicit, machine-interpretable semantics. Cross-domain metadata templates and FAIR-data consortia. Four further streams target ML-wide metadata templates or coordinate FAIR-data efforts at consortium scale, each complementary to the MLIPs ontology. Datasheets for Datasets [21] and Model Cards [39] are narrative templates for ML datasets and models, now de-facto practice in mainstream ML publishing. Croissant [1] formalizes the dataset side as a JSON-LD schema, now used by the Hugging Face Hub, Kaggle, and OpenML; Hugging Face’s own model-card metadata [30] is the YAML-frontmatter counterpart for trainedmodel descriptions. The MLIPs ontology serves the algorithm- and benchmark-side counterpart of this stack: where Croissant and Datasheets describe what is in a dataset, our TrainingDataset captures how the dataset was generated via DFT or wavefunction reference calculations, and our BenchmarkResult structures the cross-paper accuracy comparisons that Model Cards leave to freetext. At cross-sector level, the DCAT Application Profile (DCAT-AP) [48] is the European standard for data-portal metadata, implemented by data.europa.eu and many national portals; the MLIPs ontology extends DCAT-AP at the algorithm-and-benchmark level: an MLIP-related catalog entry is a DCAT-AP Dataset whose distribution carries our mlips: predicates in addition to DCATAP’s generic ones. Adjacent EMMO-aligned domain ontologies form a third stream: CHAMEO [18] formalizes characterization-method metadata across analytical chemistry, and BattINFO [11] extends EMMO to battery interfaces and electrochemistry. The MLIPs ontology aligns with the same EMMO-rooted ecosystem (§6.4); where CHAMEO and BattINFO model the underlying chemistry, our schema models the ML-driven interpolation of that chemistry. At consortium scale, the German NFDI-MatWerk [40] consortium operates an ontology registry that materials-science vocabularies (CMSO, ASMO, BattINFO, MDO) are progressively adopting; sister consortia (NFDI4Chem for chemistry, NFDI4Ing for engineering) use the same Linked Open Vocabularies pattern and are candidate alignment targets. 4

Requirements

Requirements were gathered through iterative discussions with domain experts (materials scientists and MLIP developers) in the META-LEARN project [24]. We followed the LOT (Linked Open Terms) methodology [43], whose requirements phase yielded the following competency questions: CQ1. Which MLIP algorithms exist, and what hyperparameters does each accept (with types, ranges, and default values)? CQ2. Which libraries implement a given algorithm, and what versions are available? CQ3. For a given material system (a chemical composition together with its phase or crystal structure), which training datasets are available, and what DFT code and settings were used to generate them? CQ4. What is the provenance of a training dataset (published source, in-house calculation, augmented from existing data)? CQ5. How many atomic configurations does a training dataset contain, what properties are covered (energies, forces, stresses), and along which sampling strategy were the configurations drawn (e.g., chemical, vibrational, or a combination)? CQ6. Which published studies have benchmarked a given algorithm on a given material property, and what accuracy metrics were reported? CQ7. For a given material and target property, how do different algorithm and hyperparameter combinations rank by accuracy?

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Library

Implementation

implementedIn

FunctionalForm hasFunctionalForm

hasImplementation

SimulationType

MLIPMethod

supportsSimulation

appliesMethod

LossFunction

hasLossFunction hasHyperparameter

MLIPRun

trainedWith

Hyperparameter

produces

hasHyperparameterSetting

forHyperparameter

TrainedModel

trainedUsing

HyperparameterSetting

runsOn

AtomicConfiguration

MaterialSystem

evaluatesModel

hasResult

targetMaterial

BenchmarkResult

coversMaterial

TrainingDataset

hasConfiguration

hasAccuracyMetric hasDFTCalculation

datasetProvenance coversProperty

DatasetProvenance

BenchmarkStudy

CoveredProperty

DFTCalculation

AccuracyMetric

hasDFTSettings

DFTSettings

metricType metricProperty

MetricType

MetricProperty

Fig. 2. Overview of the MLIPs ontology: three modules and their core classes and relationships. Node fill color encodes module membership (blue: Method; green: Training Data; orange: Benchmark); cross-module relationships are drawn as dashed arrows.

CQ8. Which simulation types (molecular dynamics, Monte Carlo, geometry optimization, phonon calculations, thermodynamic integration) have been performed with a given MLIP? CQ9. For a given target accuracy, which algorithms and trained models are most efficient—both in asymptotic complexity, known from the method’s design, and in measured training and inference cost, as reported by studies? We extended LOT’s intensional CQ-agreement loop with an extensional validation cycle: the seeded knowledge graph (§6.1), extracted from twenty MLIP papers via an agentic-AI protocol (§K.1), was returned to domain experts for review. Reviewing encoded data rather than the schema in isolation surfaced gaps and ambiguities most efficiently; round-trip validation per paper catches schema drift across iterations. 5

The MLIPs Ontology

The MLIPs ontology is an OWL 2 DL ontology organized into three modules that address the competency questions of Section 4; Figure 2 provides an overview. Beyond answering the competency questions, the schema reflects four engineering choices of our own—adopted as Semantic Web good practice rather than elicited from the domain experts: alignment with existing ontologies (§5.2), SHACL validation (§5.2, §7), Linked-Data integration via Wikidata (§7), and extensibility for new algorithm families and hyperparameters (candidate-vocabulary workflow, §7). The ontology uses the namespace https://w3id.org/mlips/ (prefix mlips:); Table 1 lists the external prefixes used. 5.1

Ontology Modules

Method module. MLIPMethod is the named recipe (e.g., MACE, ACE, HDNNP) for turning an atomic configuration into an energy. It bundles a parametrized functional form (FunctionalForm, via hasFunctionalForm), a loss function (LossFunction, via hasLossFunction), a training algorithm (an mls:Algorithm via hasTrainingAlgorithm, e.g., Adam, L-BFGS—the sole alignment point

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with ML-Schema), and an atomic environment descriptor (AtomicEnvironmentDescriptor) capturing the local-neighborhood representation each method uses (moment tensors for MTP, SOAP for GAP, symmetry functions for HDNNP, equivariant message passing for MACE/NequIP, atomic cluster expansion for ACE). Each method declares the Hyperparameter instances it accepts via hasHyperparameter, names its Implementations in specific Librarys and versions via hasImplementation, and marks the kinds of SimulationType it supports via supportsSimulation. An MLIPRun appliesMethod a method, runsOn a TrainingDataset, and produces a TrainedModel, with an optional hasTrainingRun to an underlying mls:Run. An MLIPRun denotes one concrete execution: training is generally non-deterministic (initialization, data shuffling, parallel reduction order), so repeated runs with identical settings are distinct individuals that may produce distinct TrainedModels. TrainedModel carries shortcut roles trainedWith and trainedOn (property chains through the run). Hyperparameter values are recorded as domain-specific datatype properties (e.g., cutoffRadius, numLayers) with QUDT-annotated units [27]. Efficiency metadata is split: prior-knowledge complexity (e.g., trainingComplexity, inferenceComplexity, supportsGPU) on MLIPMethod; measured cost (e.g., wall-clock, peak memory) on MLIPRun; measured inference cost on the corresponding BenchmarkResult. The module thus addresses CQ1 (methods and their hyperparameters), CQ2 (implementations and versions), CQ8 (supported simulation types), and CQ9 (efficiency). Training Data module. A TrainingDataset holds AtomicConfiguration instances over one or more MaterialSystem instances; numConfigurations records the dataset size, and coversProperty marks the physical properties included (energy, forces, stresses, virials). Reference data comes from a ReferenceCalculation, with two concrete subclasses (DFTCalculation and WaveFunctionCalculation1 ) each governed by its own settings type (DFTSettings, WaveFunctionSettings); method-specific data properties (xcFunctional, kPointMesh for DFT; wfMethod, basisSet for wave-function methods) live on each subtype. The DFT-specific predicates hasDFTCalculation, hasDFTSettings, and usedDFTCode are declared rdfs:subPropertyOf their family-agnostic counterparts hasReferenceCalculation, hasReferenceSettings, and usedReferenceCode, so legacy data validates and supertype queries pick up DFT-only data via sub-property entailment. datasetProvenance classifies the training data as Published, InHouse, or Augmented (with PROV-O’s prov:wasDerivedFrom tracking source datasets in the latter case); the optional samplingStrategy records how configurations were drawn (e.g., chemical, vibrational, active-learning). The module thus addresses CQ3 (datasets and their reference calculations), CQ4 (provenance), and CQ5 (size, covered properties, and sampling strategy). Benchmark module. A BenchmarkStudy contains one or more BenchmarkResult instances, each capturing a single evaluation of a TrainedModel on a material system, linked via evaluatesModel and targetMaterial. Since a trained model already encodes the method, training data, and hyperparameter settings, a result need only reference the model and the test conditions. Results report AccuracyMetric instances via hasAccuracyMetric, each characterized by a MetricType (RMSE, MAE, R2 , via metricType), a MetricProperty (energy, force, stress, via metricProperty), and a numeric value with unit (via metricValue); reportedIn links a result to its source publication. The module thus addresses CQ6 and CQ7; the “target property” of CQ7 corresponds to MetricProperty, and is distinct from the dataset-side CoveredProperty class; applied target properties (e.g., hydrogenadsorption energy) are operationalized through energy or force metrics on specific configurations, not as a first-class concept. 1We include wave-function methods (CCSD(T), MP2, CASPT2) because some MLIPs are now trained on CCSD(T) reference

data.

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PROV-O L4 L3

L5

Method L19 L20

schema.org

L18

Benchmark

MDO L1, L12, L13 L6, L17 L7, L8 L10 L11

L9

QUDT

MLS L14

L2

Training Data

L15 L16

CMSO

L21 L22

Fig. 3. Alignment graph for the MLIPs ontology. Solid blue circles are MLIPs ontology modules; dashed grey circles are external ontologies. Each arc carries the labels of the alignment axioms it represents (cf. (L1)–(L22)); arc thickness is proportional to the number of axioms collapsed onto it. Table 2. Catalogue of the 22 alignment axioms of the MLIPs ontology (cf. Fig. 3). (L1) TrainedModel ⊑ mls:Model (L2) TrainingDataset ⊑ mls:Dataset (L3) MLIPRun ⊑ prov:Activity (L4) TrainingDataset ⊑ prov:Entity (L5) BenchmarkStudy ⊑ prov:Activity (L6) MLIPMethod ⊓ mls:Algorithm ⊑ ⊥ (L7) ∃ hasTrainingRun.⊤ ⊑ MLIPRun (L8) ⊤ ⊑ ∀ hasTrainingRun.mls:Run (L9) ⊤ ⊑ ∀ hasUnit.qudt:Unit (L10) ∃ runsOn.⊤ ⊑ MLIPRun (L11) ⊤ ⊑ ∀ runsOn.TrainingDataset

5.2

(L12) Hyperparameter ⊑ mls:HyperParameter (L13) Implementation ⊑ mls:Implementation (L14) DFTCalculation ⊑ mdo:Calculation (L15) MaterialSystem ⊑ cmso:CrystallineMaterial (L16) AtomicConfiguration ⊑ cmso:AtomicStructure (L17) MLIPMethod ⊑ ∃ hasTrainingAlgorithm.mls:Algorithm (L18) ⊤ ⊑ ∀ reportedIn.schema:ScholarlyArticle (L19) ∃ evaluatesModel.⊤ ⊑ BenchmarkResult (L20) ⊤ ⊑ ∀ evaluatesModel.TrainedModel (L21) ∃ targetMaterial.⊤ ⊑ BenchmarkResult (L22) ⊤ ⊑ ∀ targetMaterial.MaterialSystem

Axioms, alignment, and meta-categorization

The schema’s formal axioms fall into three categories. Alignment axioms (22 labelled (L1)–(L22), see below) connect mlips: terms to ML-Schema, PROV-O, MDO, CMSO, schema.org, and QUDT. Metacategorization axioms (see below) are existential constraints inferred from each class’s OntoClean classification (every reified-relation class is required to carry the entity it reifies). Other axioms— existential restrictions, cardinality constraints, inverse-existence axioms, property chains, and domain restrictions—enforce data completeness and consistency at the schema level. The full catalog is published alongside the ontology at https://w3id.org/mlips/. Alignment. The MLIPs ontology reuses established vocabularies wherever an existing class or property already names the concept at hand: ML-Schema for the ML workflow, PROV-O for activity-based provenance, MDO and CMSO for materials science, schema.org for bibliographic metadata, and QUDT for units. Figure 3 shows the resulting alignment graph; each arc carries the labels of the formal alignment axioms (L1)–(L22) it represents, with line width proportional to the number of axioms collapsed onto it. The full axiom catalog is provided in Appendix 2. The single salient design decision—the disjointness in (L6) between MLIPMethod and mls:Algorithm, with hasTrainingAlgorithm (L17) as the sole connecting role—keeps the domain-level recipe distinct from the generic ML training algorithm it delegates to; the decision is discussed in detail in Appendix H. Beyond the 22 cataloged axioms, the schema carries 14 additional rdfs:subClassOf / rdfs:subPropertyOf edges from mlips: terms

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to their closest external parents (e.g., mlips:Library ⊑ schema:SoftwareApplication, mlips:HyperparameterSetting ⊑ mls:HyperParameterSetting, mlips:metricValue ⊑ qudt:value), making the alignment queryable rather than narrative-only. Enumerative classes (e.g., XCFunctional, MetricType), descriptor classes, and bespoke constructs (e.g., FunctionalForm, LossFunction, SamplingStrategy) lack a clear external parent and remain unaligned. The full edge list: • mlips:Library ⊑ schema:SoftwareApplication; • mlips:Implementation ⊑ schema:SoftwareSourceCode (in addition to L13); • mlips:BenchmarkResult ⊑ prov:Entity; • mlips:AccuracyMetric ⊑ qudt:QuantityValue; • mlips:MaterialSystem ⊑ mdo:Material (in addition to L15); • mlips:ReferenceCalculation ⊑ prov:Activity (and inherited by DFTCalculation and WaveFunctionCalculation); • mlips:TrainedModel ⊑ prov:Entity (in addition to L1); • mlips:HyperparameterSetting ⊑ mls:HyperParameterSetting; • mlips:hasHyperparameter ⊑ mls:hasHyperParameter; • mlips:hasUnit ⊑ qudt:hasUnit; • mlips:metricValue ⊑ qudt:value; • mlips:produces ⊑ prov:generated; • mlips:runsOn ⊑ prov:used; • mlips:hasResult ⊑ prov:generated. A SPARQL query over the merged ontology returns the full set of external-vocabulary parents directly. Meta-categorization. We classify every mlips: class by its OntoClean meta-properties [25] into one of four named categories (Sortal, Subordinate Sortal, Role, Reified Relation) attached as an mlips:metaSort annotation. We define the four values locally rather than importing OntoClean’s OWL serialization, which currently does not resolve and lacks a first-class entry for reified 𝑛-ary relations (the most common non-sortal kind here). One consequence is formal: each reifiedrelation class carries an existential axiom requiring its carrier (e.g., HyperparameterSetting ⊑ ∃ isSettingOf.MLIPRun); the full per-class classification, meta-property analysis, and the CONSTRUCT rules for computed labels and inverse triples are in Appendix I and, machine-readably, in the ontology source and its DaRUS deposit [26]. 6

Evaluation

We evaluate the MLIPs ontology along multiple dimensions: a seeded knowledge graph of published MLIP studies, competency question coverage via SPARQL queries against that graph, consistency verification via OWL reasoning, automated pitfall detection, and comparison with existing ontologies. 6.1

Seeded Knowledge Graph

To exercise the ontology against real data, we encoded 20 published MLIP studies into a seeded knowledge graph. The full catalog (one subsection per paper, organized around a 12-question extraction protocol with a round-trip check) is in Appendix K, and the complete triple-level encoding of the running example (Kumar et al. [36]), of which Section 2 shows the core listings, is in Appendix J; both are also archived on DaRUS [26]. The graph contains 3,561 triples across the 20 paper-graph instances and 376 more in the controlled-vocabulary file mlips-vocab.ttl; together with the 1,098-triple T-Box, this is a 5,027-triple graph.

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Table 3. Diversity axes of the seeded knowledge graph.

Axis

Coverage

Papers Method families

20 HDNNP, GAP, MTP, ANI, ACE, SchNet, MACE/NequIP/Allegro, M3GNet/CHGNet, DeepMD Reference method DFT (19), wave-function (1) XC functionals (DFT) PBE (12), PBE0 (2), PW91 (2), HSE06 (1), 𝜔B97X (2), LDA (1); 19/20 studies report an XC functional; the counts sum to 20 because lysogorskiy2021ace reports two (PBE for Cu, PW91 for Si) Pseudopotential / basis PAW (8), ultrasoft (2), norm-conserving (1), all-electron with DftBasisSet (3); 6 studies do not report a basis specification Sampling strategies vibrational/AIMD, chemical-space, active-learning, random-perturbation, surface enumeration, defect sampling Diversity. The corpus deliberately covers multiple axes of variation (Table 3). Method families span the chronological arc of the field (HDNNP from 2007 through MACE-MP-0 in 2024) and the architectural spectrum (descriptor + regressor in GAP, MTP, ACE; deep-network in HDNNP, ANI, SchNet, DeepMD; equivariant message passing in MACE, NequIP, Allegro; universal/foundation models in M3GNet, CHGNet, MACE-MP-0). Reference data is predominantly DFT, but one paper (smith2019ccx, the ANI-1ccx transfer-learning study) trains to CCSD(T) data and exercises the WaveFunctionCalculation/WaveFunctionSettings branch added in this work. Materials cover elemental crystals (Si, Cu, Fe, W), intermetallics (TiAl, Ti3 Al, Ni–Al, Ti–Al–V), Laves phases (TiCr2 ), magnetic oxides (MnO), high-entropy alloys (TaVCrW), hydrogen-bonded liquids (water and ice polymorphs), organic molecules, and universal coverage of the Materials Project (MACE-MP-0, CHGNet, M3GNet). Controlled vocabulary and extension. The vocabulary file declares named individuals (e.g., mlips:PBE, mlips:PAW, mlips:DLPNO_CCSDT) for the four open extension-point classes (XCFunctional, PseudopotentialType, WfMethod, DftBasisSet). When an encoded paper reports a value not yet in the vocabulary, the encoder mints a paper-local IRI tagged candidateForVocabulary; the corpus currently has two such candidates (Gaussian basis sets 6-31G(d) and 6-31G∗ ), both flagged for promotion review. Reportable-vs-reported gaps. A first cross-corpus pass exposes the metadata gap motivating the ontology: 18/20 studies report energy errors and 15/20 report force errors, but only 9/20 report any training- or inference-cost metadata, and 0/20 report peak memory. Per-predicate: training hardware 6, inference time per atom 5, inference hardware 4, training duration 2, GPU hours 1. The ontology can express each of these per paper; the literature reports them only intermittently. Section 6.2 formalizes this through competency-question SPARQL queries. 6.2

Competency Question Execution

All nine competency questions (Section 4) are expressible as SPARQL queries over the ontology, with several spanning all three modules (e.g. joining a benchmark result through its trained model to the underlying method and training dataset). The full query templates are in Appendix E. All nine queries return non-empty results. CQ8 initially returned zero rows, reflecting the source literature’s habit of stating supported simulation types only in prose—a metadata gap in the field,

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Table 4. Competency-question execution on the seeded corpus (5,027 triples). Row counts reflect the current corpus; the times were measured on the 0.1.0 submission corpus with the sparql Rust CLI on a single machine, no reasoner; queries in Appendix E. CQ

Rows

Time (ms)

CQ1

81

117

CQ2 CQ3

20 21

33 33

CQ4

22

31

CQ5 CQ6 CQ7 CQ8

135 46 27 38

26 37 76 74

CQ9

3

41

Note Hyperparameter metadata (hyperparameterName, datatype) populated across 13 canonical Hyperparameter individuals in mlips-vocab.ttl (cutoffRadius, numLayers, learningRate, . . . ); paper-local survivors carry the same metadata plus a candidateForVocabulary marker for a future curation pass. One implementation per paper. One DFT or wavefunction-method settings block per dataset; 21 of the 22 datasets carry the full settings tuple. Provenance recorded for every dataset (22 datasets across the 20 papers; two papers split their data). Property/sampling combinations across all datasets. 46 benchmark results across the 20 studies. RMSE-ranked rows; ordering reflects the cross-paper accuracy comparison. supportsSimulation triples are not asserted by the source literature (a metadata gap surfaced by the seeded corpus); we curated them manually for the 17 studies whose simulation types are stated in prose (6 simulation-type individuals). Only 5 of 20 papers report inferenceTimePerAtom (cf. the metadata gaps in §6.1); the threshold RMSE < 2 further trims the result set.

not in the schema; curating those prose statements into triples for the 17 studies that make them (38 rows over 6 simulation types) validated the supportsSimulation branch against real data. CQ3: Training datasets with DFT provenance. For a given material system, which training datasets are available and what DFT settings were used? This query traverses the Training Data module, joining datasets with their DFT calculations and settings—a level of detail not available from any existing ontology: SELECT ? ds ? xc ? cutoff ? pseudo WHERE { ? ds a mlips : TrainingDataset ; mlips : coversMaterial ? mat . ? mat mlips : chemicalFormula " TiCr2 " . ? ds mlips : hasDFTCalculation ? calc . ? calc mlips : hasDFTSettings ? settings . ? settings mlips : xcFunctional ? xc ; mlips : energyCutoff ? cutoff ; mlips : pseudopotentialType ? pseudo . }

CQ6: Published benchmarks for an algorithm and material. Which studies have benchmarked a given algorithm on a given material, and what accuracy metrics were reported? This is the query that motivates the ontology: it traverses all three modules, linking a benchmark study to the trained model’s algorithm and the target material system: SELECT ? study ? metric_type ? prop ? value WHERE { ? study a mlips : BenchmarkStudy ; mlips : hasResult ? result . ? result mlips : evaluatesModel ? model ; mlips : targetMaterial ? mat ; mlips : hasAccuracyMetric ? metric . ? run a mlips : MLIPRun ; mlips : produces ? model ; mlips : appliesMethod ? algo .

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}

? algo rdfs : label " MTP " . ? mat mlips : chemicalFormula " TiCr2 " . ? metric mlips : metricType ? metric_type ; mlips : metricProperty ? prop ; mlips : metricValue ? value .

CQ7: Ranking algorithm–hyperparameter combinations. For a given material and target property, how do different algorithm and hyperparameter combinations rank by accuracy? This analytical query ranks models by accuracy, enabling systematic comparison across the literature: SELECT ? algo ? value WHERE { ? result mlips : evaluatesModel ? model ; mlips : targetMaterial ? mat ; mlips : hasAccuracyMetric ? metric . ? run a mlips : MLIPRun ; mlips : produces ? model ; mlips : appliesMethod ? algo . ? mat mlips : chemicalFormula " TiCr2 " . ? metric mlips : metricType mlips : RMSE ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricValue ? value . } ORDER BY ? value LIMIT 10

6.3

Consistency and Pitfall Checks

The primary consistency check is OWL reasoning. HermiT [23] via ROBOT [31], cross-checked with ELK on the EL fragment, confirms that the ontology is consistent (no contradictions among axioms (A1)–(A27)), every class is satisfiable, and the inferred class hierarchy contains no unexpected subsumptions. HermiT completes in ≈ 4 s; the post-reasoning ontology has 669 axioms. As a supplementary check we ran the OOPS! [44] open-source CLI (reproducible via make oops), which implements seven pitfall checkers (P02–P08): P02, P03, P05, P07 return zero issues, P06 errors on a known tool-side bug, and P04 (unconnected elements) and P08 (missing annotations) each trigger one finding at minor importance. Both findings trace to external alignmenttarget classes (e.g. mdo:Material, mls:HyperParameter, schema:Person, qudt:QuantityValue, cmso:AtomicStructure, prov:Entity) that mlips: terms reference as rdfs:subClassOf parents; clearing them would require importing the external ontologies (deliberately avoided to keep the theory in OWL 2 DL and the reasoner load tractable) or redefining external classes locally. Four further OOPS! checks on the ontology header (P38–P41: missing owl:Ontology, partial descriptions, namespace hijacking, missing licence) are preempted by the schema’s complete header annotations2 including a CC BY 4.0 licence. 6.4

Comparison with Existing Ontologies

Table 6 compares the MLIPs ontology with existing ontologies from the ML and materials-science domains (the comparators). For each comparator we walked the TBox and identified the terms a SPARQL query would need to answer each of the nine competency questions of Section 4. A cell is marked answerable (•) when the comparator declares all the required terms; partially answerable (◦) when superclass reasoning approximates the question (e.g., a comparator’s general Calculation class subsumes our DFTCalculation but does not declare DFT-specific settings such as energy cutoff or pseudopotential type as data properties); and not answerable (—) when the required terms are absent from the comparator’s vocabulary. The classification is TBox-level; the assessment is independent of each comparator’s currently-deployed instance data. The full per-cell mapping is archived at 2 Full header: owl:{versionIRI,

license, issued, modified}.

versionInfo} and dcterms:{title, description, creator, contributor,

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Table 5. OOPS! pitfall results on mlips.owl, run locally via the open-source CLI (v0.3.0-SNAPSHOT). All flagged pitfalls are at minor importance. The full pitfall catalog (∼40 pitfalls) is currently only available via the public web UI; the full report is deferred to a future revision. ID

Pitfall

Triggered

P02 P03 P04 P05 P06 P07 P08

Creating synonyms as classes Creating “is” relationships Creating unconnected ontology elements Defining wrong inverse relationships Including cycles in the hierarchy Merging different concepts in the same class Missing annotations (label & comment)

0 0 1 (minor) 0 — (tool bug) 0 1 (minor)

Table 6. Competency question coverage across comparator vocabularies (MLS = ML-Schema, Cr = Croissant). • = answerable, ◦ = partially, — = not answerable.

CQ1: Algo. hyperparams CQ2: Implementations CQ3: Training data + DFT CQ4: Dataset provenance CQ5: Dataset size + coverage CQ6: Published benchmarks CQ7: Accuracy ranking CQ8: Simulation types

MLS

MDO

CMSO ASMO

EMMO

PMDco

Cr

MLIPs

◦ ◦ — — — — — —

— — ◦ — — — — —

— — ◦ — — — — ◦

— — ◦ — — — — ◦

— — ◦ — — — — —

— — ◦ ◦ ◦ — — —

• • • • • • • •

dataset/artifacts/kg/comparison/ so disagreement on any cell can be tracked to a specific term. ML-Schema partially covers CQ1–CQ2 through mls:Algorithm and mls:Implementation but lacks physics-specific hyperparameters and units; MDO and CMSO/ASMO partially cover CQ3 but do not model MLIP-specific training-data provenance or DFT settings at the required granularity. No existing ontology covers CQ4–CQ7—the benchmark–method–dataset triangle central to the MLIPs ontology. The complementary scope is captured by linking rather than duplication: ML-Schema’s mls:Run provides richer training-run metadata reachable via the optional hasTrainingRun link, and CMSO/ASMO, MDO, EMMO, and PMDco provide detailed crystal-structure descriptions linked via MaterialSystem. Croissant. Croissant [1], the dataset-side counterpart positioned in §3, exhibits the mirrorimage profile. It partially covers the dataset-centric CQ3–CQ5—dataset description, provenance via schema.org creator/citeAs, and field-level property coverage via RecordSet/Field with their dataTypes—but declares none of the method-, benchmark-, simulation-, or efficiency-specific terms (CQ1–CQ2, CQ6–CQ9), and so answers no competency question fully. Its partials are of a different kind from the comparators above: not superclass subsumption, but generic dataset metadata lacking the MLIP-specific specializations (provenance categories, sampling strategies, configuration counts). Croissant describes the training set as a distributable artifact; the MLIPs ontology describes how that set was produced and how the resulting model performs—confirming, at the level of the competency questions, the complementarity stated in §3.

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Union of comparators. The per-ontology cells could overstate the contribution if the comparators combined (via their shared alignment to PROV-O, schema.org, QUDT) close the gap. The union fully answers CQ2 (ML-Schema mls:Implementation with schema.org versioning) and CQ3 (MDO declares DFT settings as data properties); for CQ1 and CQ4–CQ9 the union remains ◦ or — because the MLIP-specific specializations (physics-specific hyperparameter individuals, dataset provenance categories, sampling strategies, the benchmark chain, efficiency metadata) are absent from every comparator. The contribution concentrates in those seven CQs. 7

Sustainability and Maintenance

The MLIPs Ontology is developed within the META-LEARN project [24], an ERC Advanced Grant (2026–2030); it is an authoring artefact of the Stuttgart Institute for Artificial Intelligence and the Institute for Materials Science, which jointly commit to maintaining it beyond the project funding period. The project’s own MLIP studies publish their metadata into the MLIPs knowledge graph as they appear, so the graph grows with the group’s research output independently of external adoption. Versioning. The ontology follows Semantic Versioning [45]: each release has a distinct version IRI under the mlips: namespace, with major increments for breaking changes, minor for backwardscompatible extensions, and patch for annotation-only fixes (current release 0.1.0). Each release also deposits a snapshot to DaRUS [54] for archival; DaRUS uses sequential dataset versioning (V1, V2, . . . ) rather than SemVer, with the mapping (SemVer MAJOR/MINOR → DaRUS major; PATCH → DaRUS minor) kept in a CHANGELOG.md. Governance and editorship. The Institute for Artificial Intelligence contributes Semantic-Web and ontology-engineering expertise plus the engineering capacity to maintain the persistent IRI service and the dataset CI infrastructure; the Institute for Materials Science provides the materials-science domain expertise that sustains the schema’s MLIP-specific concepts. The editors and contributors can annotate the ontology with comments, and have weekly meetings to discuss the comments. Three editors have special dedication to the project: Hernández, Jung, and Grabowski. Hosting and persistent identification. The persistent IRI https://w3id.org/mlips, registered with the W3C Permanent Identifier Community Group, decouples the ontology from any specific host using a redirection. The redirect target serves the ontology with HTTP content negotiation (e.g., XHTML+RDFa, Turtle, RDF/XML); institutional hosting is being provisioned at the University of Stuttgart, with the maintainer’s domain as fallback. Instance IRIs under https://w3id.org/mlips/entity/ are reserved for instance dereferencing; a content-negotiating service that renders subject pages with forward and reverse properties is planned alongside the institutional hosting. Continuous validation. Every commit to the dataset repository runs three checks: Turtle parsing with rapper; a SPARQL-based round-trip check (§K.1) that extracts each paper’s canonical triples via 11 CONSTRUCT queries and verifies bit-equivalence with the source (catching schema drift the moment a term is renamed); and OWL reasoning consistency via ROBOT with HermiT and ELK (§6.3). A fourth project-wide check runs the full competency-question battery (§6.2) on the merged corpus, surfacing schema drift and encoding-coverage regressions. Community engagement and adoption. Two pathways drive adoption. Producers: MLIP frameworks (e.g., MACE, NequIP, DeePMD-kit) already serialize the run configurations and trained-model metadata that the schema captures, so a parser layer—analogous to NOMAD’s [22] normalizers for DFT codes—can emit MLIPs-Ontology triples at training time, making the ontology self-populating;

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the 12-question protocol of Appendix K.1 covers legacy studies that predate such emitters. The motivation to populate is direct: encoded studies are the ones selection queries return—visibility for the method and its benchmark results—and the twelve-question protocol doubles as a completeness checklist that surfaces unreported metadata (§6.1) before a paper ships. Consumers: cross-paper questions reduce to single SPARQL queries against the merged graph (e.g., “which MLIPs support phonon calculations on intermetallics with RMSE < 5 meV/atom?”). The schema’s mlips:sameAsWikidata links are already populated for the major DFT and wave-function codes and for 18 of 21 encoded MaterialSystem instances; we will contribute the schema to the NFDI-MatWerk ontology registry (where CMSO and ASMO are indexed) and file interoperability proposals with NOMAD and Materials Cloud [52] so that MLIP entries can be exported in the mlips: vocabulary. The contribution infrastructure is in place: the development repository is public with an issue tracker, contribution guidelines, and a canonical citation file, and the ontology has been submitted to the LOV registry. Beyond registries, we are in contact with the maintainers of complementary materials-science vocabularies about federating semantic services for materials science, with our service contributing the MLIP metadata. 8

Conclusion

We have presented the MLIPs ontology, an OWL 2 DL ontology whose three modules—Method, Training Data, and Benchmark—fill a gap left by existing ML and materials-science ontologies: the metadata that connects an MLIP method to its training set, DFT reference settings, trained model, and benchmark results. The schema declares 27 formal axioms and aligns with ML-Schema, MDO, CMSO/ASMO, PROV-O, schema.org, and QUDT; SHACL shapes enforce these constraints at the data level. All competency questions reduce to SPARQL queries over the seeded knowledge graph, and the ontology is consistent under HermiT and ELK. Outlook: AI-driven research. A machine-readable substrate of methods, training data, and benchmarks is a prerequisite for AI-driven research in the MLIP field. The agentic extraction protocol that seeded the knowledge graph already demonstrates machine-in-the-loop population; the same structure lets autonomous agents retrieve prior training runs for a target material property, identify suitable training sets and hyperparameters, reproduce a study from its recorded settings, and plan extensions grounded in what has been tried—speeding up bespoke MLIP development and the fine-tuning of foundation models by humans and agents alike. We see the ontology as a step toward MLIP studies whose results ship as queryable data alongside the paper, supporting reproducibility of and extension from previous work. Resource Availability Statement. The MLIPs ontology (OWL file, SHACL shapes, controlled vocabulary, and full axiom catalog with examples) is available at https://w3id.org/mlips under CC BY 4.0. The 20-paper seeded knowledge graph is archived on DaRUS (DOI 10.18419/DARUS5948 [26]) for long-term availability; its extraction protocol, paper catalogue, and worked example are also included as appendices of this preprint. Acknowledgements. This work is funded by the European Research Council (ERC) under the European Union’s Horizon Europe Research and Innovation Programme, grant agreement No. 101200433, project META-LEARN. Declaration of use of Generative AI.. The authors used Claude (Anthropic) for drafting and iterating on sections of this manuscript. All content was reviewed, edited, and validated by the authors.

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Computational Materials Science 58 (2012), 218–226. doi:10.1016/j.commatsci.2012.02. 005 [16] Volker L. Deringer, Albert P. Bartók, Noam Bernstein, David M. Wilkins, Michele Ceriotti, and Gábor Csányi. 2021. Gaussian Process Regression for Materials and Molecules. Chemical Reviews 121, 16 (2021), 10073–10141. doi:10.1021/ acs.chemrev.1c00022 [17] Ralf Drautz. 2019. Atomic Cluster Expansion for Accurate and Transferable Interatomic Potentials. Physical Review B 99, 1 (2019), 014104. doi:10.1103/PhysRevB.99.014104 [18] EMMC ASBL and OYSTER project. 2023. CHAMEO: Characterisation Methodology Domain Ontology. EMMO domain ontology. https://emmo-repo.github.io/domain-characterisation-methodology/ [19] Diego Esteves, Diego Moussallem, Ciro Baron Neto, Tommaso Soru, et al. 2015. MEX Vocabulary: A Lightweight Interchange Format for Machine Learning Experiments. In Proceedings of the 11th International Conference on Semantic Systems (SEMANTiCS). ACM, 169–176. doi:10.1145/2814864.2814883 [20] Martin Foltin et al. 2024. Common Metadata Framework and Common Metadata Ontology for AI Pipeline Metadata. Frontiers in Big Data (2024). [21] Timnit Gebru, Jamie Morgenstern, Briana Vecchione, Jennifer Wortman Vaughan, Hanna Wallach, Hal Daumé III, and Kate Crawford. 2021. Datasheets for Datasets. Commun. ACM 64, 12 (2021), 86–92. doi:10.1145/3458723 [22] Luca M. Ghiringhelli, Carsten Baldauf, Tristan Bereau, et al. 2023. Shared metadata for data-centric materials science. Scientific Data 10, 1 (2023), 626. doi:10.1038/s41597-023-02501-8

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A

Class Reference

This appendix describes all 36 classes defined in the MLIPs ontology. A.1

AccuracyMetric

Label: Accuracy Metric. An accuracy measure reported in a benchmark (e.g., RMSE of energy, MAE of forces). Superclasses. QuantityValue. Outgoing properties. isMetricOf, metricProperty, metricType, metricValue. Incoming properties. hasAccuracyMetric. Example. An RMSE of energy metric reporting 1.2 meV/atom for the MACE Ti-Al evaluation. ex : metric - rmse - energy a mlips : AccuracyMetric ; mlips : metricType mlips : RMSE ; mlips : metricProperty mlips : Energy ; mlips : metricValue " 1.2 " ^^ xsd : float ; qudt : hasUnit mlips : MilliEV - PER - ATOM .

Related axioms. (A24), (A25), (A27). A.2

ArchitecturalHyperparameter

Label: Architectural Hyperparameter. A hyperparameter that specifies the model architecture. Not disjoint with PhysicalHyperparameter.

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Superclasses. Hyperparameter. Example. The number of message-passing layers in MACE is a purely architectural hyperparameter. ex :hp - num - layers a mlips : Hyperparameter , mlips : ArchitecturalHyperparameter ; mlips : hyperparameterName " num_layers " ; mlips : hyperparameterDatatype xsd : integer ; mlips : defaultValue " 2 " ^^ xsd : integer .

A.3

AtomicConfiguration

Label: Atomic Configuration. A single atomic configuration (positions, cell, properties) in a training dataset. Superclasses. AtomicStructure. Incoming properties. hasConfiguration. Example. A single atomic configuration belonging to the TiCr2 -H training dataset. ex : config -0042 a mlips : AtomicConfiguration ; rdfs : label " TiCr2 - H ␣ config ␣ #42 " . ex :ds - TiCr2H mlips : hasConfiguration ex : config -0042 .

A.4

AtomicEnvironmentDescriptor

Label: Atomic Environment Descriptor. A mathematical representation of the local atomic environment used by an MLIP method. Incoming properties. hasDescriptor. Example. The equivariant message-passing descriptor used by MACE. mlips : EquivariantMessagePassingDescriptor a mlips : AtomicEnvironmentDescriptor ; rdfs : label " Equivariant ␣ message - passing ␣ descriptor " @en ; rdfs : comment " Descriptor ␣ family ␣ used ␣ by ␣ MACE , ␣ NequIP , ␣ Allegro . " @en .

A.5

BenchmarkResult

Label: Benchmark Result. A single evaluation result: an MLIP method applied to a material system with specific hyperparameters, reporting accuracy metrics. Superclasses. Entity. Outgoing properties. evaluatesModel, hasAccuracyMetric, isResultOf, reportedIn, targetMaterial, usesAlgorithm, usesTrainingData, inferenceHardware, inferenceTimePerAtom. Incoming properties. hasResult, isEvaluatedIn, isMetricOf. Example. A benchmark result evaluating the C15-MTP model on the TiCr2 material system. ex : result - mtp - ticr2h - c15 a mlips : BenchmarkResult ; mlips : evaluatesModel ex : model - mtp - TiCr2H ; mlips : targetMaterial ex : TiCr2 ; mlips : hasAccuracyMetric ex : metric - rmse - energy ; mlips : reportedIn ex : kumar2025 .

Related axioms. (A21), (A22), (A23), (A26).

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A.6

BenchmarkStudy

Label: Benchmark Study. A published study reporting MLIP evaluation results. Superclasses. Activity. Outgoing properties. hasResult. Incoming properties. isResultOf. Example. A benchmark study by Kumar et al. (2025) [36] containing evaluation results for MTP on TiCr2 -H Laves phases. ex : kumar2025 a mlips : BenchmarkStudy ; rdfs : label " Kumar ␣ et ␣ al . ␣ 2025 " ; mlips : hasResult ex : result - mtp - ticr2h - c15 .

Related axioms. (A20). A.7

CoveredProperty

Label: Covered Property. A physical property covered by the training dataset (energy, forces, stresses, virials). Incoming properties. coversProperty. Example. A training dataset declaring that it covers energy, forces, and stresses using the predefined individuals. ex :ds - TiCr2H mlips : coversProperty mlips : Energy , mlips : Forces , mlips : Stresses .

A.8

DFTCalculation

Label: DFT Calculation. A density functional theory calculation that produced reference data for training. Superclasses. Calculation, ReferenceCalculation. Outgoing properties. hasDFTSettings. Incoming properties. hasDFTCalculation. Example. A PBE density functional theory calculation that produced reference data for the Ti-Al dataset. ex : dft - tial a mlips : DFTCalculation ; rdfs : label "Ti - Al ␣ PBE ␣ calculation " ; mlips : hasDFTSettings ex : dft - settings - pbe .

Related axioms. (A19). A.9

DFTSettings

Label: DFT Settings. Settings of a DFT calculation: exchange-correlation functional, k-point mesh, energy cutoff, pseudopotential type. Superclasses. ReferenceSettings.

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Outgoing properties. dftBasisSet, pseudopotentialType, usedDFTCode, xcFunctional, energyCutoff, kPointMesh. Incoming properties. hasDFTSettings. Example. DFT settings specifying the PBE functional, PAW pseudopotentials, and VASP as the calculation code. ex : dft - settings - pbe a mlips : DFTSettings ; mlips : xcFunctional " PBE " ; mlips : pseudopotentialType " PAW " ; mlips : energyCutoff 520.0 ; mlips : usedDFTCode ex : vasp .

A.10

DatasetProvenance

Label: Dataset Provenance. The provenance type of a training dataset. Incoming properties. datasetProvenance. Example. A training dataset using the Published provenance individual to indicate publicly available data. ex :ds - TiCr2H mlips : datasetProvenance mlips : Published .

A.11

DftBasisSet

Label: DFT Basis Set. The basis set used in a DFT calculation, when the code is all-electron or otherwise uses a localised basis (e.g., FHI-aims NAO families, LAPW, Gaussian-type orbitals such as cc-pVDZ or 6-31G). Range of mlips:dftBasisSet on DFTSettings. Plane-wave codes specify the basis through mlips:energyCutoff instead and leave this slot empty. Concrete basis sets are modelled as named individuals; an open extension point. Incoming properties. dftBasisSet. Example. A paper-local candidate-vocabulary instance for a Gaussian basis set that is not (yet) in the controlled vocabulary, plus the candidateForVocabulary flag that signals it for promotion review. ex : basis -6 -31 g -d - smith2017 a mlips : DftBasisSet ; rdfs : label " 6 -31 G ( d ) " ; rdfs : comment " Pople - style ␣ split - valence ␣ double - zeta ␣ Gaussian ␣ basis ␣ with ␣ d ␣ polarisation ." ; mlips : candidateForVocabulary mlips : DftBasisSet .

A.12

FunctionalForm

Label: Functional Form. A parametrised mapping from an atomic configuration to an energy, specified independently of parameter values. Incoming properties. hasFunctionalForm. Example. The MTP functional form: a polynomial in moment-tensor contractions evaluated over the local neighborhood. ex : mtp - functional - form a mlips : FunctionalForm ; rdfs : label " MTP ␣ moment - tensor ␣ polynomial " .

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A.13

Hyperparameter

Label: Hyperparameter. A hyperparameter of an MLIP method, with its name, data type, range, and default value. Superclasses. HyperParameter. Outgoing properties. isHyperparameterOf, defaultValue, hyperparameterDatatype, hyperparameterName, maxValue, minValue. Incoming properties. forHyperparameter, hasHyperparameter. Example. The cutoff radius hyperparameter with its name, data type, range, and default value. ex :hp - cutoff - radius a mlips : Hyperparameter ; mlips : hyperparameterName " cutoff_radius " ; mlips : hyperparameterDatatype xsd : float ; mlips : minValue " 3.0 " ^^ xsd : float ; mlips : maxValue " 8.0 " ^^ xsd : float ; mlips : defaultValue " 5.0 " ^^ xsd : float .

Related axioms. (A8). A.14

HyperparameterSetting

Label: Hyperparameter Setting. A concrete value assigned to a hyperparameter in a specific training run or configuration. Superclasses. HyperParameterSetting. Outgoing properties. forHyperparameter, isSettingOf, cutoffRadius, learningRate, numAngularBasis, numLayers, numRadialBasis, settingValue. Incoming properties. hasHyperparameterSetting, trainedUsing. Example. A concrete setting of the cutoff radius to 5.0 Å for a specific training configuration. ex : setting - cutoff a mlips : HyperparameterSetting ; mlips : forHyperparameter ex : hp - cutoff - radius ; mlips : settingValue " 5.0 " ^^ xsd : float ; mlips : cutoffRadius 5.0 ; qudt : hasUnit unit : ANGSTROM .

A.15

Implementation

Label: Implementation. A software implementation of an MLIP method in a specific library and version. Superclasses. SoftwareSourceCode. Outgoing properties. implementedIn, isImplementationOf, version. Incoming properties. hasImplementation. Example. Version 0.3 of the MACE algorithm implemented in the MACE library. ex : mace - v03 a mlips : Implementation ; mlips : implementedIn ex : mace - lib ; mlips : version " 0.3 " .

Related axioms. (A3), (A9).

An Ontology for Machine Learning Interatomic Potentials

A.16

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Library

Label: Library. A software library or tool used in MLIP research (e.g., ASE, LAMMPS, VASP, GPAW). Superclasses. SoftwareApplication. Incoming properties. implementedIn, usedDFTCode, usedReferenceCode. Example. The MACE software library used for training equivariant interatomic potentials. ex : mace - lib a mlips : Library ; rdfs : label " MACE " ; schema : url < https :// github . com / ACEsuit / mace > .

A.17

LossFunction

Label: Loss Function. A scalar objective whose minimisation fits the parameters of the functional form. Incoming properties. hasLossFunction. Example. A weighted sum of mean-squared errors on energies, forces, and stresses. ex : weighted - energy - force - stress - loss a mlips : LossFunction ; rdfs : label " Weighted ␣ MSE ␣ on ␣ energies , ␣ forces , ␣ stresses " .

A.18

MLIPMethod

Label: MLIP Method. A machine learning interatomic potential method family (e.g., MACE, ACE, HDNNP, NequIP, M3GNet, MTP). Specifies a functional form, a loss function, and a training algorithm. Disjoint from mls:Algorithm. Outgoing properties. hasDescriptor, hasFunctionalForm, hasHyperparameter, hasImplementation, hasLossFunction, hasTrainingAlgorithm, supportsSimulation, inferenceComplexity, supportsGPU, supportsParallelization, trainingComplexity. Incoming properties. appliesMethod, isHyperparameterOf, isImplementationOf, trainedWith, usesAlgorithm. Example. The MACE equivariant message-passing method with its components, hyperparameters, and supported simulations. ex : MACE a mlips : MLIPMethod ; rdfs : label " MACE " ; mlips : hasFunctionalForm ex : mace - neural - net ; mlips : hasLossFunction ex : weighted - energy - force - loss ; mlips : hasTrainingAlgorithm ex : adam ; mlips : hasHyperparameter ex : hp - cutoff - radius ; mlips : hasImplementation ex : mace - v03 ; mlips : supportsSimulation ex : molecular - dynamics . ex : adam a mls : Algorithm ; rdfs : label " Adam " .

A.19

MLIPRun

Label: MLIP Run. A concrete fitting activity for an MLIP method: it applies an MLIP method to a training dataset and produces a trained model. Superclasses. Activity.

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Outgoing properties. appliesMethod, hasHyperparameterSetting, hasTrainingRun, produces, runsOn, gpuHours, peakMemory, trainingDuration, trainingHardware. Incoming properties. isProducedBy, isSettingOf, wasRunBy. Example. An MLIP run that applies the MTP method on a TiCr2 -H dataset and produces a trained model. ex : run - mtp - TiCr2H a mlips : MLIPRun ; mlips : appliesMethod ex : MTP ; mlips : runsOn ex : ds - TiCr2H ; mlips : produces ex : model - mtp - TiCr2H .

A.20

MaterialSystem

Label: Material System. A material system studied in a dataset: element, alloy, compound, or complex microstructure. Superclasses. CrystallineMaterial, Material. Outgoing properties. chemicalFormula, materialClass, microstructuralFeature. Incoming properties. coversMaterial, targetMaterial. Example. A Ti-Al binary alloy system with its chemical formula and material class. ex : TiAl a mlips : MaterialSystem ; mlips : chemicalFormula " TiAl " ; mlips : materialClass " binary ␣ alloy " ; mlips : sameAsWikidata wd : Q2549811 .

A.21

MetaSort

Label: Meta-Sort. An OntoClean-style meta-category used to classify classes of the ontology. Example. TODO: add example. A.22

MetricProperty

Label: Metric Property. The physical property being measured (energy, force, stress). Incoming properties. metricProperty. Example. An accuracy metric using the predefined Energy metric property individual. ex : metric - rmse - energy mlips : metricProperty mlips : Energy .

A.23

MetricType

Label: Metric Type. Type of accuracy metric (RMSE, MAE, R2, etc.). Incoming properties. metricType. Example. An accuracy metric using the predefined RMSE metric type individual. ex : metric - rmse - energy mlips : metricType mlips : RMSE .

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PhysicalHyperparameter

Label: Physical Hyperparameter. A hyperparameter that has a direct physical meaning. Not disjoint with ArchitecturalHyperparameter. Superclasses. Hyperparameter. Example. The cutoff radius is a physical hyperparameter: its value bounds the physical interaction range of the potential. ex :hp - cutoff - radius a mlips : Hyperparameter , mlips : PhysicalHyperparameter ; mlips : hyperparameterName " R_cut " ; mlips : hyperparameterDatatype xsd : double ; mlips : defaultValue " 5.0 " ^^ xsd : double .

A.25

PseudopotentialType

Label: Pseudopotential Type. A family of pseudopotentials used in a plane-wave DFT calculation (e.g., PAW, ultrasoft, norm-conserving). Range of mlips:pseudopotentialType on DFTSettings. All-electron codes leave this slot empty. Concrete pseudopotential families are modelled as named individuals; an open extension point. Incoming properties. pseudopotentialType. Example. mlips:PAW from the controlled vocabulary. mlips : PAW a mlips : PseudopotentialType ; rdfs : label " PAW " ; rdfs : comment " Projector ␣ augmented - wave ␣ method . " .

A.26

ReferenceCalculation

Label: Reference Calculation. A first-principles calculation that produced reference energies, forces, or stresses for MLIP training. Generalisation of DFTCalculation that also covers wave-function methods (e.g., CCSD(T), MP2, CASPT2) and other ab initio approaches. Superclasses. Activity, Calculation. Outgoing properties. hasReferenceSettings. Incoming properties. hasReferenceCalculation. Example. A reference calculation can be either a DFT calculation or a wave-function calculation; the supertype is what is required by the dataset. ex :ds - water mlips : hasReferenceCalculation ex : ccsdt - water . ex : ccsdt - water a mlips : WaveFunctionCalculation . # subclass of ReferenceCalculation

A.27 ReferenceSettings Label: Reference Settings. Settings of a reference calculation, abstracted across method families. Concrete subclasses (DFTSettings, WaveFunctionSettings) carry the method-specific parameters; the supertype carries cross-family slots such as the software code used. Outgoing properties. usedReferenceCode. Incoming properties. hasReferenceSettings.

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Example. Reference settings are abstracted across method families; concrete subclasses carry the specific parameters. ex : ccsdt - water mlips : hasReferenceSettings ex : ccsdt - settings . ex : ccsdt - settings a mlips : WaveFunctionSettings ; # subclass of ReferenceSettings mlips : usedReferenceCode ex : lib - pyscf .

A.28

SamplingStrategy

Label: Sampling Strategy. A strategy used to sample the atomic configurations in a training dataset (e.g., chemical sampling across compositions, vibrational sampling across thermal snapshots, or a combination). Concrete sampling strategies are modeled as instances and will be developed in future work; this class is left open as an extension point. Incoming properties. samplingStrategy. Example. An ad-hoc ChemicalSampling individual declared inline. ex : ChemicalSampling a mlips : SamplingStrategy ; rdfs : label " Chemical ␣ sampling " ; rdfs : comment " Configurations ␣ sampled ␣ across ␣ compositions . " .

A.29

SimulationType

Label: Simulation Type. A type of atomistic simulation: molecular dynamics, Monte Carlo, geometry optimization, phonon calculations, thermodynamic integration, etc. Incoming properties. supportsSimulation. Example. Molecular dynamics as a simulation type supported by an MLIP algorithm. ex : molecular - dynamics a mlips : SimulationType ; rdfs : label " Molecular ␣ Dynamics " ; mlips : sameAsWikidata wd : Q901663 .

A.30

TrainedModel

Label: Trained Model. The concrete artifact produced by fitting an MLIP method on a specific dataset with specific hyperparameter settings—the learned parameters (weights) that can be used for prediction. Superclasses. Model, Entity. Outgoing properties. isEvaluatedIn, isProducedBy, trainedOn, trainedUsing, trainedWith. Incoming properties. evaluatesModel, produces. Example. A trained C15-MTP for TiCr2 -H, linking back to method and training data. ex : model - mtp - TiCr2H a mlips : TrainedModel ; rdfs : label " C15 - MTP ␣ for ␣ TiCr2 - H " ; mlips : trainedWith ex : MTP ; mlips : trainedOn ex : ds - TiCr2H .

Related axioms. (A7). A.31

TrainingDataset

Label: Training Dataset. A dataset of atomic configurations used for MLIP training, with provenance, size, property coverage, and DFT settings.

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Superclasses. Dataset, Entity. Outgoing properties. coversMaterial, coversProperty, datasetProvenance, hasConfiguration, hasDFTCalculation, hasReferenceCalculation, samplingStrategy, wasRunBy, numConfigurations. Incoming properties. runsOn, trainedOn, usesTrainingData. Example. A published Ti-Al DFT dataset with 15 000 configurations covering energy, forces, and stresses. ex : tial - dataset a mlips : TrainingDataset ; mlips : numConfigurations 15000 ; mlips : coversMaterial ex : TiAl ; mlips : coversProperty mlips : Energy ; mlips : datasetProvenance mlips : Published .

Related axioms. (A15), (A16), (A17), (A18). A.32

TrainingHyperparameter

Label: Training Hyperparameter. A hyperparameter of the training procedure. Superclasses. Hyperparameter. Example. The optimiser learning rate is a training hyperparameter — it governs how the model is fitted, not what the model is. ex :hp - learning - rate a mlips : Hyperparameter , mlips : TrainingHyperparameter ; mlips : hyperparameterName " learning_rate " ; mlips : hyperparameterDatatype xsd : double ; mlips : defaultValue " 0.001 " ^^ xsd : double .

A.33

WaveFunctionCalculation

Label: Wave Function Calculation. A wave-function-based reference calculation (e.g., Hartree-Fock, MP2, CCSD, CCSD(T), CASPT2). An alternative to DFTCalculation as a source of reference data, typically more accurate but more expensive. Superclasses. ReferenceCalculation. Outgoing properties. hasWaveFunctionSettings. Example. A CCSD(T) calculation used to generate reference data for an MLIP study. ex : ccsdt - water a mlips : WaveFunctionCalculation ; mlips : hasWaveFunctionSettings ex : ccsdt - settings .

A.34

WaveFunctionSettings

Label: Wave Function Settings. Settings of a wave-function-based reference calculation: the method (e.g., CCSD(T), MP2), the basis set (e.g., cc-pVTZ, aug-cc-pVDZ), and frozen-core treatment. Superclasses. ReferenceSettings. Outgoing properties. wfMethod, basisSet, frozenCore. Incoming properties. hasWaveFunctionSettings.

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Example. CCSD(T) with the cc-pVTZ basis, frozen-core approximation, run in PySCF. ex : ccsdt - settings a mlips : WaveFunctionSettings ; mlips : wfMethod " CCSD ( T ) " ; mlips : basisSet " cc - pVTZ " ; mlips : frozenCore true ; mlips : usedReferenceCode ex : lib - pyscf .

A.35

WfMethod

Label: Wave Function Method. A wave-function correlation method used to produce reference data (e.g., HF, MP2, CCSD, CCSD(T), DLPNO-CCSD(T), CASPT2, NEVPT2). Range of mlips:wfMethod on WaveFunctionSettings. Concrete methods are modelled as named individuals; an open extension point. Incoming properties. wfMethod. Example. mlips:DLPNO_CCSDT from the controlled vocabulary, used by smith2019ccx. mlips : DLPNO_CCSDT a mlips : WfMethod ; rdfs : label " DLPNO - CCSD ( T ) " ; rdfs : comment " Domain - based ␣ local ␣ pair ␣ natural ␣ orbital ␣ approximation ␣ to ␣ CCSD ( T ) . " .

A.36

XCFunctional

Label: Exchange-Correlation Functional. A density-functional approximation to the exchangecorrelation energy used in a DFT calculation (e.g., LDA, PBE, PBE0, HSE06, SCAN, BLYP, omegaB97X). Range of mlips:xcFunctional on DFTSettings. Concrete functionals are modelled as named individuals; an open extension point. Incoming properties. xcFunctional. Example. mlips:PBE from the controlled vocabulary, declared in artifacts/kg/mlipsvocab.ttl. mlips : PBE a mlips : XCFunctional ; rdfs : label " PBE " ; rdfs : comment " Perdew - Burke - Ernzerhof ; ␣ GGA ␣ family . " .

B

Object Property Reference

This appendix describes all 53 object properties defined in the MLIPs ontology. B.1

appliesMethod

Label: applies method. Links an MLIP run to the MLIP method it fits. Domain: MLIPRun. Range: MLIPMethod. Example. An MLIP run applies the MTP method. ex : run - mtp - TiCr2H mlips : appliesMethod ex : MTP .

B.2

candidateForVocabulary

Label: candidate for vocabulary. Annotates a paper-local instance with the controlled-vocabulary class to which it should be considered for promotion. Used when an encoded paper introduces an entity that is not yet a named individual in mlips-vocab.ttl. The deduplication audit collects these candidates; a curator promotes, merges, or leaves them paper-local.

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31

Example. A paper-local instance flagged for vocabulary review. ex : basis -6 -31 g -d - smith2017 mlips : candidateForVocabulary mlips : DftBasisSet .

B.3

coversMaterial

Label: covers material. Domain: TrainingDataset. Range: MaterialSystem. Example. A training dataset covers the TiCr2 -H material system. ex :ds - TiCr2H mlips : coversMaterial ex : TiCr2 .

Related axioms. (A15). B.4

coversProperty

Label: covers property. Domain: TrainingDataset. Range: CoveredProperty. Example. A training dataset covers total energy as a reference property. ex :ds - TiAl mlips : coversProperty mlips : Energy .

Related axioms. (A16). B.5

datasetProvenance

Label: dataset provenance. Domain: TrainingDataset. Range: DatasetProvenance. Example. A training dataset records its provenance as published data. ex :ds - TiCr2H mlips : datasetProvenance mlips : Published .

Related axioms. (A17). B.6

dftBasisSet

Label: DFT basis set. The basis set used by an all-electron or localised-basis DFT calculation (FHI-aims NAO, LAPW, Gaussian-type orbitals such as cc-pVDZ or 6-31G). Plane-wave codes specify the basis through mlips:energyCutoff and leave this slot empty. Domain: DFTSettings. Range: DftBasisSet. Example. An all-electron DFT settings node references its NAO basis set. ex : dft - settings - fhi - aims mlips : dftBasisSet mlips : NAOIntermediate .

B.7

evaluatesModel

Label: evaluates model. Links a benchmark result to the trained model being evaluated. Domain: BenchmarkResult. Range: TrainedModel. Example. A benchmark result evaluates the trained MTP model for TiCr2 -H. ex : result -01 mlips : evaluatesModel ex : model - mtp - TiCr2H .

Related axioms. (A21).

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B.8

forHyperparameter

Label: for hyperparameter. Links a setting to the hyperparameter it configures. Domain: HyperparameterSetting. Range: Hyperparameter. Example. A hyperparameter setting references the cutoff radius hyperparameter it configures. ex : setting - cutoff -5 A mlips : forHyperparameter ex : cutoff - radius .

B.9

hasAccuracyMetric

Label: has accuracy metric. Domain: BenchmarkResult. Range: AccuracyMetric. Example. A benchmark result includes an RMSE accuracy metric for energy. ex : result -01 mlips : hasAccuracyMetric ex : metric - RMSE - E .

Related axioms. (A23), (A27). B.10

hasConfiguration

Label: has configuration. Domain: TrainingDataset. Range: AtomicConfiguration. Example. A training dataset contains an atomic configuration. ex :ds - TiAl mlips : hasConfiguration ex : config -0001 .

Related axioms. (A18). B.11

hasDFTCalculation

Label: has DFT calculation. Domain: TrainingDataset. Range: DFTCalculation. Example. A training dataset includes a DFT calculation that produced its reference data. ex :ds - TiAl mlips : hasDFTCalculation ex : dft - calc - TiAl .

B.12

hasDFTSettings

Label: has DFT settings. Domain: DFTCalculation. Range: DFTSettings. Example. A DFT calculation has associated computational settings. ex : dft - calc - TiAl mlips : hasDFTSettings ex : dft - PBE - PAW .

Related axioms. (A19). B.13

hasDescriptor

Label: has descriptor. Links an MLIP method to the atomic environment descriptor it uses. Domain: MLIPMethod. Range: AtomicEnvironmentDescriptor. Example. MACE uses an equivariant message-passing descriptor. ex : MACE mlips : hasDescriptor mlips : EquivariantMessagePassingDescriptor .

An Ontology for Machine Learning Interatomic Potentials

B.14

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hasFunctionalForm

Label: has functional form. Links an MLIP method to its parametrised functional form. Domain: MLIPMethod. Range: FunctionalForm. Example. The MTP method has a moment-tensor polynomial functional form. ex : MTP mlips : hasFunctionalForm ex : mtp - functional - form .

B.15

hasHyperparameter

Label: has hyperparameter. Links an MLIP method to a hyperparameter it accepts. Domain: MLIPMethod. Range: Hyperparameter. Example. The MACE algorithm accepts a cutoff radius hyperparameter. ex : MACE mlips : hasHyperparameter ex : cutoff - radius .

Related axioms. (A1), (A8), (A12). B.16

hasHyperparameterSetting

Label: has hyperparameter setting. Links an MLIP run to a concrete hyperparameter setting used in that run. Domain: MLIPRun. Range: HyperparameterSetting. Example. A benchmark result records the hyperparameter setting used during evaluation. ex : result -01 mlips : hasHyperparameterSetting ex : setting - cutoff -5 A .

B.17

hasImplementation

Label: has implementation. Links an MLIP method to a software implementation. Domain: MLIPMethod. Range: Implementation. Example. The MACE algorithm has a version 0.3 implementation. ex : MACE mlips : hasImplementation ex : MACE - v03 .

Related axioms. (A9), (A13). B.18

hasLossFunction

Label: has loss function. Links an MLIP method to the loss function whose minimisation fits its parameters. Domain: MLIPMethod. Range: LossFunction. Example. The MTP method is fitted by minimising a weighted energy/force/stress MSE. ex : MTP mlips : hasLossFunction ex : weighted - energy - force - stress - loss .

B.19

hasReferenceCalculation

Label: has reference calculation. Links a training dataset to the first-principles calculation that produced its reference data. Generalises hasDFTCalculation to wave-function and other ab initio methods. Domain: TrainingDataset. Range: ReferenceCalculation.

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Example. A training dataset whose reference data was produced by a wave-function calculation. hasDFTCalculation is a subproperty, so a query on hasReferenceCalculation also matches DFT-based datasets. ex :ds - water mlips : hasReferenceCalculation ex : ccsdt - water .

B.20

hasReferenceSettings

Label: has reference settings. Links a reference calculation to its method-specific settings. Generalises hasDFTSettings to wave-function and other ab initio methods. Domain: ReferenceCalculation. Range: ReferenceSettings. Example. Generic link from a reference calculation to its settings. hasDFTSettings is the DFT-specific subproperty. ex : ccsdt - water mlips : hasReferenceSettings ex : ccsdt - settings .

B.21

hasResult

Label: has result. Domain: BenchmarkStudy. Range: BenchmarkResult. Example. A benchmark study contains an individual evaluation result. ex : study - kumar2025 mlips : hasResult ex : result -01 .

Related axioms. (A20), (A26). B.22

hasTrainingAlgorithm

Label: has training algorithm. Links an MLIP method to the ML-Schema algorithm used to fit its functional form. Domain: MLIPMethod. Range: Algorithm. Example. The MTP method uses L-BFGS as its training algorithm. The training algorithm is an mls:Algorithm, which is the sole alignment point between MLIPs ontology and ML-Schema. ex : MTP mlips : hasTrainingAlgorithm ex : lbfgs . ex : lbfgs a mls : Algorithm ; rdfs : label "L - BFGS " .

B.23

hasTrainingRun

Label: has training run. Optional link from an MLIP run to an ML-Schema run recording the training algorithm execution. Domain: MLIPRun. Range: Run. Example. An MLIP run may optionally be linked to an underlying ML-Schema run that records the training algorithm execution. ex : run - mtp - TiCr2H mlips : hasTrainingRun ex : mls - run - mtp - TiCr2H . ex : mls - run - mtp - TiCr2H a mls : Run ; mls : executes ex : lbfgs .

B.24

hasUnit

Label: has unit. Links a numeric value to its QUDT unit. Range: Unit.

An Ontology for Machine Learning Interatomic Potentials

Example. An accuracy metric has meV/atom as its unit. ex : metric - RMSE -E mlips : hasUnit mlips : MilliEV - PER - ATOM .

B.25

hasWaveFunctionSettings

Label: has wave function settings. Domain: WaveFunctionCalculation. Range: WaveFunctionSettings. Example. A wave-function calculation linked to its method-specific settings. ex : ccsdt - water mlips : hasWaveFunctionSettings ex : ccsdt - settings .

B.26

implementedIn

Label: implemented in. Links an implementation to the library that provides it. Domain: Implementation. Range: Library. Example. The MACE v0.3 implementation is provided by the MACE library. ex : MACE - v03 mlips : implementedIn ex : MACE - lib .

Related axioms. (A3). B.27

isEvaluatedIn

Label: is evaluated in. Inverse of mlips:evaluatesModel. Domain: TrainedModel. Range: BenchmarkResult. Example. TODO: add example. B.28

isHyperparameterOf

Label: is hyperparameter of. Inverse of mlips:hasHyperparameter. Domain: Hyperparameter. Range: MLIPMethod. Example. TODO: add example. B.29

isImplementationOf

Label: is implementation of. Inverse of mlips:hasImplementation. Domain: Implementation. Range: MLIPMethod. Example. TODO: add example. B.30

isMetricOf

Label: is metric of. Inverse of mlips:hasAccuracyMetric. Domain: AccuracyMetric. Range: BenchmarkResult. Example. TODO: add example. B.31

isProducedBy

Label: is produced by. Inverse of mlips:produces. Domain: TrainedModel. Range: MLIPRun. Example. TODO: add example.

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B.32

isResultOf

Label: is result of. Inverse of mlips:hasResult. Domain: BenchmarkResult. Range: BenchmarkStudy. Example. TODO: add example. B.33

isSettingOf

Label: is setting of. Inverse of mlips:hasHyperparameterSetting. Domain: HyperparameterSetting. Range: MLIPRun. Example. TODO: add example. B.34

metricProperty

Label: metric property. Domain: AccuracyMetric. Range: MetricProperty. Example. An accuracy metric measures total energy. ex : metric - RMSE -E mlips : metricProperty mlips : EnergyProperty .

Related axioms. (A25). B.35

metricType

Label: metric type. Domain: AccuracyMetric. Range: MetricType. Example. An accuracy metric is classified as RMSE. ex : metric - RMSE -E mlips : metricType mlips : RMSE .

Related axioms. (A24). B.36

produces

Label: produces. Links an MLIP run to the trained model it produces. Domain: MLIPRun. Range: TrainedModel. Example. A training run produces a trained model artifact. ex : run - mtp - TiCr2H mlips : produces ex : model - mtp - TiCr2H .

Related axioms. (A6), (A7). B.37

pseudopotentialType

Label: pseudopotential type. The family of pseudopotentials used in a plane-wave DFT calculation (PAW, ultrasoft, norm-conserving). All- electron codes leave this slot empty and use mlips:dftBasisSet instead. Domain: DFTSettings. Range: PseudopotentialType. Example. A plane-wave DFT settings node uses PAW pseudopotentials. ex : dft - settings - foo mlips : pseudopotentialType mlips : PAW .

An Ontology for Machine Learning Interatomic Potentials

B.38

37

reportedIn

Label: reported in. Domain: BenchmarkResult. Range: ScholarlyArticle. Example. A benchmark result is reported in a scholarly article. ex : result -01 mlips : reportedIn ex : publication -2025 .

B.39

runsOn

Label: runs on. Links an MLIP run to the training dataset it uses. Domain: MLIPRun. Range: TrainingDataset. Example. A training run uses the Ti–Al training dataset. ex : run - MACE - TiAl mlips : runsOn ex : ds - TiAl .

Related axioms. (A5). B.40

sameAsWikidata

Label: same as Wikidata. Links an entity to its corresponding Wikidata item. Example. The TiCr2 material system is linked to the Wikidata entry for Laves phases. ex : TiCr2 mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q15724720 > .

B.41

samplingStrategy

Label: sampling strategy. Records the sampling strategy or strategies used to construct a training dataset. Optional and multi-valued: a dataset may combine several sampling strategies (e.g., chemical and vibrational). Domain: TrainingDataset. Range: SamplingStrategy. Example. A training dataset that mixes chemical and vibrational sampling. ex :ds - TiAl mlips : samplingStrategy ex : ChemicalSampling , ex : VibrationalSampling .

B.42

supportsSimulation

Label: supports simulation. Links an MLIP method to the simulation types it supports. Domain: MLIPMethod. Range: SimulationType. Example. The MACE algorithm supports molecular dynamics simulations. ex : MACE mlips : supportsSimulation ex : MolecularDynamics .

Related axioms. (A2), (A14). B.43

targetMaterial

Label: target material. Domain: BenchmarkResult. Range: MaterialSystem.

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Example. A benchmark result targets the Ti–Al material system. ex : result -01 mlips : targetMaterial ex : TiAl .

Related axioms. (A22). B.44

trainedOn

Label: trained on. Shortcut: links a trained model directly to the training dataset it was fitted on. Domain: TrainedModel. Range: TrainingDataset. Example. A trained model is linked directly to its training dataset via the shortcut property. ex : model - mtp - TiCr2H mlips : trainedOn ex : ds - TiCr2H .

Related axioms. (A11). B.45

trainedUsing

Label: trained using. Shortcut: links a trained model directly to a hyperparameter setting used during the MLIP run that produced it. Domain: TrainedModel. Range: HyperparameterSetting. Example. The trained model is linked directly to the hyperparameter setting used to fit it (the long path goes via the run that produced it). ex : model - mtp - TiAl mlips : trainedUsing ex : setting - cutoff -5 A .

B.46

trainedWith

Label: trained with. Shortcut: links a trained model directly to the MLIP method it applies. Domain: TrainedModel. Range: MLIPMethod. Example. A trained model is linked directly to its algorithm via the shortcut property. ex : model - MACE - TiAl mlips : trainedWith ex : MACE .

Related axioms. (A10). B.47

usedDFTCode

Label: used DFT code. The DFT software used (e.g., VASP, GPAW). Domain: DFTSettings. Range: Library. Example. The DFT settings specify VASP as the calculation software. ex : dft - PBE - PAW mlips : usedDFTCode ex : VASP .

B.48

usedReferenceCode

Label: used reference code. The software code used to perform the reference calculation (e.g., VASP, GPAW for DFT; Molpro, PySCF, ORCA for wave-function methods). Generalises usedDFTCode. Domain: ReferenceSettings. Range: Library. Example. A wave-function calculation used PySCF as the software code. The DFT-specific usedDFTCode is a subproperty. ex : ccsdt - settings mlips : usedReferenceCode ex : lib - pyscf .

An Ontology for Machine Learning Interatomic Potentials

B.49

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usesAlgorithm

Label: uses algorithm. Domain: BenchmarkResult. Range: MLIPMethod. Example. A benchmark result references the MLIP algorithm that was evaluated (legacy property). ex : result -01 mlips : usesAlgorithm ex : MACE .

B.50 usesTrainingData Label: uses training data. Domain: BenchmarkResult. Range: TrainingDataset. Example. A benchmark result references the training dataset used (legacy property). ex : result -01 mlips : usesTrainingData ex : ds - TiCr2H .

B.51

wasRunBy

Label: was run by. Inverse of mlips:runsOn. Domain: TrainingDataset. Range: MLIPRun. Example. TODO: add example. B.52

wfMethod

Label: wave-function method. The wave-function correlation method used to produce reference data (e.g., HF, MP2, CCSD, CCSD(T), DLPNO-CCSD(T), CASPT2, NEVPT2). Range is WfMethod; concrete methods are named individuals in mlips-vocab.ttl. Domain: WaveFunctionSettings. Range: WfMethod. Example. A wave-function settings node points to the canonical DLPNO-CCSD(T) IRI. ex :wf - settings - foo mlips : wfMethod mlips : DLPNO_CCSDT .

B.53

xcFunctional

Label: exchange-correlation functional. The exchange-correlation functional used in a DFT calculation (e.g., LDA, PBE, PBE0, HSE06, SCAN, omegaB97X). Range is XCFunctional; concrete functionals are named individuals in mlips-vocab.ttl. Domain: DFTSettings. Range: XCFunctional. Example. A DFT settings node points to the canonical mlips:PBE IRI. ex : dft - settings - foo mlips : xcFunctional mlips : PBE .

C

Datatype Property Reference

This appendix describes all 31 datatype properties defined in the MLIPs ontology. C.1

basisSet

Label: basis set. The Gaussian basis set used in a wave-function calculation, e.g., cc-pVTZ, aug-cc-pVDZ, def2-TZVP. Domain: WaveFunctionSettings. Range: string.

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Example. A correlation-consistent triple-zeta basis set used in a CCSD(T) calculation. ex : ccsdt - settings mlips : basisSet " cc - pVTZ " .

C.2

chemicalFormula

Label: chemical formula. Domain: MaterialSystem. Range: string. Example. The chemical formula of the TiCr2 material system. ex : TiCr2 mlips : chemicalFormula " TiCr2 " .

C.3

cutoffRadius

Label: cutoff radius. Cutoff radius for atomic interactions, in angstroms. Domain: HyperparameterSetting. Range: double. Example. A cutoff radius of 5.0 Å for atomic interactions. ex : setting - cutoff -5 A mlips : cutoffRadius " 5.0 " ^^ xsd : double .

C.4

defaultValue

Label: default value. Domain: Hyperparameter. Range: Literal. Example. The default value of the cutoff radius hyperparameter. ex : cutoff - radius mlips : defaultValue " 5.0 " .

C.5

energyCutoff

Label: energy cutoff. Plane-wave energy cutoff in eV. Domain: DFTSettings. Range: double. Example. The plane-wave energy cutoff is 520.0 eV. ex : dft - PBE - PAW mlips : energyCutoff " 520.0 " ^^ xsd : double .

C.6

frozenCore

Label: frozen core. Whether core electrons are kept frozen during the post-Hartree-Fock correlation treatment in a wave-function calculation. True for the standard frozen-core approximation; false for all-electron correlation. Domain: WaveFunctionSettings. Range: boolean. Example. The frozen-core approximation was applied (only valence electrons correlated). ex : ccsdt - settings mlips : frozenCore true .

C.7 gpuHours Label: GPU hours. Domain: MLIPRun. Range: double.

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41

Example. A training run that consumed 100 GPU-hours in total. ex : run - mtp - TiCr2H mlips : gpuHours " 100 " ^^ xsd : integer .

C.8

hyperparameterDatatype

Label: hyperparameter datatype. The expected datatype of this hyperparameter (e.g., float, int, string). Domain: Hyperparameter. Range: string. Example. The expected datatype of the cutoff radius hyperparameter is a floating-point number. ex : cutoff - radius mlips : hyperparameterDatatype " float " .

C.9

hyperparameterName

Label: hyperparameter name. Domain: Hyperparameter. Range: string. Example. The programmatic name of the cutoff radius hyperparameter. ex : cutoff - radius mlips : hyperparameterName " cutoff_radius " .

C.10

inferenceComplexity

Label: inference complexity. Asymptotic computational complexity of inference. Domain: MLIPMethod. Range: string. Example. Most local potentials (MTP, MACE, ACE) have linear-scaling inference cost in the number of atoms. ex : MTP mlips : inferenceComplexity " O ( N ) " .

C.11

inferenceHardware

Label: inference hardware. Domain: BenchmarkResult. Range: string. Example. The hardware on which the inference benchmark was performed. ex : result - mtp - ticr2h - c15 mlips : inferenceHardware " NVIDIA ␣ A100 " .

C.12

inferenceTimePerAtom

Label: inference time per atom. Inference time per atom (microseconds). Domain: BenchmarkResult. Range: double. Example. A benchmark that measured 1.5 𝜇s per atom inference time on the test system. ex : result - mtp - ticr2h - c15 mlips : inferenceTimePerAtom " 1.5 " ^^ xsd : double .

C.13 kPointMesh Label: k-point mesh. K-point mesh specification (e.g., ’4x4x4’). Domain: DFTSettings. Range: string.

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Example. The DFT settings specify a 4 × 4 × 4 k-point mesh. ex : dft - PBE - PAW mlips : kPointMesh " 4 x4x4 " .

C.14

learningRate

Label: learning rate. Learning rate used during model training. Domain: HyperparameterSetting. Range: double. Example. A learning rate of 0.001 used during model training. ex : setting - lr mlips : learningRate " 0.001 " ^^ xsd : double .

C.15

materialClass

Label: material class. E.g., element, binary alloy, ternary compound, HEA. Domain: MaterialSystem. Range: string. Example. TiCr2 is classified as a Laves phase. ex : TiCr2 mlips : materialClass " Laves ␣ phase " .

C.16

maxValue

Label: maximum value. Domain: Hyperparameter. Range: Literal. Example. The maximum accepted value for the cutoff radius. ex : cutoff - radius mlips : maxValue " 10.0 " .

C.17

metricValue

Label: metric value. Domain: AccuracyMetric. Range: double. Example. The energy RMSE metric has a value of 1.2 meV/atom. ex : metric - RMSE -E mlips : metricValue " 1.2 " ^^ xsd : double .

C.18

microstructuralFeature

Label: microstructural feature. E.g., point defect, dislocation, surface, grain boundary. Domain: MaterialSystem. Range: string. Example. The material system features point defects in its configurations. ex : TiCr2 mlips : microstructuralFeature " point ␣ defect " .

C.19

minValue

Label: minimum value. Domain: Hyperparameter. Range: Literal. Example. The minimum accepted value for the cutoff radius. ex : cutoff - radius mlips : minValue " 1.0 " .

An Ontology for Machine Learning Interatomic Potentials

C.20

numAngularBasis

Label: number of angular basis functions. Number of angular basis functions in the descriptor. Domain: HyperparameterSetting. Range: integer. Example. The descriptor uses 6 angular basis functions. ex : setting - angular mlips : numAngularBasis 6 .

C.21

numConfigurations

Label: number of configurations. Domain: TrainingDataset. Range: integer. Example. The training dataset contains 1 019 atomic configurations. ex :ds - TiCr2H mlips : numConfigurations 1019 .

C.22

numLayers

Label: number of layers. Number of layers in the neural network architecture. Domain: HyperparameterSetting. Range: integer. Example. A network architecture with 4 message-passing layers. ex : setting - layers -4 mlips : numLayers 4 .

C.23

numRadialBasis

Label: number of radial basis functions. Number of radial basis functions in the descriptor. Domain: HyperparameterSetting. Range: integer. Example. The descriptor uses 8 radial basis functions. ex : setting - radial mlips : numRadialBasis 8 .

C.24

peakMemory

Label: peak memory. Peak memory during training (GB). Domain: MLIPRun. Range: double. Example. A training run with peak GPU memory usage of 24 GB. ex : run - mtp - TiCr2H mlips : peakMemory " 24.0 " ^^ xsd : double .

C.25

settingValue

Label: setting value. Domain: HyperparameterSetting. Range: Literal. Example. The concrete value assigned to a hyperparameter setting. ex : setting - cutoff -5 A mlips : settingValue " 5.0 " .

C.26

supportsGPU

Label: supports GPU. Domain: MLIPMethod. Range: boolean.

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Example. MACE’s canonical implementation supports GPU acceleration. ex : MACE mlips : supportsGPU " true " ^^ xsd : boolean .

C.27

supportsParallelization

Label: supports parallelization. Domain: MLIPMethod. Range: boolean. Example. MACE supports multi-node and multi-core parallel training and inference (e.g., via DDP or MPI). ex : MACE mlips : supportsParallelization " true " ^^ xsd : boolean .

C.28

trainingComplexity

Label: training complexity. Asymptotic computational complexity of training. Domain: MLIPMethod. Range: string. Example. MTP has linear-scaling training cost in the number of atomic configurations (per epoch). ex : MTP mlips : trainingComplexity " O ( N ) " .

C.29

trainingDuration

Label: training duration. Measured wall-clock training time (hours). Domain: MLIPRun. Range: double. Example. A training run that took 4.2 wall-clock hours. ex : run - mtp - TiCr2H mlips : trainingDuration " 4.2 " ^^ xsd : double .

C.30 trainingHardware Label: training hardware. Domain: MLIPRun. Range: string. Example. A training run executed on an NVIDIA A100 GPU. ex : run - mtp - TiCr2H mlips : trainingHardware " NVIDIA ␣ A100 " .

C.31

version

Label: version. Domain: Implementation. Range: string. Example. The version string of a software implementation. ex : MACE - v03 mlips : version " 0.3.0 " .

D

Axiom Catalog

This appendix enumerates all axioms in the MLIPs ontology, organized by module. For each axiom we give the formal statement and a concrete example illustrating its effect.

An Ontology for Machine Learning Interatomic Potentials

D.1

Method Module

D.1.1

Every method has at least one hyperparameter. MLIPMethod ⊑ ∃ hasHyperparameter.Hyperparameter

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(A1)

Example. The MACE method declares hyperparameters such as cutoff radius and number of layers. An MLIPMethod instance without any hasHyperparameter link would violate this axiom. D.1.2

Every method supports at least one simulation type. MLIPMethod ⊑ ∃ supportsSimulation.SimulationType

(A2)

Example. MACE supports molecular dynamics and geometry optimization. A method that does not declare any supported simulation type is incomplete. D.1.3

Every method has a functional form. MLIPMethod ⊑ ∃ hasFunctionalForm.FunctionalForm

(A3)

Example. The MTP method has a moment-tensor polynomial functional form; MACE has an equivariant message-passing ansatz. A method whose functional form is not recorded cannot be reproduced. D.1.4

Every method has a loss function. MLIPMethod ⊑ ∃ hasLossFunction.LossFunction

(A4)

Example. Most MLIP methods use a weighted sum of mean-squared errors on energies, forces, and stresses as their loss. A method without a recorded loss is underspecified. D.1.5

Every method has a training algorithm. MLIPMethod ⊑ ∃ hasTrainingAlgorithm.mls:Algorithm

(A5)

Example. MTP is typically fitted with L-BFGS; MACE with Adam. The training algorithm is recorded as an mls:Algorithm instance, which is the sole alignment point between the MLIPs ontology and ML-Schema. D.1.6

Methods are disjoint from ML-Schema algorithms. MLIPMethod ⊓ mls:Algorithm ⊑ ⊥

(A6)

Example. MACE is an MLIPMethod; Adam is an mls:Algorithm. The two refer to fundamentally different kinds of thing—a named functional-form-plus-loss-plus-training-procedure recipe versus a parameter-optimisation procedure—and are declared disjoint. The hasTrainingAlgorithm role links them. D.1.7

Every implementation specifies its library. Implementation ⊑ ∃ implementedIn.Library

(A7)

Example. “MACE v0.3” is an implementation in the MACE library. An Implementation without an implementedIn link is invalid. D.1.8

Every MLIP run applies exactly one method. MLIPRun ⊑ (=1 appliesMethod.MLIPMethod)

(A8)

Example. An MLIP run that produces a C15-MTP for TiCr2 -H applies the MTP method—not two methods simultaneously, and not zero.

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Every MLIP run uses exactly one training dataset. MLIPRun ⊑ (=1 runsOn.TrainingDataset)

(A9)

Example. The MLIP run uses the TiCr2 -H DFT dataset with 1,019 configurations. If a run combines multiple datasets, they should be represented as a single merged TrainingDataset. D.1.10

Every MLIP run produces exactly one trained model. MLIPRun ⊑ (=1 produces.TrainedModel)

(A10)

Example. The MLIP run produces a single C15-MTP model for TiCr2 -H. If the same run produces checkpoints, only the final model is recorded. D.1.11

Every trained model was produced by some MLIP run. TrainedModel ⊑ ∃ produces− .MLIPRun

(A11)

Example. A TrainedModel instance “C15-MTP-TiCr2H-v1” must be linked to an MLIPRun that produced it. A model cannot exist without provenance about how it was trained. D.1.12

Every hyperparameter belongs to some method. Hyperparameter ⊑ ∃ hasHyperparameter− .MLIPMethod

(A12)

Example. The hyperparameter “cutoff radius” is defined for the MTP method. A Hyperparameter instance that is not linked to any method via hasHyperparameter− is an orphan and violates this axiom. D.1.13

Every implementation belongs to some method. Implementation ⊑ ∃ hasImplementation− .MLIPMethod

(A13)

Example. “MLIP-2 v2.0” is an implementation of the MTP method. An Implementation that is not linked to any MLIPMethod via hasImplementation− is invalid. D.1.14

Shortcut: trainedWith is a property chain. trainedWith ≡ produces− ◦ appliesMethod

(A14)

Example. If an MLIPRun produces model 𝑚 and applies method 𝑎, then 𝑚 trainedWith 𝑎 is inferred. This allows querying “which method was used to train this model?” without navigating through the run. D.1.15

Shortcut: trainedOn is a property chain. trainedOn ≡ produces− ◦ runsOn

(A15)

Example. If an MLIPRun produces model 𝑚 and runs on dataset 𝑑, then 𝑚 trainedOn 𝑑 is inferred. This allows querying “which dataset was used to train this model?” directly. D.1.16

Shortcut: trainedUsing is a property chain. trainedUsing ≡ produces− ◦ hasHyperparameterSetting

(A16)

Example. If an MLIPRun produces model 𝑚 and has hyperparameter setting 𝑠 (e.g., 𝑅cut = 5.0 Å), then 𝑚 trainedUsing 𝑠 is inferred. This allows querying “which hyperparameter settings were used to train this model?” without navigating through the run.

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D.1.17

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Domain axioms for method-specific roles. ∃ hasHyperparameter.⊤ ⊑ MLIPMethod

(A17)

∃ hasImplementation.⊤ ⊑ MLIPMethod

(A18)

∃ supportsSimulation.⊤ ⊑ MLIPMethod

(A19)

Example. If an entity has a hasHyperparameter link, it must be an MLIPMethod. This prevents, e.g., a TrainingDataset from accidentally being assigned hyperparameters. D.2

Training Data Module

D.2.1

Every dataset covers at least one material system. TrainingDataset ⊑ ∃ coversMaterial.MaterialSystem

(A20)

Example. A TiCr2 -H training dataset covers the TiCr2 material system. A dataset without any coversMaterial link is incomplete. D.2.2

Every dataset covers at least one physical property. TrainingDataset ⊑ ∃ coversProperty.CoveredProperty

(A21)

Example. The TiCr2 -H dataset covers energies, forces, and stresses. A dataset must declare at least one covered property. D.2.3

Every dataset has a provenance classification. TrainingDataset ⊑ ∃ datasetProvenance.DatasetProvenance

(A22)

Example. The TiCr2 -H dataset is classified as Published. Every dataset must indicate whether it is published, in-house, or augmented. D.2.4

Every dataset contains at least one atomic configuration. TrainingDataset ⊑ ∃ hasConfiguration.AtomicConfiguration

(A23)

Example. The TiCr2 -H C15 dataset contains 1,019 atomic configurations. A dataset without any configurations is empty and invalid. D.2.5

Every DFT calculation has settings. DFTCalculation ⊑ ∃ hasDFTSettings.DFTSettings

(A24)

Example. A DFT calculation specifies PBE as the exchange-correlation functional, a 4×4×4 k-point mesh, and PAW pseudopotentials. A DFTCalculation without hasDFTSettings is incomplete. D.3

Benchmark Module

D.3.1

Every study contains at least one result. BenchmarkStudy ⊑ ∃ hasResult.BenchmarkResult

(A25)

Example. A study by Kumar et al. (2025) [36] reports evaluation results for MTP on TiCr2 -H. A BenchmarkStudy without any hasResult link contains no data and is invalid. D.3.2

Every result evaluates exactly one trained model. BenchmarkResult ⊑ (=1 evaluatesModel.TrainedModel)

(A26)

Example. A benchmark result evaluates the “C15-MTP-TiCr2H-v1” model. Each result is tied to exactly one model; comparing two models requires two separate BenchmarkResult instances.

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Every result targets at least one material system. BenchmarkResult ⊑ ∃ targetMaterial.MaterialSystem

(A27)

Example. The benchmark result targets the TiCr2 material system for testing. A result must specify what material was used for evaluation. D.3.4

Every result reports at least one accuracy metric. BenchmarkResult ⊑ ∃ hasAccuracyMetric.AccuracyMetric

(A28)

Example. The result reports RMSE of energy (3.17 meV/atom). A benchmark result without any accuracy metric carries no evaluation data. D.3.5

Every accuracy metric has exactly one type. AccuracyMetric ⊑ (=1 metricType.MetricType)

(A29)

Example. The metric is of type RMSE. A metric cannot be both RMSE and MAE simultaneously, nor can it lack a type. D.3.6

Every accuracy metric measures exactly one property. AccuracyMetric ⊑ (=1 metricProperty.MetricProperty)

(A30)

Example. The RMSE metric measures energy. A single AccuracyMetric instance measures one property; separate metrics are created for energy, force, and stress. D.3.7

Every result belongs to some study. BenchmarkResult ⊑ ∃ hasResult− .BenchmarkStudy

(A31)

Example. The benchmark result for MTP on TiCr2 -H belongs to the Kumar et al. (2025) study. A result cannot exist without a parent study. D.3.8

Every accuracy metric belongs to some result. AccuracyMetric ⊑ ∃ hasAccuracyMetric− .BenchmarkResult

(A32)

Example. The RMSE of energy metric belongs to a specific benchmark result. An orphan metric with no parent result is invalid. D.4

Axioms Under Discussion

The following axioms are candidates for inclusion but require further discussion with domain experts. D.4.1

Every DFT settings belongs to some calculation. DFTSettings ⊑ ∃ hasDFTSettings− .DFTCalculation

Example. DFT settings (PBE, 4×4×4 k-points) belong to a specific calculation. Discussion: Settings could potentially be shared across calculations as templates, in which case this axiom would be too restrictive. D.4.2

Every atomic configuration belongs to some dataset. AtomicConfiguration ⊑ ∃ hasConfiguration− .TrainingDataset

Example. An atomic configuration of TiCr2 -H belongs to the TiCr2 -H training dataset. Discussion: Configurations could belong to multiple datasets (e.g., an augmented dataset reuses configurations from a published one), which would still satisfy this axiom but complicates provenance tracking.

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D.4.3

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Every hyperparameter setting references a hyperparameter. HyperparameterSetting ⊑ ∃ forHyperparameter.Hyperparameter

Example. A setting “cutoff radius = 5.0 Å” references the hyperparameter “cutoff radius”. Discussion: This axiom is straightforward but raises the question of whether settings should also be existentially dependent on an MLIPRun or TrainedModel. E

SPARQL Query Templates for All Competency Questions

This appendix provides SPARQL query templates for all eight competency questions. CQ3, CQ6, and CQ7 are discussed in the main paper (Section 6.2); the remaining queries are presented here. E.1

CQ1: Method hyperparameters

Which MLIP methods exist, and what hyperparameters does each accept? SELECT ? algo ? hp ? name ? type ? default WHERE { ? algo a mlips : MLIPMethod ; mlips : hasHyperparameter ? hp . ? hp mlips : hyperparameterName ? name ; mlips : hyperparameterDatatype ? type . OPTIONAL { ? hp mlips : defaultValue ? default } }

E.2

CQ2: Implementations and versions

Which libraries implement a given method? SELECT ? algo ? impl ? lib ? version WHERE { ? algo a mlips : MLIPMethod ; mlips : hasImplementation ? impl . ? impl mlips : implementedIn ? lib ; mlips : version ? version . }

E.3

CQ4: Dataset provenance

What is the provenance of a training dataset? SELECT ? ds ? label ? prov WHERE { ? ds a mlips : TrainingDataset ; rdfs : label ? label ; mlips : datasetProvenance ? prov . }

E.4

CQ5: Dataset size and property coverage

How many configurations does a dataset contain, and what properties are covered? SELECT ? ds ? nconfig ? prop WHERE { ? ds a mlips : TrainingDataset ; mlips : numConfigurations ? nconfig ; mlips : coversProperty ? prop . }

E.5

CQ8: Simulation types supported by a method

Which simulation types have been performed with a given MLIP? SELECT ? algo ? sim WHERE { ? algo a mlips : MLIPMethod ; mlips : supportsSimulation ? sim . }

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CQ9: Efficiency of methods and trained models

For a given target accuracy, which methods and trained models are most efficient, combining asymptotic complexity (prior knowledge on the method) with measured training and inference cost? SELECT ? algo ? inf_complexity ? gpu_hours ? t_inf ? rmse WHERE { ? result a mlips : BenchmarkResult ; mlips : evaluatesModel ? model ; mlips : hasAccuracyMetric ? metric ; mlips : inferenceTimePerAtom ? t_inf . ? metric mlips : metricType mlips : RMSE ; mlips : metricValue ? rmse . FILTER (? rmse < 2.0) ? model mlips : trainedWith ? algo . ? algo mlips : inferenceComplexity ? inf_complexity . ? run mlips : produces ? model ; mlips : gpuHours ? gpu_hours . } ORDER BY ? t_inf

F

Description Logic Query Formulations

This appendix provides description logic formulations for the competency questions evaluated in Section 6.2. Each query is expressed as a conjunctive query over the MLIPs ontology T-Box. F.1

CQ1: Method hyperparameters

Retrieve all pairs of methods and their hyperparameters: 𝑞(𝑥, 𝑦) ← MLIPMethod(𝑥) ∧ hasHyperparameter(𝑥, 𝑦) ∧ Hyperparameter(𝑦) F.2

CQ2: Implementations and versions

Retrieve implementations with their libraries: 𝑞(𝑥, 𝑦, 𝑧) ← MLIPMethod(𝑥) ∧ hasImplementation(𝑥, 𝑦) ∧ implementedIn(𝑦, 𝑧) F.3

CQ3: Training datasets for a material system

Retrieve datasets for a material with their DFT settings: 𝑞(𝑑, 𝑠) ← TrainingDataset(𝑑) ∧ coversMaterial(𝑑, 𝑚)∧ hasDFTCalculation(𝑑, 𝑐) ∧ hasDFTSettings(𝑐, 𝑠) F.4

CQ4: Dataset provenance

Retrieve provenance classification of datasets: 𝑞(𝑑, 𝑝) ← TrainingDataset(𝑑) ∧ datasetProvenance(𝑑, 𝑝) F.5

CQ5: Dataset size and property coverage

Retrieve dataset size and covered properties: 𝑞(𝑑, 𝑛, 𝑝) ← TrainingDataset(𝑑) ∧ numConfigurations(𝑑, 𝑛) ∧ coversProperty(𝑑, 𝑝)

An Ontology for Machine Learning Interatomic Potentials

F.6

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CQ6: Published benchmarks

Retrieve benchmark results for a method on a material, with accuracy metrics: 𝑞(𝑠, 𝑣) ← BenchmarkStudy(𝑠) ∧ hasResult(𝑠, 𝑟 ) ∧ evaluatesModel(𝑟, 𝑚)∧ trainedWith(𝑚, 𝑎) ∧ targetMaterial(𝑟, 𝑡)∧ hasAccuracyMetric(𝑟, 𝑐) ∧ metricValue(𝑐, 𝑣) F.7

CQ7: Ranking combinations by accuracy

Retrieve method–material pairs ordered by accuracy (instantiated for RMSE of energy): 𝑞(𝑎, 𝑣) ← evaluatesModel(𝑟, 𝑚) ∧ trainedWith(𝑚, 𝑎)∧ hasAccuracyMetric(𝑟, 𝑐) ∧ metricType(𝑐, RMSE)∧ metricProperty(𝑐, EnergyProperty) ∧ metricValue(𝑐, 𝑣) F.8

CQ8: Simulation types

Retrieve simulation types supported by each method: 𝑞(𝑥, 𝑦) ← MLIPMethod(𝑥) ∧ supportsSimulation(𝑥, 𝑦) ∧ SimulationType(𝑦) G

Design Discussion: MLIP Run and Shortcut Properties

In ML-Schema, the relationship between a trained model and its algorithm is mediated by mls:Run, which represents a training execution: mls:executes

mls:hasOutput

mls:Algorithm ←−−−−−−−−− mls:Run −−−−−−−−−−−→ mls:Model mls:hasInput

mls:Dataset ←−−−−−−−−− mls:Run The MLIPs ontology follows this activity-mediated pattern but departs from ML-Schema in an important way. Because MLIPMethod is disjoint from mls:Algorithm (see Section 5.1 and Appendix H), an MLIPRun cannot be a subclass of mls:Run: mls:Run’s mls:executes property ranges over mls:Algorithm, whereas an MLIPRun applies a method, not an algorithm. We therefore make MLIPRun a subclass of prov:Activity only, and introduce a dedicated role appliesMethod with range MLIPMethod in place of mls:executes. An optional hasTrainingRun links an MLIPRun to an underlying mls:Run whenever the training algorithm itself is modelled in ML-Schema. On top of this, we provide the shortcut roles trainedWith and trainedOn directly on TrainedModel, defined as property chains through the MLIP run. These shortcuts enable direct queries without navigating the run entity, which is important because our primary data source—published MLIP literature—rarely reports the operational details of training runs (hardware, duration, random seeds). In many cases, the MLIPRun entity will carry only its method, dataset, and model links, making the shortcut properties the more natural query path. Critical assessment. The shortcut properties introduce redundancy: the same information is accessible both directly on the model and via the run. While the property chain axioms guarantee consistency in principle, in practice data entry errors could create inconsistencies if shortcuts and run-mediated paths are populated independently. We mitigate this through SHACL shapes that validate consistency between the two paths. An alternative design would omit the shortcuts entirely and always require navigation through MLIPRun. This would be cleaner from an ontology engineering perspective but would make common queries (“which method produced this model?”) unnecessarily verbose, particularly for

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data extracted from publications where the run carries no additional information beyond the links already captured by the shortcuts. H

Design Discussion: “Method” vs. “Algorithm” Granularity

A referee raised a subtle but important point: what the MLIP community calls an “algorithm” is not, strictly speaking, an algorithm in the ML-Schema sense. This appendix documents the granularity mismatch, the terminology choice, and the design we have adopted—an MLIPMethod class that is disjoint from mls:Algorithm and is decomposed into its three conceptual components, with the training algorithm contributed as the sole alignment point with ML-Schema. H.1

The mismatch

In ML-Schema, mls:Algorithm is defined as “a computational procedure”—typically a training algorithm such as stochastic gradient descent, Adam, or L-BFGS. The procedure consumes data and hyperparameters and produces a fitted mls:Model. This is the classical ML view: model family and training procedure are conceptually distinct, and mls:Algorithm names only the latter. In the MLIP community, a named “algorithm” (MACE, MTP, ACE, NequIP) typically bundles four different things: (1) a descriptor of the local atomic environment (moment tensors, SOAP, symmetry functions, equivariant messages); (2) a functional form that maps descriptor features to the local energy (linear expansion in basis functions, neural network, kernel regression); (3) a loss function for training (typically a weighted combination of energy error, force error, and stress error); and (4) a training procedure in the ML-Schema sense (an optimizer, sampling scheme, and stopping criterion). Only item (4) aligns directly with mls:Algorithm. Items (1)–(3) are properties of the model family rather than of any training procedure, and the bundle as a whole is what the community refers to by a single name. H.2

Analogy: knowledge graph embeddings

The same mismatch arises in other machine-learning sub-communities. Consider TransE [12], a standard knowledge graph embedding method. “TransE” as used in the KGE literature bundles: • an entity representation (points in R𝑑 ); • a relation representation (translation vectors in R𝑑 ); • a scoring function 𝑓 (ℎ, 𝑟, 𝑡) = ∥ℎ + 𝑟 − 𝑡 ∥; and • a training procedure (stochastic gradient descent with margin-based ranking loss and negative sampling). Asked “what is TransE in ML-Schema?”, a strict reading splits it across mls:Algorithm (the SGD procedure) and mls:Model (the fitted embeddings). ML-Schema has no single class for the bundle that the community actually names and identifies. The same structural issue surfaces in graph neural networks (GCN, GAT, GIN), generative models (VAE, GAN), and many other ML sub-communities where a named “algorithm” is a bundle of model-family choices plus a training recipe. H.3

Terminology: “Algorithm”, “Method”, or “Formalism”?

Given that MTP and its siblings are not algorithms in ML-Schema’s sense, it is worth asking which of three candidate words is most accurate and most widely used.

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Algorithm. Narrowly, an algorithm is a computational procedure—a sequence of steps. MTP is not a sequence of steps; it is a mathematical framework that defines what energy function is being fitted plus the machinery to fit it. “The MTP algorithm” is used casually in the literature but is semantically imprecise. Method. Generic: “a named approach or recipe”. MTP is clearly a method: a recipe for constructing a potential from a particular descriptor (moment tensors), a particular functional form (linear expansion in basis functions), a particular loss (weighted energy/force/stress), and a particular training algorithm. Semantically clean; carries no specific structural commitment beyond “named bundle”. Formalism. Emphasises the mathematical framework. In physics and chemistry, “formalism” is the standard word for “a mathematical structure that defines what a class of objects looks like and how they behave”—e.g., “the Lagrangian formalism”, “the density functional theory formalism”, “the Standard Model formalism”. MTP fits this usage well: the moment tensor expansion defines what MTP potentials are, before any specific one is fitted. This is the tightest of the three for MTP-the-mathematical-framework but carries a physics-flavoured connotation. Literature usage across MLIP papers. “Method” dominates in practice (Novikov et al. 2021, Batatia et al. 2022, Bartók et al. 2010). “Formalism” and “framework” appear when authors want to emphasise the mathematical structure (Drautz 2019 for ACE, and occasionally in the MTP literature). “Algorithm” is used casually but rarely in formal technical contexts. Cross-community applicability. For an upper ontology targeting multiple ML sub-communities, “Method” is the most portable label: it reads naturally for MLIPs, KGE, GNNs, generative models, and classical ML alike. “Formalism” is accurate for physics-adjacent fields but heavy in KGE (“the TransE formalism” is correct but uncommon) and uncommon in GNN/CV/NLP. “Algorithm” is semantically wrong everywhere. Decision. We adopt Method as the class name at the domain layer (MLIPMethod). Author freedom to use “formalism” or “framework” in prose when the mathematical-structure emphasis is appropriate is retained; the class name does not prescribe author vocabulary. H.4

The design adopted

Rather than align MLIPMethod with mls:Algorithm by subsumption — which would conflate the named bundle with the training procedure it uses—we declare them disjoint and decompose the bundle into its three non-training components, with the training algorithm contributed as the sole alignment point with ML-Schema: MLIPMethod ⊓ mls:Algorithm ⊑ ⊥ MLIPMethod ⊑ ∃ hasFunctionalForm.FunctionalForm MLIPMethod ⊑ ∃ hasLossFunction.LossFunction MLIPMethod ⊑ ∃ hasTrainingAlgorithm.mls:Algorithm Here mls:Algorithm is used in its narrow ML-Schema sense (the optimiser/training procedure only). The bundle MLIPMethod is not a subclass of mls:Algorithm; instead, one of its components is an mls:Algorithm. The atomic-environment descriptor is modelled separately via hasDescriptor, alongside the method’s hyperparameters, implementations, and supported simulation types. Concrete instances then look like: entity : MACE a mlips : MLIPMethod ; rdfs : label " MACE " ;

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# narrow ML - Schema sense

For the same reason of disjointness, MLIPRun is a subclass of prov:Activity only, not of mls:Run: mls:Run.mls:executes ranges over mls:Algorithm, which is disjoint from MLIPMethod. A dedicated role appliesMethod replaces mls:executes for the MLIP case. An optional hasTrainingRun links an MLIPRun to an mls:Run when the training algorithm is itself modelled in ML-Schema. Benefits. • The alignment with ML-Schema is tight and semantically correct: only the training procedure is an mls:Algorithm. • Each component is independently queryable and comparable across methods: “which methods share the same descriptor?”, “which methods use a margin-based ranking loss?” • The pattern generalises: TransE, GCN, VAE, and other community-named bundles can be modelled analogously in sibling domain ontologies. Costs. • MLIP researchers commonly leave the training procedure unspecified (it is often a detail not worth naming), so in practice many MLIPMethod instances carry only a placeholder hasTrainingAlgorithm link. The value of making it explicit is mostly conceptual, but is what enables the alignment with ML-Schema to be both tight and narrow. • The functional-form and loss-function components are often also left implicit in the literature; the ontology makes them first-class but does not require extensive axiomatisation of their internal structure. I

Meta-categorisation: Sortals, Roles, and Reified Relations

This appendix expands the modelling discipline introduced in §5.2. It documents (i) why we adopted OntoClean as a methodology while defining our own annotation vocabulary instead of importing the OntoClean OWL serialisation, (ii) the four meta-categories we use, and (iii) the case-by-case classification of every class in the MLIPs ontology. I.1

Methodology vs. vocabulary: why a bespoke annotation set

OntoClean [25] is a meta-property framework for validating the ontological adequacy of taxonomic relations. Its central distinctions are four meta-properties that classes may carry—rigidity (whether the class essentially applies to its instances), identity (whether the class supplies criteria of identity), unity (whether instances are unitary wholes), and dependence (whether instances depend existentially on others)—together with a small set of named categories (Type, Role, Phase, Mixin, Category) defined as combinations of the four meta-properties. We adopt OntoClean’s meta-property analysis as the discipline behind our class design: every class in the MLIPs ontology has been examined for its rigidity, identity, unity, and dependence profile, and the resulting classification influences both axiom choices (existence axioms, disjointness) and label policies (§I.2 below). We do not, however, import the OntoClean OWL serialisation. Two considerations drove this decision. Resolvability. The canonical OntoClean OWL document at loa.istc.cnr.it/ontologies/OntoClean. owl did not resolve when we attempted to dereference it during the writing of this paper. Other

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Laboratory for Applied Ontology (LOA) vocabularies at sibling paths (DUL, DLP, DOLCE-Lite) resolve; OntoClean specifically does not. A resource paper that emphasises FAIR-resolvability for its own artefacts cannot in good conscience import a vocabulary whose canonical IRI is not retrievable. Categorial fit. OntoClean’s named categories were developed to discipline unary class hierarchies. Reified n-ary relations—which represent the majority of our non-sortal classes (HyperparameterSetting is a 3-place relation; BenchmarkResult is a 4-place relation; AccuracyMetric is a 3-place relation)—have no first-class entry in OntoClean’s category set. Within OntoClean they would be classified by meta-properties as anti-rigid (∼𝑅), without own identity (−𝐼 ), without unity (−𝑈 ), and externally dependent (+𝐷); the closest named category is Role, but Role is canonically illustrated by one-place classes like Student, and forcing a 3-place reification into the same category obscures rather than illuminates the modelling intent. We therefore define four named meta-categories locally, as named individuals of an annotation vocabulary mlips:MetaSort, and attach them to classes via an annotation property mlips:metaSort: • mlips:Sortal—a class whose instances carry their own identity criteria, rigid, with unity, not externally dependent. OntoClean profile: +𝑅, +𝐼 , +𝑈 , −𝐷. Example: MaterialSystem. • mlips:SubordinateSortal—a sortal whose instances depend existentially on a parent entity but are themselves rigid and identity-bearing. OntoClean profile: +𝑅, +𝐼 , +𝑈 , +𝐷. Example: Implementation, which is identity-bearing (a release/commit/DOI) but exists only of a method and in a library. • mlips:Role—an anti-rigid class whose instances are roles played by sortal individuals and depend existentially on those sortals. OntoClean profile: ∼𝑅, −𝐼 (identity inherited from the carrier), −𝑈 , +𝐷. The MLIPs ontology currently has no class in this category, but the slot is reserved for future extensions. • mlips:ReifiedRelation—a class that reifies an 𝑛-ary relation between sortals. Instances have no identity outside their relata. OntoClean profile: ∼𝑅, −𝐼 , −𝑈 , +𝐷. Examples: HyperparameterSetting, BenchmarkResult, AccuracyMetric. The classification itself is attached to every class in the ontology source as a single mlips:metaSort triple. The full set of classifications and the meta-property analysis behind each is provided in this appendix (Table 7) and the dataset repository; the artefacts are archived at the University of Stuttgart’s Dataverse repository (DaRUS [26]) for long-term availability. I.2

Consequences for axioms and labels

Two practical consequences follow from the classification. Existential dependence axioms. For every class C marked as ReifiedRelation or SubordinateSortal, the schema carries an existential axiom on each of its dependencies. Concretely: • HyperparameterSetting ⊑ ∃ isSettingOf.MLIPRun (in addition to the existing HyperparameterSetting ⊑ ∃ forHyperparameter.Hyperparameter); • AccuracyMetric ⊑ ∃ hasAccuracyMetric− .BenchmarkResult (already in the appendixaxiom catalogue); and • BenchmarkResult ⊑ ∃ evaluatesModel.TrainedModel. Computed labels. Reified-relation instances are opaque under their IRI alone: a reader who encounters ex:setting-rcut-behler2007 cannot tell from the IRI fragment what hyperparameter is set to what value in which run. We therefore compute rdfs:label values for instances of every

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reified-relation class by a SPARQL CONSTRUCT that joins the relation type, the value, and the carrier, producing labels of the form “<relation-type-label> = <value> for <carrier-label>”. The CONSTRUCT rules live in the dataset repository (archived for long-term availability on DaRUS [26]); the computed triples are materialised into a separate computed TTL file that is not tracked alongside the canonical TTL but is regenerated as part of the build pipeline. Inverse triples are computed by an analogous CONSTRUCT pass. I.3

Per-class classification

Table 7 gives the meta-sort assignment for every class in the MLIPs ontology. Where the classification required a non-obvious modelling decision, the row carries a brief rationale; otherwise the assignment is the canonical case described in §I.1. Table 7. Meta-sort classification of every class in the MLIPs ontology. Sortal = identity-bearing, rigid, not dependent; SubordinateSortal = identity-bearing but existentially dependent on a parent; Role = anti-rigid, identity inherited; ReifiedRelation = reification of an 𝑛-ary relation, no identity outside the relata. Class

Meta-sort

Notes

Sortals (canonical) MLIPMethod MaterialSystem TrainingDataset TrainedModel BenchmarkStudy Library Hyperparameter FunctionalForm LossFunction AtomicEnvironmentDescriptor SimulationType XCFunctional PseudopotentialType WfMethod DftBasisSet MetricType MetricProperty CoveredProperty DatasetProvenance SamplingStrategy ArchitecturalHyperparameter

Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal Sortal

“recipe” for an MLIP family

PhysicalHyperparameter

Sortal

TrainingHyperparameter

Sortal

AtomicConfiguration

Sortal

MetaSort

Sortal

a fitted model is a thing a published study a software package the type-level definition

enumerative enumerative enumerative enumerative enumerative enumerative enumerative enumerative enumerative subclass of Hyperparameter; identity inherited subclass of Hyperparameter; identity inherited subclass of Hyperparameter; identity inherited a concrete structure has identity (subclass of cmso:AtomicStructure) enumerative; the four named individuals partition the schema

Subordinate sortals continued on next page

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(continued) Class

Meta-sort

Notes

Implementation

SubordinateSortal

MLIPRun

SubordinateSortal

DFTCalculation

SubordinateSortal

ReferenceCalculation

SubordinateSortal

WaveFunctionCalculation

SubordinateSortal

identity by release/commit; depends on a method and a library event-with-identity (timestamp, training algorithm); depends on method, dataset, and produces a model a calculation event; depends on a settings block superclass of DFTCalculation, same status parallel to DFTCalculation; calculation event depending on a settings block

Reified relations HyperparameterSetting BenchmarkResult

ReifiedRelation ReifiedRelation

AccuracyMetric

ReifiedRelation

Discussed DFTSettings

ReifiedRelation → Sortal

ReferenceSettings WaveFunctionSettings

ReifiedRelation → Sortal ReifiedRelation → Sortal

J

3-place: carrier × hyperparameter × value 4-place: study × model × material × accuracy 3-place: result × metric type × value currently per-calculation (reified); planned switch to canonical-template (sortal) in a future release, after a deduplication pass over the seeded corpus superclass of DFTSettings, same status parallel to DFTSettings; same trajectory

Concrete Worked Examples

This appendix presents one fully-worked encoding of a published MLIP study in the MLIPs ontology, extracting every fact that the ontology can express into Turtle listings and ending with a discussion of what the source paper does not report—i.e., gaps that the ontology (or its aligned upper ontologies) could record but that no paper is currently structured enough to provide. These gaps are the practical motivation for the MLIPs ontology: making them visible is the first step towards filling them in future publications. The shorter, protocol-driven catalogue of additional encoded studies appears in Appendix K. J.1

Kumar et al. (2025): MTP for TiCr2 -H Laves Phases

This subsection encodes the study by Kumar, Körmann, Grabowski, and Ikeda [36]. The authors train two Moment Tensor Potentials (MTPs)—one per phase of the TiCr2 Laves compound—for hydrogen absorption over the concentration range 0 < 𝑥 ≤ 6 in TiCr2 H𝑥 . The walkthrough below uses the C15 (cubic) phase artefacts to keep the listings readable; the canonical TTL (kumar2025.ttl) carries a parallel C14 (hexagonal) chain with its own training dataset, MTP run, trained model, and benchmark result with energy and force RMSE. Material system. TiCr2 is an intermetallic compound (composition AB2 , 𝐴 = Ti, 𝐵 = Cr) and a Laves phase. The paper considers two crystallographic forms; the example below uses the C15 cubic form. Crystal-structure attributes (space group, Pearson symbol, Strukturbericht designation) are not first-class concepts of the MLIPs ontology; we record them as materialClass strings and defer a structured Phase concept to future work (§J.1.1).

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Listing 5. Material system. entity : mat - TiCr2 a mlips : MaterialSystem ; rdfs : label " TiCr2 ␣ ( C15 ␣ Laves ␣ phase ) " ; mlips : chemicalFormula " TiCr2 " ; mlips : materialClass " Laves ␣ phase , ␣ C15 ␣ cubic ␣ ( Fd -3 m ) " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q15724720 > .

DFT reference calculations. DFT calculations were performed in VASP using the projector augmented-wave (PAW) method, the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional, an energy cutoff of 400 eV, and a Γ-centred 4×4×4 k-point mesh with Methfessel–Paxton smearing of width 0.1 eV. Calculations are non-spin-polarised (the authors verified that magnetic moments do not influence the predicted energies and forces). Each supercell is a 2 × 2 × 2 expansion of the primitive C15 cell, containing 48 metal atoms plus a variable number of hydrogen atoms. Listing 6. DFT calculation and settings. entity : dft - TiCr2H - c15 a mlips : DFTCalculation ; mlips : hasDFTSettings entity : dft - settings - TiCr2H - c15 . entity : dft - settings - TiCr2H - c15 a mlips : DFTSettings ; mlips : usedDFTCode mlips : VASP ; mlips : xcFunctional mlips : PBE ; mlips : pseudopotentialType mlips : PAW ; mlips : energyCutoff " 400 " ^^ xsd : double ; mlips : kPointMesh " 4 x4x4 ␣ Gamma - centred " .

Training dataset. The C15 dataset reported in Step 1 of the active-learning pipeline contains 1,019 atomic configurations (the C14 step-1 set has 3,766); later steps (random hydrogen placement, ab initio MD trajectories, configurations sampled during basin-hopping Monte Carlo) further extend the set. The dataset covers energies, forces, and stresses, and the configurations span the chemical degree of freedom (variable 𝑥) and the vibrational degree of freedom (MD snapshots). We record the sampling strategy through the new samplingStrategy property (§5.1); concrete strategy individuals are modelled as instances with rdfs:label until a controlled vocabulary is developed in the journal extension. Listing 7. Training dataset and sampling strategies. entity :ds - TiCr2H - c15 a mlips : TrainingDataset ; rdfs : label " TiCr2 - Hx ␣ training ␣ set , ␣ C15 ␣ phase , ␣ step ␣ 1 " ; mlips : coversMaterial entity : mat - TiCr2 ; mlips : coversProperty mlips : Energy , mlips : Forces , mlips : Stresses ; mlips : datasetProvenance mlips : Published ; mlips : numConfigurations 1019 ; mlips : hasDFTCalculation entity : dft - TiCr2H - c15 ; mlips : samplingStrategy entity : chem - sampling , entity : vib - sampling , entity : active - learning - sampling . entity : chem - sampling a mlips : SamplingStrategy ; rdfs : label " Chemical ␣ sampling " ; rdfs : comment " Configurations ␣ across ␣ hydrogen ␣ concentrations ␣ 0 ␣ <␣ x ␣ <= ␣ 6. " . entity : vib - sampling a mlips : SamplingStrategy ; rdfs : label " Vibrational ␣ sampling ␣ ( DFT ␣ MD ) " ; rdfs : comment " Snapshots ␣ from ␣ ab ␣ initio ␣ molecular ␣ dynamics ␣ at ␣ 500 ␣ K . " . entity : active - learning - sampling a mlips : SamplingStrategy ; rdfs : label " Active ␣ learning " ; rdfs : comment " Extrapolation - grade ␣ filtering ␣ with ␣ threshold ␣ gamma ␣ >~ ␣ 1. " .

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Method, hyperparameters, and implementation. The MTP method is fitted with the BFGS optimiser as implemented in the MLIP-2 software. Of the four MTP hyperparameters declared by the ontology, the paper reports the maximum complexity level levmax = 16 explicitly; the cutoff radius 𝑅cut , minimum interatomic distance 𝑅min , and number of radial basis functions 𝑁𝑄 are not stated and are presumably defaults of MLIP-2. We record the explicit setting and flag the missing values in §J.1.1. The loss-function weights (1, 0.01, 0.001 on energy, force, and stress times volume) are method-level descriptors of the loss; we capture them in the loss-function instance. Listing 8. Method, training algorithm, and implementation. entity : MTP a mlips : MLIPMethod ; rdfs : label " Moment ␣ Tensor ␣ Potential " ; mlips : hasFunctionalForm entity : mtp - functional - form ; mlips : hasLossFunction entity : mtp - loss - w1 -001 -0001 ; mlips : hasTrainingAlgorithm entity : bfgs ; mlips : hasHyperparameter entity : hp - rcut , entity : hp - rmin , entity : hp - nq , entity : hp - levmax ; mlips : hasImplementation entity : mlip - package - v2 . entity : mtp - functional - form a mlips : FunctionalForm ; rdfs : label " MTP ␣ moment - tensor ␣ polynomial " . entity : mtp - loss -w1 -001 -0001 a mlips : LossFunction ; rdfs : label " Weighted ␣ MSE ␣ ( energy ␣ 1 , ␣ force ␣ 0.01 , ␣ stress * V ␣ 0.001) " . entity : bfgs a mls : Algorithm ; rdfs : label " BFGS " . entity : mlip - package - v2 a mlips : Implementation ; mlips : implementedIn mlips : MLIP ; mlips : version " 2 " .

MLIP run, hyperparameter settings, and trained model. The C15-MTP is the trained model produced by an MLIP run that applies the MTP method on the C15 dataset. Only the explicit hyperparameter setting (lev_max=16) is recorded; the implicit settings are discussed in §J.1.1. Listing 9. MLIP run, hyperparameter settings, and trained model. entity : run - mtp - TiCr2H - c15 a mlips : MLIPRun ; rdfs : label " MTP ␣ training ␣ run , ␣ C15 ␣ phase " ; mlips : appliesMethod entity : MTP ; mlips : runsOn entity : ds - TiCr2H - c15 ; mlips : hasHyperparameterSetting entity : setting - levmax -16 ; mlips : produces entity : model - mtp - TiCr2H - c15 . entity : setting - levmax -16 a mlips : HyperparameterSetting ; mlips : forHyperparameter entity : hp - levmax ; mlips : settingValue " 16 " . entity : model - mtp - TiCr2H - c15 a mlips : TrainedModel ; rdfs : label " C15 - MTP ␣ for ␣ TiCr2 - H " .

Benchmark study, result, and accuracy metrics. The paper reports two RMSE values per phase. The C15-MTP achieves 3.17 meV/atom on energies and 0.134 eV/Å on per-component forces (Fig. 7c); the C14-MTP reaches 2.81 meV/atom and 0.100 eV/Å. We record both per-property metrics with their QUDT units; the listing below shows the C15 result. Listing 10. Benchmark study and result. entity : study - kumar2025 a mlips : BenchmarkStudy ; rdfs : label " Kumar ␣ et ␣ al . ␣ (2025) : ␣ MTP ␣ for ␣ TiCr2 - H ␣ Laves ␣ phases " ; mlips : reportedIn entity : article - kumar2025 ; mlips : hasResult entity : result - mtp - ticr2h - c15 .

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entity : article - kumar2025 a schema : ScholarlyArticle ; schema : sameAs < https :// doi . org /10.1016/ j . actamat .2025.121319 > ; schema : datePublished " 2025 " ^^ xsd : gYear ; schema : name " Machine ␣ Learning ␣ Potentials ␣ for ␣ Hydrogen ␣ ␣ ␣␣␣␣␣␣␣␣␣␣␣␣␣␣␣ Absorption ␣ in ␣ TiCr2 ␣ Laves ␣ Phases " ; schema : author < https :// orcid . org /0000 -0002 -3661 -5870 > , < https :// orcid . org /0000 -0003 -3050 -6291 > , < https :// orcid . org /0000 -0003 -4281 -5665 > , < https :// orcid . org /0000 -0001 -9176 -3270 > . < https :// orcid . org /0000 -0002 -3661 -5870 > a schema : Person ; schema : name " Pranav ␣ Kumar " ; schema : givenName " Pranav " ; schema : familyName " Kumar " ; schema : identifier < https :// orcid . org /0000 -0002 -3661 -5870 > . < https :// orcid . org /0000 -0003 -3050 -6291 > a schema : Person ; schema : name " Fritz ␣ K ö rmann " ; schema : givenName " Fritz " ; schema : familyName " K ö rmann " ; schema : identifier < https :// orcid . org /0000 -0003 -3050 -6291 > . < https :// orcid . org /0000 -0003 -4281 -5665 > a schema : Person ; schema : name " Blazej ␣ Grabowski " ; schema : givenName " Blazej " ; schema : familyName " Grabowski " ; schema : identifier < https :// orcid . org /0000 -0003 -4281 -5665 > . < https :// orcid . org /0000 -0001 -9176 -3270 > a schema : Person ; schema : name " Yuji ␣ Ikeda " ; schema : givenName " Yuji " ; schema : familyName " Ikeda " ; schema : identifier < https :// orcid . org /0000 -0001 -9176 -3270 > . # schema : affiliation links from each Person to the canonical # Organization IRIs in mlips - vocab . ttl . < https :// orcid . org /0000 -0002 -3661 -5870 > schema : affiliation mlips : UniversityOfStuttgart . < https :// orcid . org /0000 -0003 -3050 -6291 > schema : affiliation mlips : UniversityOfStuttgart . < https :// orcid . org /0000 -0003 -3050 -6291 > schema : affiliation mlips : RuhrUniversityBochum . < https :// orcid . org /0000 -0003 -4281 -5665 > schema : affiliation mlips : UniversityOfStuttgart . < https :// orcid . org /0000 -0001 -9176 -3270 > schema : affiliation mlips : UniversityOfStuttgart . entity : result - mtp - ticr2h - c15 a mlips : BenchmarkResult ; mlips : evaluatesModel entity : model - mtp - TiCr2H - c15 ; mlips : targetMaterial entity : mat - TiCr2 ; mlips : hasAccuracyMetric entity : metric - rmse - energy - c15 , entity : metric - rmse - forces - c15 . entity : metric - rmse - energy - c15 a mlips : AccuracyMetric ; mlips : metricType mlips : RMSE ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricValue 3.17 ; mlips : hasUnit mlips : MilliEV - PER - ATOM . entity : metric - rmse - forces - c15 a mlips : AccuracyMetric ; mlips : metricType mlips : RMSE ; mlips : metricProperty mlips : ForceProperty ; mlips : metricValue 0.134 ; mlips : hasUnit unit : EV - PER - ANGSTROM .

J.1.1 What is missing from the paper. The Kumar et al. paper is among the more methodologically explicit MLIP papers, yet it leaves several pieces of metadata implicit or absent. Each item below is expressible in the MLIPs ontology (or in an ontology we are aligned to) but is not provided by the source.

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Hyperparameter values that defaulted silently. The MTP cutoff radius (𝑅cut ), minimum interatomic distance (𝑅min ), and number of radial basis functions (𝑁𝑄 ) are not stated. Reproducing the model requires either the MLIP-2 default values at the time of training or the configuration files. The ontology models these as HyperparameterSetting instances with no recorded settingValue; consumers can detect this through a SPARQL query and surface a warning. Training-cost metadata. trainingDuration, gpuHours, trainingHardware, and peakMemory (data properties on MLIPRun) are all absent. CPU hours, the number of DFT calls during active learning, and the cost of the basin-hopping Monte Carlo loop would all be valuable for comparing this work against alternative MLIP architectures (CQ9 in the requirements). Inference-cost metadata. inferenceTimePerAtom, inferenceHardware, and peakMemory on the trained model are not reported. For a hydrogen-storage screening application this matters: the practical value of the MTP comes from its inference cost relative to DFT, which is alluded to but not quantified. Crystal-phase metadata as a first-class entity. The C15/C14 distinction is reduced to a string in materialClass. Aligned ontologies (CMSO, EMMO) provide crystal-structure, space-group, and Pearson-symbol concepts, but the MLIPs ontology does not currently expose these slots. Adding a Phase class and aligning to CMSO’s cmso:CrystalStructure hierarchy is part of the planned journal-extension work. Step-by-step training provenance. The active-learning pipeline runs four distinct steps, each producing an intermediate MTP and an extended training set. We collapse this into a single MLIPRun on a single dataset; a faithful encoding would chain four MLIPRun instances and four TrainingDataset versions linked through prov:wasDerivedFrom. The ontology already supports this (datasets reuse PROV-O), but doing so was beyond the scope of the original paper’s reporting. Reference-method and dataset deposit. Where the trained MTP and the training dataset live (DaRUS, Materials Cloud, NOMAD, a personal repository) is not specified, so a datasetProvenance of Published is the only handle the ontology has. Linking the dataset to a persistent identifier (DOI, URN, or a Materials-Cloud entry IRI) is the kind of FAIR metadata that the ontology is built to encode but that the paper does not yet provide. Note on non-DFT references. Kumar et al. used DFT throughout, so DFTCalculation and DFTSettings are the right slots. Had they instead used CCSD(T) (or another wavefunction method) for some configurations, the encoding would replace DFTCalculation with WaveFunctionCalculation and carry WaveFunctionSettings with wfMethod = "CCSD(T)", basisSet = "cc-pVTZ", and frozenCore = true. The dataset-to-calculation link hasReferenceCalculation remains the same; the change is local to the calculation subtype. K

Encoded Paper Catalogue

This appendix catalogues a corpus of recently published MLIP studies encoded in the MLIPs ontology. The first subsection (§K.1) defines the extraction protocol used to produce the per-paper reports; the remaining subsections apply that protocol to one paper each. The corpus underpins the competency-question evaluation in §6.2: the seeded knowledge graph used by the SPARQL templates is the union of the per-paper canonical Turtle files listed below. The detailed Kumar et al. (2025) worked example in §J.1 is the prose-rich reference for what each encoding aspires to; the catalogue entries below follow the leaner, protocol-driven format.

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Extraction Protocol

The Kumar et al. worked example (§J.1) is the reference for what an encoded MLIP paper should look like. To replicate that quality across the catalogue at scale—and to give a future agentic-AI tool something concrete to follow—we fix a 12-question extraction protocol. The protocol has two artefacts per paper: a canonical Turtle file carrying the encoded data, and a subsection in this appendix carrying the prose. The two are kept in sync by an automated round-trip check described at the end of this subsection. Overview of the flow. For each paper we ask the same 12 questions in fixed order. Each question (a) produces a Turtle fragment that is appended to the paper’s canonical file artifacts/kg/papers/paper-id.ttl, and (b) a short commentary paragraph in the paper’s subsection. Each of questions Q1–Q11 has an associated CONSTRUCT query that, when run against the paper’s canonical file, regenerates the Turtle listing shown under that question’s commentary. The union of the 11 CONSTRUCT outputs is required (modulo blank-node renaming and prefix declarations) to reproduce the canonical file—this is the round-trip check. Q12 is prose-only (gaps are not always reducible to triples) and is excluded from the round-trip. The 12 questions. Grouped into five phases: Phase A. Identification. Q1. What are the bibliographic details of the source paper? Title, authors, year, venue, DOI. Targets: schema : ScholarlyArticle, BenchmarkStudy, reportedIn. Phase B. Training data. Q2. What material system(s) are studied? Chemical formula, material class (alloy, intermetallic, Laves phase, molecular, oxide), structural specifics (phase, space group, defect type), Wikidata link if available. Targets: MaterialSystem and its data properties. Q3. What method produced the reference data? DFT, wave-function (CCSD(T), MP2, CASPT2, . . . ), AIMD, or experimental. Targets: ReferenceCalculation and its concrete subtype. Q4. What reference-method settings are reported? For DFT: xcFunctional, kPointMesh, energyCutoff, pseudopotentialType. For wave-function: wfMethod, basisSet, frozenCore. For both: software code via usedReferenceCode (or its DFT-specific sub-property). Targets: ReferenceSettings subtypes and Library. Q5. How is the training dataset characterised? Number of configurations, covered physical properties (energies, forces, stresses, virials), provenance class, link to the reference calculation. Targets: TrainingDataset, DatasetProvenance, CoveredProperty, hasReferenceCalculation. Q6. What sampling strategies were used? Chemical, vibrational or MD-driven, active-learning, perturbation-based, exhaustive enumeration, or combinations. Targets: SamplingStrategy instances and samplingStrategy. Phase C. Method, run, and model. Q7. What MLIP method is used, and what are its components? Functional form, loss function, training algorithm (the ML-Schema alignment point), software implementation and version. Targets: MLIPMethod, FunctionalForm, LossFunction, hasTrainingAlgorithm, Implementation, Library. Q8. What hyperparameter settings does the paper explicitly report? Cutoff radius, MTP level, number of layers, learning rate, etc. Implicit defaults are recorded as not reported but

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referenced in Q12. Targets: HyperparameterSetting and forHyperparameter. Q9. What is the structure of the run? Single training run vs. multi-step active-learning pipeline; one trained model vs. a per-phase or per-fold ensemble. Targets: MLIPRun, TrainedModel, appliesMethod, runsOn, produces, hasHyperparameterSetting. Phase D. Evaluation. Q10. What benchmark results does the paper report? Each accuracy metric is recorded with its type (RMSE, MAE, . . . ), the property it measures (energy, forces, stresses, downstream properties), and its numerical value with units. Targets: BenchmarkResult, AccuracyMetric, MetricType, MetricProperty, evaluatesModel, targetMaterial. Q11. What computational-resource metadata is reported? Training duration, GPU hours, training hardware, peak memory; inference time per atom, inference hardware. Targets: data properties on MLIPRun and TrainedModel. Phase E. Gaps. Q12. What concepts that the ontology can express does the paper not report? Free-form, prose-only. This question produces no Turtle and is excluded from the round-trip check. Per-paper subsection template. A protocol-derived subsection contains 12 paragraphs corresponding to Q1–Q12 (in order). Each paragraph for Q1–Q11 has the structure: (i) a 2–4 sentence prose answer derived from the source paper; (ii) a Turtle listing produced by the question’s CONSTRUCT query; and (iii) where the paper does not report a piece of data the ontology can model, an explicit not reported marker so that Q12 has a complete inventory to summarise. Q12 is prose-only. Files and naming. Per-paper data and queries live under artifacts/kg/: • papers/paper-id.ttl—canonical Turtle for one paper. Identifiers use a firstauthor-year convention (kumar2025.ttl, qi2023.ttl, . . . ). • queries/q01-bibliographic.rq . . . queries/q11-resources.rq—one CONSTRUCT query per question Q1–Q11. The queries are paper-agnostic; they are parameterised only by the prefix declarations of the paper they are run against. • check-roundtrip.sh paper-id—runs the 11 CONSTRUCT queries against papers/paper-id.ttl, takes their union, and diff-canonicalises against the canonical file. Exits non-zero on drift. • build-listings.sh paper-id—runs the 11 queries and emits Turtle listings ready for inclusion in the paper’s subsection. Round-trip check. At the end of every paper’s encoding pass, we run check-roundtrip.sh. The check parses the 11 query outputs into N-triples (via rapper -o ntriples), sorts and dedups, and diffs against the same canonicalisation of the paper’s .ttl file. Two outcomes are possible: • Pass. The 11 questions partition the paper’s data; the subsection is a faithful presentation of the canonical file. • Fail. A triple is in the canonical file but not in any CONSTRUCT output (encoded but never asked about), or vice versa. The protocol is then revised: either a question’s scope is widened, or a new question is introduced and back-applied to all prior papers. Limits and assumptions. Two assumptions worth flagging. First, the protocol assumes one paper ≡ one MLIP method × one material system. Papers training multiple potentials or covering multiple

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systems (e.g., Kumar et al. 2025 has separate C15 and C14 potentials) instantiate the protocol per phase or per system, with the appropriate identifiers (kumar2025-c15, kumar2025-c14). Second, papers occasionally report ontology-relevant data the protocol does not capture (uncertainty quantification, transferability claims, foundation-model fine-tuning tags). When such data appears in three or more papers we treat that as a signal to revise the protocol. K.2

Behler & Parrinello (2007): high-dimensional NN potential for bulk silicon

Q1 – Bibliographic identification. Behler and Parrinello introduce the foundational highdimensional neural-network potential (HDNNP) construction: total energy as a sum of per-atom subnet contributions over shared-weight feed-forward NNs that take atom-centred symmetry functions as input. The method is demonstrated on bulk silicon. Published in Phys. Rev. Lett. 98, 146401 (2007). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -6550 -3272 > a schema : Person ; schema : affiliation entity : org - ETHZurich - behler2007 ; schema : familyName " Parrinello " ; schema : givenName " Michele " ; schema : identifier < https :// orcid . org /0000 -0001 -6550 -3272 > ; schema : name " Michele ␣ Parrinello " . < https :// orcid . org /0000 -0002 -1220 -1542 > a schema : Person ; schema : affiliation entity : org - ETHZurich - behler2007 ; schema : familyName " Behler " ; schema : givenName " J ö rg " ; schema : identifier < https :// orcid . org /0000 -0002 -1220 -1542 > ; schema : name "Jö rg ␣ Behler " . entity : article - behler2007 a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0001 -6550 -3272 > , < https :// orcid . org /0000 -0002 -1220 -1542 > ; schema : datePublished " 2007 " ^^ xsd : gYear ; schema : name " Generalized ␣ Neural - Network ␣ Representation ␣ of ␣ High - Dimensional ␣ Potential Energy ␣ Surfaces " ; schema : sameAs < https :// doi . org /10.1103/ PhysRevLett .98.146401 > . entity : org - ETHZurich - behler2007 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " ETH ␣ Zurich " ; schema : identifier < https :// ror . org /05 a28rw58 > ; schema : name " ETH ␣ Zurich " . entity : study - behler2007 a mlips : BenchmarkStudy ; rdfs : label " Behler ␣ & ␣ Parrinello ␣ (2007) : ␣ high - dimensional ␣ NN ␣ potential ␣ for ␣ bulk ␣ silicon " ; mlips : reportedIn entity : article - behler2007 .

Q2 – Material system. The demonstration system is bulk silicon. The training set covers the diamond-cubic semiconducting phase, the high-pressure phases (including 𝛽-tin), and the liquid metallic phase, so we record Si as a single MaterialSystem at the elemental level with the phase coverage captured in materialClass. @base < http :// example . org / > .

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@prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat -Si - behler2007 a mlips : MaterialSystem ; rdfs : label " Bulk ␣ silicon ␣ ( across ␣ solid ␣ and ␣ liquid ␣ phases ) " ; mlips : chemicalFormula " Si " ; mlips : materialClass " Elemental ␣ crystalline ␣ solid ; ␣ covers ␣ diamond ␣ cubic , ␣ high - pressure ␣ phases ␣(e. g . ␣ beta - tin ) ,␣ and ␣ the ␣ liquid ␣ metallic ␣ phase " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q670 > .

Q3 – Reference calculation method. Reference data are produced from DFT calculations in the local density approximation (LDA). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - behler2007 a mlips : DFTCalculation .

Q4 – Reference settings. DFT calculations are carried out with PWscf using a 20 Ry (≈ 272 eV) plane-wave cutoff in combination with a Vanderbilt ultrasoft pseudopotential, a 3 × 3 × 3 k-point mesh, and Fermi smearing of 0.1 eV (to aid convergence in the metallic phases). Frozen-core treatment beyond the ultrasoft-pseudopotential partition is not explicitly reported. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - behler2007 mlips : hasDFTSettings entity : dft - settings - behler2007 . entity : dft - settings - behler2007 a mlips : DFTSettings ; rdfs : comment " Vanderbilt - style ␣ ultrasoft ␣ pseudopotential . " ; mlips : energyCutoff 272 ; mlips : kPointMesh " 3 x3x3 ␣k - point ␣ mesh , ␣ Fermi ␣ smearing ␣ 0.1 ␣ eV " ; mlips : pseudopotentialType mlips : Ultrasoft ; mlips : usedDFTCode mlips : QuantumESPRESSO ; mlips : xcFunctional mlips : LDA .

Q5 – Training dataset. Approximately 9,000 DFT energies are computed in total: 8,200 are used for training the NN and 800 form a held-out test set. The dataset is in-house and covers energies and atomic forces. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > .

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Hernández et al. @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds -Si - behler2007 a mlips : TrainingDataset ; rdfs : label " Bulk - Si ␣ HDNNP ␣ DFT - LDA ␣ dataset ␣ (~9000 ␣ total : ␣ 8200 ␣ train ␣ + ␣ 800 ␣ test ) " ; mlips : coversMaterial entity : mat - Si - behler2007 ; mlips : coversProperty mlips : Energy , mlips : Forces ; mlips : datasetProvenance mlips : InHouse ; mlips : hasDFTCalculation entity : dft - behler2007 ; mlips : numConfigurations 9000 ; mlips : wasRunBy entity : run - hdnnp - Si - behler2007 .

Q6 – Sampling strategies. Three strategies are used: enumeration of crystal structures (including high-pressure polymorphs), DFT MD snapshots at different pressures and temperatures, and a self-consistent iterative refinement loop in which best fits drive MD, hybrid Monte Carlo, and metadynamics runs whose representative configurations are recalculated with DFT and added to the training set when their RMSE exceeds the current fit error—a precursor to today’s active-learning workflows. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : crystal - sampling - behler2007 a mlips : SamplingStrategy ; rdfs : comment " Initial ␣ training ␣ structures ␣ taken ␣ from ␣ known ␣ crystalline ␣ silicon ␣ structures ␣ including ␣ high - pressure ␣ phases . " ; rdfs : label " Crystal - structure ␣ enumeration " . entity :ds -Si - behler2007 mlips : samplingStrategy entity : crystal - sampling - behler2007 , entity : md - sampling behler2007 , entity : self - consistent - sampling - behler2007 . entity :md - sampling - behler2007 a mlips : SamplingStrategy ; rdfs : comment " MD ␣ snapshots ␣ at ␣ different ␣ pressures ␣ and ␣ temperatures ␣ used ␣ to ␣ populate ␣ the ␣ training ␣ set . " ; rdfs : label " Vibrational ␣ sampling ␣ ( DFT ␣ MD ) " . entity : self - consistent - sampling - behler2007 a mlips : SamplingStrategy ; rdfs : comment " Best ␣ fits ␣ used ␣ to ␣ drive ␣ MD , ␣ hybrid ␣ Monte ␣ Carlo , ␣ and ␣ metadynamics ; ␣ representative ␣ structures ␣ are ␣ recalculated ␣ with ␣ DFT ␣ and ␣ added ␣ to ␣ the ␣ training ␣ set ␣ if ␣ RMSE ␣ exceeds ␣ the ␣ fit ␣ error ␣ --␣ a ␣ precursor ␣ to ␣ active ␣ learning . " ; rdfs : label " Self - consistent ␣ iterative ␣ refinement " .

Q7 – MLIP method, components, implementation. The method is the Í original Behler–Parrinello high-dimensional NN potential: the total energy decomposes as 𝐸 = 𝑖 𝐸𝑖 , with each 𝐸𝑖 produced by a shared-weight feed-forward subnet whose inputs are atom-centred symmetry functions (radial Gaussian sums and angular triplet sums). The training loss is the mean squared error on the per-configuration total DFT energy. The implementation is an in-house extension of the Lorenz–Groß–Scheffler NN code; the training algorithm is not explicitly named. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > .

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@prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : HDNNP - behler2007 . entity : HDNNP - behler2007 a mlips : MLIPMethod ; rdfs : label " High - Dimensional ␣ Neural ␣ Network ␣ Potential ␣ ( Behler - Parrinello ) " ; mlips : hasDescriptor mlips : SymmetryFunctionDescriptor ; mlips : hasFunctionalForm entity : hdnnp - functional - form - behler2007 ; mlips : hasHyperparameter mlips : cutoffRadius , entity : hp - numhidden - behler2007 , entity : hp numsf - behler2007 ; mlips : hasImplementation entity : impl - hdnnp - behler2007 ; mlips : hasLossFunction entity : hdnnp - loss - behler2007 ; mlips : supportsSimulation mlips : MolecularDynamics . entity : hdnnp - functional - form - behler2007 a mlips : FunctionalForm ; rdfs : label " Sum ␣ of ␣ per - atom ␣ subnet ␣ energies ␣ E ␣ = ␣ sum_i ␣ E_i ␣ with ␣ shared - weight ␣ feed forward ␣ NN ␣ subnets ␣ and ␣ Behler - Parrinello ␣ atom - centred ␣ symmetry - function ␣ inputs ␣ ( radial ␣ Gaussian ␣ and ␣ angular ␣ triplet ␣ sums ) " . entity : hdnnp - loss - behler2007 a mlips : LossFunction ; rdfs : label " Mean ␣ squared ␣ error ␣ on ␣ per - configuration ␣ total ␣ DFT ␣ energy " . entity :hp - numhidden - behler2007 a mlips : Hyperparameter ; rdfs : label " HDNNP ␣ per - element ␣ hidden - unit ␣ count " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : integer ; mlips : hyperparameterName " num_hidden " ; mlips : isHyperparameterOf entity : HDNNP - behler2007 . entity :hp - numsf - behler2007 a mlips : Hyperparameter ; rdfs : label " HDNNP ␣ per - element ␣ symmetry - function ␣ count " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : integer ; mlips : hyperparameterName " num_symmetry_functions " ; mlips : isHyperparameterOf entity : HDNNP - behler2007 . entity : impl - hdnnp - behler2007 a mlips : Implementation ; mlips : implementedIn entity : lib - hdnnp - behler2007 ; mlips : isImplementationOf entity : HDNNP - behler2007 . entity : lib - hdnnp - behler2007 a mlips : Library ; rdfs : label "In - house ␣ extension ␣ of ␣ the ␣ Lorenz - Gross - Scheffler ␣ neural - network ␣ code " .

Q8 – Hyperparameter settings. Reported hyperparameter settings: a cutoff radius of 6 Å, 48 symmetry functions per atom, and subnets with 2 hidden layers of ≈ 40 nodes each (a few thousand fitting parameters in total). The hyperbolic tangent is the hidden-layer activation; the output layer uses a linear activation. Numerical Gaussian parameters 𝜂, 𝑅𝑠 , 𝜁 are not enumerated. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - numhidden - behler2007 a mlips : HyperparameterSetting ; rdfs : label " HDNNP ␣ per - element ␣ hidden - unit ␣ count ␣ = ␣ 2 ␣ hidden ␣ layers , ␣ ~40 ␣ nodes ␣ each ␣ for ␣ HDNNP ␣ training ␣ run , ␣ bulk ␣ silicon " ; mlips : forHyperparameter entity : hp - numhidden - behler2007 ; mlips : isSettingOf entity : run - hdnnp - Si - behler2007 ; mlips : settingValue " 2 ␣ hidden ␣ layers , ␣ ~40 ␣ nodes ␣ each " . entity : setting - numsf - behler2007 a mlips : HyperparameterSetting ; rdfs : label " HDNNP ␣ per - element ␣ symmetry - function ␣ count ␣ = ␣ 48 ␣ for ␣ HDNNP ␣ training ␣ run , ␣ bulk ␣ silicon " ;

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Hernández et al. mlips : forHyperparameter entity : hp - numsf - behler2007 ; mlips : isSettingOf entity : run - hdnnp - Si - behler2007 ; mlips : settingValue 48 . entity : setting - rcut - behler2007 a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 6 ␣ for ␣ HDNNP ␣ training ␣ run , ␣ bulk ␣ silicon " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - hdnnp - Si - behler2007 ; mlips : settingValue 6 .

Q9 – MLIP run and trained model. A single training run produces one HDNNP for bulk silicon. The self-consistent iterative refinement is recorded as a sampling strategy in Q6 rather than as a multi-stage run. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - hdnnp - Si - behler2007 a mlips : TrainedModel ; rdfs : label " Behler - Parrinello ␣ HDNNP ␣ for ␣ bulk ␣ silicon " . entity : run - hdnnp -Si - behler2007 a mlips : MLIPRun ; rdfs : label " HDNNP ␣ training ␣ run , ␣ bulk ␣ silicon " ; mlips : appliesMethod entity : HDNNP - behler2007 ; mlips : hasHyperparameterSetting entity : setting - numhidden - behler2007 , entity : setting numsf - behler2007 , entity : setting - rcut - behler2007 ; mlips : produces entity : model - hdnnp - Si - behler2007 ; mlips : runsOn entity : ds - Si - behler2007 .

Q10 – Benchmark results. Headline accuracy figures are an energy RMSE of 4–5 meV/atom on the optimisation set and 5–6 meV/atom on the independent test set, plus a force-component RMSE of ≈ 0.2 eV/Å (vs. DFT-LDA). Downstream qualitative checks include reproducing the DFT energy–volume curves and transition pressures across the silicon polymorphs, and the radial distribution function of the 3000 K silicon melt. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - rmse - energy - behler2007 a mlips : AccuracyMetric ; rdfs : label " Energy ␣ RMSE ␣ on ␣ the ␣ held - out ␣ test ␣ set ␣ ( vs . ␣ DFT - LDA ) " , " RMSE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 5.5 ␣ [ millielectronvolt ␣ per ␣ atom ] " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - hdnnp - Si - energy - behler2007 ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 5.5 . entity : metric - rmse - forces - behler2007 a mlips : AccuracyMetric ; rdfs : label " Atomic - force ␣ RMSE ␣ ( vs . ␣ DFT - LDA ) " , " RMSE ␣ of ␣ Force ␣ = ␣ 0.2 ␣ [ EV - PER - ANGSTROM ] " ; mlips : hasUnit unit : EV - PER - ANGSTROM ; mlips : isMetricOf entity : result - hdnnp - Si - forces - behler2007 ; mlips : metricProperty mlips : ForceProperty ;

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mlips : metricType mlips : RMSE ; mlips : metricValue 0.2 . entity : result - hdnnp - Si - energy - behler2007 a mlips : BenchmarkResult ; rdfs : label " Behler - Parrinello ␣ HDNNP ␣ for ␣ bulk ␣ silicon ␣ on ␣ Bulk ␣ silicon ␣ ( across ␣ solid ␣ and ␣ liquid ␣ phases ) ␣ in ␣ Behler ␣ & ␣ Parrinello ␣ (2007) : ␣ high - dimensional ␣ NN ␣ potential ␣ for ␣ bulk ␣ silicon " ; mlips : evaluatesModel entity : model - hdnnp - Si - behler2007 ; mlips : hasAccuracyMetric entity : metric - rmse - energy - behler2007 ; mlips : isResultOf entity : study - behler2007 ; mlips : targetMaterial entity : mat - Si - behler2007 . entity : result - hdnnp - Si - forces - behler2007 a mlips : BenchmarkResult ; rdfs : label " Behler - Parrinello ␣ HDNNP ␣ for ␣ bulk ␣ silicon ␣ on ␣ Bulk ␣ silicon ␣ ( across ␣ solid ␣ and ␣ liquid ␣ phases ) ␣ in ␣ Behler ␣ & ␣ Parrinello ␣ (2007) : ␣ high - dimensional ␣ NN ␣ potential ␣ for ␣ bulk ␣ silicon " ; mlips : evaluatesModel entity : model - hdnnp - Si - behler2007 ; mlips : hasAccuracyMetric entity : metric - rmse - forces - behler2007 ; mlips : isResultOf entity : study - behler2007 ; mlips : targetMaterial entity : mat - Si - behler2007 . entity : study - behler2007 mlips : hasResult entity : result - hdnnp - Si - energy - behler2007 , entity : result - hdnnp - Si forces - behler2007 .

Q11 – Computational resources. Not reported. The paper gives no training duration, GPU hours, training hardware, peak memory, or per-atom inference time. They do quote a relative inference speed of ∼5 orders of magnitude faster than DFT for a 64-atom cell—a comparative figure rather than an ontology-recordable inferenceTimePerAtom value. # Q11 - resources : no triples ( paper does not report this ) .

Q12 – Gaps. Beyond Q11 (compute resources entirely absent), the following ontology-expressible items are not reported: the training algorithm or optimiser used to fit the NN weights; softwareimplementation versioning (this is a precursor to today’s named HDNNP packages such as RuNNer or n2p2); explicit frozenCore treatment beyond the ultrasoft-pseudopotential partition; numerical values of the symmetry-function parameters 𝜂, 𝑅𝑠 , 𝜁 ; and a controlled-vocabulary individual for the self-consistent iterative refinement (encoded as an ad-hoc rdfs:label/rdfs:comment sampling instance, since active learning post-dates this paper). K.3

Bartók et al. (2010): Gaussian Approximation Potentials

Q1 – Bibliographic identification. Bartók, Payne, Kondor, and Csányi introduce the Gaussian Approximation Potential (GAP): Gaussian-process regression on a bispectrum-based descriptor of the local atomic environment. The method is demonstrated on bulk semiconductors (C, Si, Ge), GaN, and 𝛼-Fe; we encode bulk silicon as the lead system. Published in Phys. Rev. Lett. 104, 136403 (2010); arXiv:0910.1019. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0002 -4347 -8819 > a schema : Person ; schema : affiliation mlips : UniversityofCambridge ; schema : familyName " Bart ó k " ; schema : givenName " Albert ␣ P . " ; schema : identifier < https :// orcid . org /0000 -0002 -4347 -8819 > ; schema : name " Albert ␣ P . ␣ Bart ó k " .

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Hernández et al. < https :// orcid . org /0000 -0002 -4458 -6598 > a schema : Person ; schema : affiliation mlips : UniversityofCambridge , entity : org CaliforniaInstituteofTechnology - bartok2010 ; schema : familyName " Kondor " ; schema : givenName " Risi " ; schema : identifier < https :// orcid . org /0000 -0002 -4458 -6598 > ; schema : name " Risi ␣ Kondor " . < https :// orcid . org /0000 -0002 -5250 -8549 > a schema : Person ; schema : affiliation mlips : UniversityofCambridge ; schema : familyName " Payne " ; schema : givenName " Mike ␣ C . " ; schema : identifier < https :// orcid . org /0000 -0002 -5250 -8549 > ; schema : name " Mike ␣ C . ␣ Payne " . < https :// orcid . org /0000 -0002 -8180 -2034 > a schema : Person ; schema : affiliation mlips : UniversityofCambridge ; schema : familyName " Cs á nyi " ; schema : givenName " G á bor " ; schema : identifier < https :// orcid . org /0000 -0002 -8180 -2034 > ; schema : name "Gá bor ␣ Cs á nyi " . entity : article - bartok2010 a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0002 -4347 -8819 > , < https :// orcid . org /0000 -0002 -4458 -6598 > , < https :// orcid . org /0000 -0002 -5250 -8549 > , < https :// orcid . org /0000 -0002 -8180 -2034 > ; schema : datePublished " 2010 " ^^ xsd : gYear ; schema : name " Gaussian ␣ Approximation ␣ Potentials : ␣ The ␣ Accuracy ␣ of ␣ Quantum ␣ Mechanics , ␣ without ␣ the ␣ Electrons " ; schema : sameAs < https :// doi . org /10.1103/ PhysRevLett .104.136403 > . entity : org - CaliforniaInstituteofTechnology - bartok2010 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " California ␣ Institute ␣ of ␣ Technology " ; schema : identifier < https :// ror . org /05 dxps055 > ; schema : name " California ␣ Institute ␣ of ␣ Technology " . entity : study - bartok2010 a mlips : BenchmarkStudy ; rdfs : label " Bartok ␣ et ␣ al . ␣ (2010) : ␣ GAP ␣ for ␣ bulk ␣ crystals ␣ ( Si ␣ as ␣ lead ␣ system ) " ; mlips : reportedIn entity : article - bartok2010 .

Q2 – Material system. The lead demonstration system encoded here is bulk silicon in its diamond-cubic phase. The paper also reports analogous GAP fits for diamond (carbon), germanium, GaN, and 𝛼-iron; those systems are flagged in Q12. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat -Si - bartok2010 a mlips : MaterialSystem ; rdfs : label " Bulk ␣ silicon ␣ ( diamond - cubic ␣ phase , ␣ lead ␣ demonstration ␣ system ) " ; mlips : chemicalFormula " Si " ; mlips : materialClass " Elemental ␣ crystalline ␣ solid ; ␣ diamond - cubic ␣ phase ␣ as ␣ the ␣ lead ␣ demonstration ␣ system . ␣ The ␣ paper ␣ also ␣ demonstrates ␣ GAP ␣ on ␣ diamond ␣ ( carbon ) ,␣ germanium , ␣ GaN , ␣ and ␣ alpha - Fe . " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q670 > .

Q3 – Reference calculation method. Reference data are produced from plane-wave DFT calculations. @base < http :// example . org / > .

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@prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - bartok2010 a mlips : DFTCalculation .

Q4 – Reference settings. The DFT engine is CASTEP. Specific exchange–correlation functional, plane-wave cutoff, k-mesh, and pseudopotential type are reported in the Supplementary Information rather than the main letter, so they are not encoded here. Not reported in the main text. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - bartok2010 mlips : hasDFTSettings entity : dft - settings - bartok2010 . entity : dft - settings - bartok2010 a mlips : DFTSettings ; mlips : usedDFTCode mlips : CASTEP .

Q5 – Training dataset. Reference configurations are produced by random atomic and lattice displacements (up to 0.2 Å) of equilibrium 2-, 8-, 16-, and 64-atom cubic Si unit cells, with energies and forces from CASTEP. The model is later extended with random displacements around a diamond vacancy and a graphite-to-diamond transition path. numConfigurations is not enumerated in the main text; provenance is in-house. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds -Si - bartok2010 a mlips : TrainingDataset ; rdfs : label " Si ␣ GAP ␣ training ␣ set : ␣ random ␣ atomic ␣ and ␣ lattice ␣ displacements ␣ ( up ␣ to ␣ 0.2 ␣ A ) ␣ of ␣ equilibrium ␣ unit ␣ cells ␣ of ␣ 2 , ␣ 8 , ␣ 16 , ␣ and ␣ 64 ␣ atoms " ; mlips : coversMaterial entity : mat - Si - bartok2010 ; mlips : coversProperty mlips : Energy , mlips : Forces ; mlips : datasetProvenance mlips : InHouse ; mlips : hasDFTCalculation entity : dft - bartok2010 ; mlips : wasRunBy entity : run - gap - Si - bartok2010 .

Q6 – Sampling strategies. A single sampling strategy applies: random atomic and lattice displacements of small cubic unit cells, supplemented at the end of the paper with isolated-defect (vacancy) and reaction-pathway (graphite→diamond) configurations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > .

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Hernández et al. entity : displacement - sampling - bartok2010 a mlips : SamplingStrategy ; rdfs : comment " Reference ␣ configurations ␣ are ␣ obtained ␣ by ␣ randomly ␣ displacing ␣ the ␣ atoms ␣ and ␣ the ␣ lattice ␣ vectors ␣ from ␣ their ␣ equilibrium ␣ values ␣ in ␣ 2 - , ␣ 8 - , ␣ 16 - , ␣ and ␣ 64 - atom ␣ cubic ␣ unit ␣ cells ␣ by ␣ up ␣ to ␣ 0.2 ␣ A . ␣ The ␣ model ␣ is ␣ later ␣ extended ␣ with ␣ random ␣ displacements ␣ around ␣ a ␣ diamond ␣ vacancy ␣ and ␣ a ␣ graphite - to - diamond ␣ transition ␣ path . " ; rdfs : label " Random ␣ atomic ␣ and ␣ lattice ␣ displacements " . entity :ds -Si - bartok2010 mlips : samplingStrategy entity : displacement - sampling - bartok2010 .

Q7 – MLIP method, components, implementation. GAP is Gaussian-process regression on a fourdimensional bispectrum descriptor of the atomic neighbour density inside a smooth cosine cutoff; total energy is the sum over atoms. Training is sparse GP regression with 𝑀 randomly selected representative atomic-neighbourhood configurations. The implementation is the QUIP/GAP suite (libatoms.org). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : GAP - bartok2010 . mlips : numSparseConfigs mlips : isHyperparameterOf entity : GAP - bartok2010 . entity : GAP - bartok2010 a mlips : MLIPMethod ; rdfs : label " Gaussian ␣ Approximation ␣ Potential ␣ ( GAP ) ␣ with ␣ bispectrum ␣ descriptors " ; mlips : hasDescriptor mlips : SOAPDescriptor ; mlips : hasFunctionalForm entity : gap - functional - form - bartok2010 ; mlips : hasHyperparameter mlips : cutoffRadius , mlips : numSparseConfigs , entity : hp - jmax bartok2010 ; mlips : hasImplementation entity : impl - gap - bartok2010 ; mlips : hasLossFunction entity : gap - loss - bartok2010 ; mlips : hasTrainingAlgorithm entity : gpr - bartok2010 ; mlips : supportsSimulation mlips : MolecularDynamics , mlips : PhononCalculation . entity : gap - functional - form - bartok2010 a mlips : FunctionalForm ; rdfs : label " Gaussian - process ␣ regression ␣ on ␣ a ␣ four - dimensional ␣ bispectrum ␣ descriptor ␣ of ␣ the ␣ atomic ␣ neighbour ␣ density ␣ inside ␣ a ␣ smooth ␣ cosine ␣ cutoff ; ␣ total ␣ energy ␣ is ␣ the ␣ sum ␣ over ␣ atoms " . entity : gap - loss - bartok2010 a mlips : LossFunction ; rdfs : label " GP ␣ regression ␣ with ␣ regularised ␣ pseudo - covariance ␣ on ␣ energies ␣ and ␣ forces ␣ ( sparse - GP ␣ marginal - likelihood ␣ objective ) " . entity : gpr - bartok2010 a mls : Algorithm ; rdfs : label " Sparse ␣ Gaussian - process ␣ regression ␣ with ␣ random ␣ selection ␣ of ␣ M ␣ sparse ␣ atomic - neighbourhood ␣ configurations " . entity :hp - jmax - bartok2010 a mlips : Hyperparameter ; rdfs : label " GAP ␣ bispectrum ␣ truncation ␣ Jmax " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : integer ; mlips : hyperparameterName " j_max " ; mlips : isHyperparameterOf entity : GAP - bartok2010 . entity : impl - gap - bartok2010 a mlips : Implementation ; mlips : implementedIn mlips : QUIP ; mlips : isImplementationOf entity : GAP - bartok2010 .

Q8 – Hyperparameter settings. The main letter does not tabulate explicit numerical values for the descriptor cutoff 𝑟𝑐 , bispectrum truncation 𝐽max , or sparse-point count 𝑀 (these are reported in the

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SI). We therefore record no HyperparameterSetting instances in the canonical encoding and flag them as Q12 gaps. # Q08 - hyperparameter - settings : no triples ( paper does not report this ) .

Q9 – MLIP run and trained model. A single sparse-GP training run produces one GAP for diamondcubic Si. We attach the per-atom inference time (inferenceTimePerAtom = 0.01 s/atom/timestep, single CPU core) to the trained model. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - gap -Si - bartok2010 a mlips : TrainedModel ; rdfs : label " GAP ␣ for ␣ bulk ␣ silicon ␣ ( diamond - cubic ) " . entity : run - gap -Si - bartok2010 a mlips : MLIPRun ; rdfs : label " GAP ␣ training ␣ run , ␣ bulk ␣ silicon " ; mlips : appliesMethod entity : GAP - bartok2010 ; mlips : produces entity : model - gap - Si - bartok2010 ; mlips : runsOn entity : ds - Si - bartok2010 .

Q10 – Benchmark results. The headline accuracy figure is an energy RMSE bound of < 1 meV/atom on near-bulk Si configurations, with the same bound holding for diamond and iron. We record the bound as the value (1 meV/atom) on the silicon BenchmarkResult. Phonon dispersions, elastic constants, and defect-formation energies are also reported but in derived form rather than as separate BenchmarkResult instances. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - rmse - energy - bartok2010 a mlips : AccuracyMetric ; rdfs : label " Energy ␣ RMSE ␣ on ␣ near - bulk ␣ Si ␣ configurations ␣ ( paper ␣ bound : ␣ <1 ␣ meV / atom ; ␣ the ␣ same ␣ bound ␣ holds ␣ for ␣ diamond ␣ and ␣ iron ) " , " RMSE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 1 ␣ [ millielectronvolt ␣ per ␣ atom ] " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - gap - Si - energy - bartok2010 ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 1 . entity : result - gap -Si - energy - bartok2010 a mlips : BenchmarkResult ; rdfs : label " GAP ␣ for ␣ bulk ␣ silicon ␣ ( diamond - cubic ) ␣ on ␣ Bulk ␣ silicon ␣ ( diamond - cubic ␣ phase , ␣ lead ␣ demonstration ␣ system ) ␣ in ␣ Bartok ␣ et ␣ al . ␣ (2010) : ␣ GAP ␣ for ␣ bulk ␣ crystals ␣ ( Si ␣ as ␣ lead ␣ system ) " ; mlips : evaluatesModel entity : model - gap - Si - bartok2010 ; mlips : hasAccuracyMetric entity : metric - rmse - energy - bartok2010 ; mlips : isResultOf entity : study - bartok2010 ; mlips : targetMaterial entity : mat - Si - bartok2010 . entity : study - bartok2010 mlips : hasResult entity : result - gap - Si - energy - bartok2010 .

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Q11 – Computational resources. The paper reports a per-atom inference cost of 0.01 s/atom/timestep on a single CPU core (encoded on the trained model in Q9). It also notes that the 216-atom unit-cell timestep takes 191 s/atom in CASTEP—about 20,000× slower than GAP. Training duration, training hardware, peak memory, and inference hardware are not reported. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - gap -Si - bartok2010 mlips : inferenceTimePerAtom 0.01 .

Q12 – Gaps. Beyond Q11, the main letter does not tabulate: (i) DFT-side parameters (exchange– correlation functional, plane-wave cutoff, k-mesh, pseudopotential type) which live in the SI; (ii) the explicit number of training configurations numConfigurations; (iii) explicit HyperparameterSetting values for 𝑟𝑐 , 𝐽max , 𝑀, GP kernel parameters, and per-channel noise; (iv) the GP hyperparameter optimiser; (v) any frozenCore treatment beyond the CASTEP pseudopotential. The companion systems (C, Ge, GaN, 𝛼-Fe) are not encoded here; each would live in a sibling file under the same BenchmarkStudy aegis. K.4

Shapeev (2016): Moment Tensor Potentials

Q1 – Bibliographic identification. Shapeev introduces the Moment Tensor Potential (MTP), a class of systematically improvable nonparametric interatomic potentials based on permutation-, rotation-, and reflection-invariant polynomials of moment tensors of the local atomic environment. The numerical experiments fit MTP to the publicly available tungsten DFT database of Szlachta– Bartók–Csányi (libatoms.org) and benchmark accuracy and CPU cost against GAP. Published in Multiscale Model. Simul. 14(3), 1153–1173 (2016); arXiv:1512.06054. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0002 -7497 -5594 > a schema : Person ; schema : affiliation entity : org - SkolkovoInstituteofScienceandTechnology - shapeev2016 ; schema : familyName " Shapeev " ; schema : givenName " Alexander ␣ V . " ; schema : identifier < https :// orcid . org /0000 -0002 -7497 -5594 > ; schema : name " Alexander ␣ V . ␣ Shapeev " . entity : article - shapeev2016 a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0002 -7497 -5594 > ; schema : datePublished " 2016 " ^^ xsd : gYear ; schema : name " Moment ␣ Tensor ␣ Potentials : ␣ a ␣ class ␣ of ␣ systematically ␣ improvable ␣ interatomic ␣ potentials " ; schema : sameAs < https :// doi . org /10.1137/15 M1054183 > . entity : org - SkolkovoInstituteofScienceandTechnology - shapeev2016 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Skolkovo ␣ Institute ␣ of ␣ Science ␣ and ␣ Technology " ; schema : identifier < https :// ror . org /03 f9nc143 > ; schema : name " Skolkovo ␣ Institute ␣ of ␣ Science ␣ and ␣ Technology " .

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entity : study - shapeev2016 a mlips : BenchmarkStudy ; rdfs : label " Shapeev ␣ (2016) : ␣ Moment ␣ Tensor ␣ Potentials , ␣ demonstrated ␣ on ␣ tungsten " ; mlips : reportedIn entity : article - shapeev2016 .

Q2 – Material system. The lead demonstration system is body-centred-cubic tungsten, inheriting the configuration set (bulk, surfaces, defects, and finite-temperature MD snapshots) from the published GAP-tungsten database. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat -W - shapeev2016 a mlips : MaterialSystem ; rdfs : label " Tungsten ␣ ( BCC , ␣ demonstration ␣ system ) " ; mlips : chemicalFormula " W " ; mlips : materialClass " Elemental ␣ BCC ␣ transition ␣ metal ; ␣ configurations ␣ in ␣ the ␣ Szlachta / Bartok / Csanyi ␣ tungsten ␣ database ␣ ( bulk , ␣ surfaces , ␣ defects , ␣ liquid ) " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q743 > .

Q3 – Reference calculation method. Reference data are produced from Kohn–Sham DFT calculations (inherited from the libatoms tungsten database). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - shapeev2016 a mlips : DFTCalculation .

Q4 – Reference settings. The DFT settings inherited from the libatoms tungsten database are CASTEP with the PBE/GGA exchange–correlation functional and norm-conserving pseudopotentials, with k-point meshes converged per-cell and finite-temperature electronic broadening at 1000 K. The plane-wave energy cutoff used for the database is not restated in this methodological paper, so we omit energyCutoff here and flag this in Q12. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - settings - shapeev2016 a mlips : DFTSettings ; rdfs : comment " CASTEP - default ␣ norm - conserving ␣ pseudopotentials . " ; mlips : kPointMesh " Brillouin - zone ␣ meshes ␣ converged ␣ per - cell ; ␣ finite - temperature ␣ electronic ␣ broadening ␣ at ␣ 1000 ␣ K " ; mlips : pseudopotentialType mlips : NormConserving ; mlips : usedDFTCode mlips : CASTEP ; mlips : xcFunctional mlips : PBE . entity : dft - shapeev2016

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Hernández et al. mlips : hasDFTSettings entity : dft - settings - shapeev2016 .

Q5 – Training dataset. The fit uses 9,693 configurations of tungsten (with nearly 150,000 individual atomic environments) from the libatoms tungsten database. Energies and forces are covered. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds -W - shapeev2016 a mlips : TrainingDataset ; rdfs : label " Tungsten ␣ DFT ␣ database ␣ from ␣ Szlachta - Bartok - Csanyi ␣ ( libatoms . org ) ; ␣ 9693 ␣ configurations , ␣ ~150000 ␣ atomic ␣ environments " ; mlips : coversMaterial entity : mat -W - shapeev2016 ; mlips : coversProperty mlips : Energy , mlips : Forces ; mlips : datasetProvenance mlips : Published ; mlips : hasDFTCalculation entity : dft - shapeev2016 ; mlips : numConfigurations 9693 ; mlips : wasRunBy entity : run - mtp -W - shapeev2016 .

Q6 – Sampling strategies. The libatoms tungsten database combines bulk and surface enumeration, point-defect and dislocation sampling, and DFT MD snapshots. We record three sampling instances reflecting those classes; the present paper does not author the database and hence does not contribute new sampling strategies. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : bulk - sampling - shapeev2016 a mlips : SamplingStrategy ; rdfs : comment " Crystalline ␣ bulk ␣ and ␣ surface ␣ configurations ␣ of ␣ tungsten ␣ from ␣ the ␣ Szlachta / Bartok / Csanyi ␣ GAP - tungsten ␣ database ␣ used ␣ for ␣ training . " ; rdfs : label " Bulk ␣ and ␣ surface ␣ enumeration ␣ ( inherited ␣ from ␣ libatoms ␣ tungsten ␣ database ) " . entity : defect - sampling - shapeev2016 a mlips : SamplingStrategy ; rdfs : comment " Vacancies , ␣ self - interstitials , ␣ and ␣ screw - dislocation ␣ core ␣ configurations ␣ from ␣ the ␣ libatoms ␣ tungsten ␣ database . " ; rdfs : label " Point - defect ␣ and ␣ dislocation ␣ sampling ␣ ( inherited ␣ from ␣ libatoms ␣ tungsten ␣ database )" . entity :ds -W - shapeev2016 mlips : samplingStrategy entity : bulk - sampling - shapeev2016 , entity : defect - sampling shapeev2016 , entity : md - sampling - shapeev2016 . entity :md - sampling - shapeev2016 a mlips : SamplingStrategy ; rdfs : comment " Finite - temperature ␣ DFT ␣ MD ␣ snapshots ␣ from ␣ the ␣ libatoms ␣ tungsten ␣ database . " ; rdfs : label " Vibrational ␣ sampling ␣ ( DFT ␣ MD ␣ snapshots , ␣ inherited ) " .

Q7 – MLIP method, components, implementation. The method is the original MTP: total energy as a sum of local contributions 𝑉 (𝐷𝑥𝑘 ), with 𝑉 expanded as a linear combination of moment-tensor basis functions 𝐵𝛼 (𝑢) that are permutation-, rotation-, and reflection-invariant polynomials of

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moment tensors 𝑀𝜇,𝜈 . The loss is a regularised least-squares loss on energies and forces, with ℓ2 or ℓ0 regularisation; the regularisation parameter 𝛾 is selected by 16-fold cross-validation. The implementation used for the GAP comparison is the QUIP MTP prototype. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : MTP - shapeev2016 . mlips : minInteratomicDistance mlips : isHyperparameterOf entity : MTP - shapeev2016 . mlips : momentLevel mlips : isHyperparameterOf entity : MTP - shapeev2016 . entity : MTP - shapeev2016 a mlips : MLIPMethod ; rdfs : label " Moment ␣ Tensor ␣ Potential ␣ ( MTP ) " ; mlips : hasDescriptor mlips : MomentTensorDescriptor ; mlips : hasFunctionalForm entity : mtp - functional - form - shapeev2016 ; mlips : hasHyperparameter mlips : cutoffRadius , mlips : minInteratomicDistance , mlips : momentLevel , entity : hp - reg - shapeev2016 ; mlips : hasImplementation entity : impl - mtp - shapeev2016 ; mlips : hasLossFunction entity : mtp - loss - shapeev2016 . entity :hp - reg - shapeev2016 a mlips : Hyperparameter ; rdfs : label " MTP ␣ regularisation ␣ parameter " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : double ; mlips : hyperparameterName " regularisation " ; mlips : isHyperparameterOf entity : MTP - shapeev2016 . entity : impl - mtp - shapeev2016 a mlips : Implementation ; mlips : implementedIn mlips : QUIP ; mlips : isImplementationOf entity : MTP - shapeev2016 . entity : mtp - functional - form - shapeev2016 a mlips : FunctionalForm ; rdfs : label " Linear ␣ combination ␣ of ␣ moment - tensor ␣ basis ␣ functions ␣ B_alpha ( u ) : ␣ permutation - , ␣ rotation - , ␣ reflection - invariant ␣ polynomials ␣ of ␣ moment ␣ tensors ␣ M_ { mu , nu }" . entity : mtp - loss - shapeev2016 a mlips : LossFunction ; rdfs : label " Regularised ␣ least ␣ squares ␣ on ␣ energies ␣ and ␣ forces ␣ ( l_2 ␣ or ␣ l_0 ␣ regularisation ; ␣ gamma ␣ chosen ␣ by ␣ 16 - fold ␣ cross - validation ) " .

Q8 – Hyperparameter settings. Reported hyperparameter settings: cutoff radius 𝑅cut = 4.9 Å, minimal distance 𝑅min = 1.9 Å, and two MTP variants—MTP1 (deg(𝐵𝛼 ) + 8(#𝛼) ≤ 62, #𝛼 ≤ 4, 𝜇 ≤ 5, 𝜈 ≤ 4, 11,133 basis functions) and MTP2 (deg(𝐵𝛼 ) + 8(#𝛼) ≤ 52, #𝛼 ≤ 5, 𝜇 ≤ 3, 𝜈 ≤ 5; 760 basis functions extracted via the ℓ0 algorithm with 𝑁 cap = 4). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - mtp1 - shapeev2016 a mlips : HyperparameterSetting ; rdfs : label " MTP ␣ moment ␣ level ␣ = ␣ MTP_1 : ␣ deg ( B_alpha ) +8(# alpha ) ␣ <= ␣ 62 , ␣ # alpha ␣ <= ␣ 4 , ␣ mu ␣ <= ␣5,␣ nu ␣ <=␣ 4 ␣ (11133 ␣ basis ␣ functions ) ␣ for ␣ MTP ␣ training ␣ run , ␣ tungsten ␣ ( production ␣ MTP_1 )" ;

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Hernández et al. mlips : forHyperparameter mlips : momentLevel ; mlips : isSettingOf entity : run - mtp -W - shapeev2016 ; mlips : settingValue " MTP_1 : ␣ deg ( B_alpha ) +8(# alpha ) ␣ <= ␣ 62 , ␣ # alpha ␣ <= ␣ 4 , ␣ mu ␣ <= ␣ 5 , ␣ nu ␣ <= ␣ 4 ␣ (11133 ␣ basis ␣ functions ) " . entity : setting - mtp2 - shapeev2016 a mlips : HyperparameterSetting ; rdfs : label " MTP ␣ moment ␣ level ␣ = ␣ MTP_2 : ␣ deg ( B_alpha ) +8(# alpha ) ␣ <= ␣ 52 , ␣ # alpha ␣ <= ␣ 5 , ␣ mu ␣ <= ␣3,␣ nu ␣ <=␣ 5; ␣ 760 ␣ basis ␣ functions ␣ extracted ␣ via ␣ l_0 ␣ regularisation ␣ ( N_cap =4) ␣ for ␣ MTP ␣ training ␣ run , ␣ tungsten ␣ ( production ␣ MTP_1 ) " ; mlips : forHyperparameter mlips : momentLevel ; mlips : isSettingOf entity : run - mtp -W - shapeev2016 ; mlips : settingValue " MTP_2 : ␣ deg ( B_alpha ) +8(# alpha ) ␣ <= ␣ 52 , ␣ # alpha ␣ <= ␣ 5 , ␣ mu ␣ <= ␣ 3 , ␣ nu ␣ <= ␣ 5; ␣ 760 ␣ basis ␣ functions ␣ extracted ␣ via ␣ l_0 ␣ regularisation ␣ ( N_cap =4) " . entity : setting - rcut - shapeev2016 a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 4.9 ␣ for ␣ MTP ␣ training ␣ run , ␣ tungsten ␣ ( production ␣ MTP_1 ) " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - mtp -W - shapeev2016 ; mlips : settingValue 4.9 . entity : setting - rmin - shapeev2016 a mlips : HyperparameterSetting ; rdfs : label " minimum ␣ interatomic ␣ distance ␣ = ␣ 1.9 ␣ for ␣ MTP ␣ training ␣ run , ␣ tungsten ␣ ( production ␣ MTP_1 ) " ; mlips : forHyperparameter mlips : minInteratomicDistance ; mlips : isSettingOf entity : run - mtp -W - shapeev2016 ; mlips : settingValue 1.9 .

Q9 – MLIP run and trained model. A single training run produces the production tungsten MTP, with two basis-set variants (MTP1 and MTP2 ) recorded as hyperparameter settings on the same run rather than as separate runs/models. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - mtp -W - shapeev2016 a mlips : TrainedModel ; rdfs : label " Tungsten ␣ MTP ␣ ( lead ␣ model ␣ MTP_1 ; ␣ rcut =4.9 ␣A , ␣ rmin =1.9 ␣ A ) " . entity : run - mtp -W - shapeev2016 a mlips : MLIPRun ; rdfs : label " MTP ␣ training ␣ run , ␣ tungsten ␣ ( production ␣ MTP_1 ) " ; mlips : appliesMethod entity : MTP - shapeev2016 ; mlips : hasHyperparameterSetting entity : setting - mtp1 - shapeev2016 , entity : setting - mtp2 shapeev2016 , entity : setting - rcut - shapeev2016 , entity : setting - rmin - shapeev2016 ; mlips : produces entity : model - mtp -W - shapeev2016 ; mlips : runsOn entity : ds -W - shapeev2016 .

Q10 – Benchmark results. Headline accuracy: MTP1 attains a force RMSE of 0.0427 eV/Å on the full training set (relative RMS 2.8%) and 0.0511 eV/Å under 16-fold cross-validation (relative RMS 3.4%) versus DFT-PBE; on the same database GAP attains 0.0633 eV/Å (4.2%). MTP2 matches GAP’s accuracy with ∼ 13× fewer parameters. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - rmse - forces - cv - shapeev2016

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a mlips : AccuracyMetric ; rdfs : label " Force ␣ RMSE ␣ of ␣ MTP_1 ␣ from ␣ 16 - fold ␣ cross - validation ␣ ( vs . ␣ DFT - PBE ; ␣ 3.4% ␣ relative )" , " RMSE ␣ of ␣ Force ␣ = ␣ 0.0511 ␣ [ EV - PER - ANGSTROM ] " ; mlips : hasUnit unit : EV - PER - ANGSTROM ; mlips : isMetricOf entity : result - mtp -W - cv - shapeev2016 ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 0.0511 . entity : metric - rmse - forces - fit - shapeev2016 a mlips : AccuracyMetric ; rdfs : label " Force ␣ RMSE ␣ of ␣ MTP_1 ␣ on ␣ the ␣ full ␣ training ␣ set ␣ ( vs . ␣ DFT - PBE ; ␣ 2.8% ␣ relative ) " , " RMSE ␣ of ␣ Force ␣ = ␣ 0.0427 ␣ [ EV - PER - ANGSTROM ] " ; mlips : hasUnit unit : EV - PER - ANGSTROM ; mlips : isMetricOf entity : result - mtp -W - fit - shapeev2016 ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 0.0427 . entity : result - mtp -W - cv - shapeev2016 a mlips : BenchmarkResult ; rdfs : label " Tungsten ␣ MTP ␣ ( lead ␣ model ␣ MTP_1 ; ␣ rcut =4.9 ␣A , ␣ rmin =1.9 ␣ A ) ␣ on ␣ Tungsten ␣ ( BCC , ␣ demonstration ␣ system ) ␣ in ␣ Shapeev ␣ (2016) : ␣ Moment ␣ Tensor ␣ Potentials , ␣ demonstrated ␣ on ␣ tungsten " ; mlips : evaluatesModel entity : model - mtp -W - shapeev2016 ; mlips : hasAccuracyMetric entity : metric - rmse - forces - cv - shapeev2016 ; mlips : isResultOf entity : study - shapeev2016 ; mlips : targetMaterial entity : mat -W - shapeev2016 . entity : result - mtp -W - fit - shapeev2016 a mlips : BenchmarkResult ; rdfs : label " Tungsten ␣ MTP ␣ ( lead ␣ model ␣ MTP_1 ; ␣ rcut =4.9 ␣A , ␣ rmin =1.9 ␣ A ) ␣ on ␣ Tungsten ␣ ( BCC , ␣ demonstration ␣ system ) ␣ in ␣ Shapeev ␣ (2016) : ␣ Moment ␣ Tensor ␣ Potentials , ␣ demonstrated ␣ on ␣ tungsten " ; mlips : evaluatesModel entity : model - mtp -W - shapeev2016 ; mlips : hasAccuracyMetric entity : metric - rmse - forces - fit - shapeev2016 ; mlips : isResultOf entity : study - shapeev2016 ; mlips : targetMaterial entity : mat -W - shapeev2016 . entity : study - shapeev2016 mlips : hasResult entity : result - mtp -W - cv - shapeev2016 , entity : result - mtp -W - fit shapeev2016 .

Q11 – Computational resources. Per-atom inference time is reported in Table 1: 2.9 ms/atom for MTP1 , 0.8 ms/atom for MTP2 , and 134.2 ms/atom for the GAP baseline, on a single core of an Intel i7-2675QM laptop CPU. We encode MTP1 ’s 2.9 ms/atom as the headline inferenceTimePerAtom figure with a free-text inferenceHardware. Training duration, total CPU hours, and peak memory are not reported. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - mtp -W - shapeev2016 mlips : inferenceHardware " Single - core ␣ Intel ␣ i7 -2675 QM ␣ laptop ␣ CPU ␣ ( ms ␣ per ␣ atom ) " ; mlips : inferenceTimePerAtom 2.9 .

Q12 – Gaps. Beyond the partial Q11 reporting (training-cost metadata absent; only per-atom inference time is given), the following ontology-expressible items are not reported in this paper itself: the DFT plane-wave energyCutoff used for the inherited tungsten database; explicit frozenCore treatment beyond the pseudopotential partition; software versioning of the QUIP MTP prototype; an explicit named individual for the cross-validation training algorithm. The protocol assumes one method × one material per file; the present paper is methodological, so the

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tungsten benchmark is encoded as the lead system and the absence of additional materials is itself a deliberate simplification. K.5

Smith, Isayev, Roitberg (2017): ANI-1 transferable NNP for organics

Q1 – Bibliographic identification. Smith, Isayev, and Roitberg introduce the ANI (ANAKIN-ME) class of high-dimensional neural-network potentials, in which atom-type-specific feed-forward NNs take a modified Behler–Parrinello atomic environment vector (AEV) as input. The flagship ANI-1 potential is a single transferable model covering organic molecules made of H, C, N, and O. Published in Chem. Sci. 8, 3192–3203 (2017). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -7314 -7896 > a schema : Person ; schema : affiliation mlips : UniversityofFlorida ; schema : familyName " Smith " ; schema : givenName " J . ␣ S . " ; schema : identifier < https :// orcid . org /0000 -0001 -7314 -7896 > ; schema : name "J. ␣ S . ␣ Smith " . < https :// orcid . org /0000 -0001 -7581 -8497 > a schema : Person ; schema : affiliation entity : org - CommunitiesInSchoolsofOrangeCounty - smith2017 , entity : org - InstituteofMedicinalPlantDevelopment - smith2017 , entity : org UniversityofNorthCarolinaatChapelHill - smith2017 ; schema : familyName " Isayev " ; schema : givenName " O . " ; schema : identifier < https :// orcid . org /0000 -0001 -7581 -8497 > ; schema : name "O. ␣ Isayev " . < https :// orcid . org /0000 -0003 -3963 -8784 > a schema : Person ; schema : affiliation mlips : UniversityofFlorida ; schema : familyName " Roitberg " ; schema : givenName " A . ␣ E . " ; schema : identifier < https :// orcid . org /0000 -0003 -3963 -8784 > ; schema : name "A. ␣ E . ␣ Roitberg " . entity : article - smith2017 a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0001 -7314 -7896 > , < https :// orcid . org /0000 -0001 -7581 -8497 > , < https :// orcid . org /0000 -0003 -3963 -8784 > ; schema : datePublished " 2017 " ^^ xsd : gYear ; schema : name " ANI -1: ␣ an ␣ extensible ␣ neural ␣ network ␣ potential ␣ with ␣ DFT ␣ accuracy ␣ at ␣ force ␣ field ␣ computational ␣ cost " ; schema : sameAs < https :// doi . org /10.1039/ C6SC05720A > . entity : org - CommunitiesInSchoolsofOrangeCounty - smith2017 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Communities ␣ In ␣ Schools ␣ of ␣ Orange ␣ County " ; schema : identifier < https :// ror . org /00 bzst557 > ; schema : name " Communities ␣ In ␣ Schools ␣ of ␣ Orange ␣ County " . entity : org - InstituteofMedicinalPlantDevelopment - smith2017 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Institute ␣ of ␣ Medicinal ␣ Plant ␣ Development " ; schema : identifier < https :// ror . org /052 nj8f19 > ; schema : name " Institute ␣ of ␣ Medicinal ␣ Plant ␣ Development " . entity : org - UniversityofNorthCarolinaatChapelHill - smith2017 a schema : Organization ;

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rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " University ␣ of ␣ North ␣ Carolina ␣ at ␣ Chapel ␣ Hill " ; schema : identifier < https :// ror . org /0130 frc33 > ; schema : name " University ␣ of ␣ North ␣ Carolina ␣ at ␣ Chapel ␣ Hill " . entity : study - smith2017 a mlips : BenchmarkStudy ; rdfs : label " Smith , ␣ Isayev , ␣ Roitberg ␣ (2017) : ␣ ANI -1 ␣ transferable ␣ NNP ␣ for ␣ H / C / N / O ␣ organics " ; mlips : reportedIn entity : article - smith2017 .

Q2 – Material system. The chemical scope is closed-shell, neutral, singlet organic molecules over the four-element space {H, C, N, O}, with training molecules drawn from the GDB-11 enumeration of up to 8 heavy atoms. The benchmark molecules range from 10 to 54 atoms, including pharmaceutical compounds (Retinol, Fentanyl, Lisdexamfetamine). The protocol’s “one MaterialSystem per paper” assumption is a tight fit here: we encode this as a single molecular material with the chemical scope captured in materialClass rather than enumerating every benchmark molecule. No Wikidata entity is used, since the system is a chemical space rather than a single substance. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat - organic - smith2017 a mlips : MaterialSystem ; rdfs : comment " Wikidata ␣ Q174211 ␣ ( ' organic ␣ compound ') ␣ is ␣ the ␣ most ␣ generic ␣ appropriate ␣ entry ;␣ the ␣ H / C / N / O ␣ chemical - space ␣ slice ␣ from ␣ GDB -11 ␣ has ␣ no ␣ dedicated ␣ Wikidata ␣ entry ␣ as ␣ of ␣ 2026 -04 -28. " ; rdfs : label " Organic ␣ molecules ␣ (H , ␣C , ␣N , ␣ O ) " ; mlips : chemicalFormula "H ,C ,N , O ␣ molecular ␣ space " ; mlips : materialClass " Molecular : ␣ neutral ␣ closed - shell ␣ organic ␣ molecules ␣ in ␣ the ␣ singlet ␣ spin ␣ state , ␣ configurations ␣ drawn ␣ from ␣ GDB -11 ␣ ( up ␣ to ␣ 8 ␣ heavy ␣ atoms ␣ in ␣ training ; ␣ benchmarked ␣ on ␣ molecules ␣ with ␣ up ␣ to ␣ 54 ␣ atoms ) " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q174211 > .

Q3 – Reference calculation method. Reference data are produced from molecular DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - smith2017 a mlips : DFTCalculation .

Q4 – Reference settings. DFT calculations are performed with Gaussian 09 using the 𝜔B97X range-separated hybrid meta-GGA functional and the 6-31G(d) Pople basis set on an ultra-fine integration grid. There is no Brillouin-zone sampling (molecular calculations); all-electron Gaussian-basis methodology obviates the explicit plane-wave energyCutoff slot. Frozen-core treatment is not explicitly reported. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > .

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Hernández et al. @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : basis -6 -31 g -d - smith2017 a mlips : DftBasisSet ; rdfs : comment " Pople - style ␣ split - valence ␣ double - zeta ␣ Gaussian ␣ basis ␣ with ␣ d ␣ polarisation ␣ on ␣ heavy ␣ atoms ; ␣ molecular ␣ all - electron ␣ DFT . " ; rdfs : label " 6 -31 G ( d ) " ; mlips : candidateForVocabulary mlips : DftBasisSet . entity : dft - settings - smith2017 a mlips : DFTSettings ; rdfs : comment " Range - separated ␣ hybrid ␣ meta - GGA . ␣ All - electron ␣ Gaussian - type ␣ basis ␣ ( no ␣ pseudopotential ) . " ; mlips : dftBasisSet entity : basis -6 -31 g -d - smith2017 ; mlips : kPointMesh " Molecular ␣ calculations ␣ ( no ␣ Brillouin - zone ␣ sampling ) ; ␣ ultra - fine ␣ DFT ␣ integration ␣ grid " ; mlips : usedDFTCode mlips : Gaussian ; mlips : xcFunctional mlips : omegaB97X . entity : dft - smith2017 mlips : hasDFTSettings entity : dft - settings - smith2017 .

Q5 – Training dataset. The ANI-1 dataset comprises about 17.2 million molecular conformations generated from ∼ 57 951 small molecules (GDB-11, up to 8 heavy atoms, fluorine removed). 80% of the data points are used for training, 10% for validation, and 10% for the held-out test set. Energies (single-point) are the sole covered property; atomic forces are not part of the training labels. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - ANI1 - smith2017 a mlips : TrainingDataset ; rdfs : label " ANI -1 ␣ dataset : ␣ ~17.2 ␣ M ␣ conformations ␣ of ␣ ~57951 ␣ small ␣ molecules ␣ from ␣ GDB -11 ␣( up ␣ to ␣8␣ heavy ␣ atoms ; ␣ 80% ␣ used ␣ for ␣ training ) " ; mlips : coversMaterial entity : mat - organic - smith2017 ; mlips : coversProperty mlips : Energy ; mlips : datasetProvenance mlips : InHouse ; mlips : hasDFTCalculation entity : dft - smith2017 ; mlips : numConfigurations 17200000 ; mlips : wasRunBy entity : run - ANI1 - smith2017 .

Q6 – Sampling strategies. Two strategies are combined: configurational sampling from the GDB-11 chemical database (SMILES converted to 3D structures with RDKit, then DFT-optimised), and conformational Normal Mode Sampling (NMS), in which the equilibrium structure is displaced along normal-mode coordinates with random magnitudes drawn from a harmonic-temperature distribution; 𝐾 = 𝑆 (3𝑁 − 6) structures are generated per molecule, with 𝑆 tuned per GDB subset. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - ANI1 - smith2017

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mlips : samplingStrategy entity : gdb - sampling - smith2017 , entity : nms - sampling - smith2017 . entity : gdb - sampling - smith2017 a mlips : SamplingStrategy ; rdfs : comment " All ␣ molecules ␣ with ␣ up ␣ to ␣ 8 ␣ heavy ␣ atoms ␣ (C , ␣N , ␣ O ; ␣ F ␣ removed ) ␣ from ␣ GDB -11; ␣ SMILES ␣ converted ␣ to ␣ 3 D ␣ structures ␣ using ␣ RDKit , ␣ then ␣ DFT - optimised . " ; rdfs : label " Configurational ␣ sampling ␣ from ␣ the ␣ GDB -11 ␣ chemical ␣ database " . entity : nms - sampling - smith2017 a mlips : SamplingStrategy ; rdfs : comment " Per - molecule ␣ conformational ␣ sampling : ␣ equilibrium ␣ structure ␣ displaced ␣ along ␣ normal - mode ␣ coordinates ␣ with ␣ random ␣ magnitudes ␣ drawn ␣ from ␣ a ␣ harmonic temperature ␣ distribution ; ␣ K ␣ = ␣ S (3 N -6) ␣ structures ␣ per ␣ molecule , ␣ with ␣ S ␣ an ␣ empirical ␣ constant ␣ tuned ␣ per ␣ GDB ␣ subset . " ; rdfs : label " Normal ␣ Mode ␣ Sampling ␣ ( NMS ) " .

Q7 – MLIP method, components, implementation. The method is ANI: an HDNNP with atomtype-specific subnets taking modified Behler–Parrinello AEVs as input (radial shifted-Gaussian channels, angular shifted-cosine channels with an additional radial-shell factor; channels split
per Í DFT ) 2 with atom-type pair). The training loss is the exponential cost 𝐶 = 𝜏 exp 𝜏 −1 𝑗 (𝐸 ANI − 𝐸 𝑗 𝑗 𝜏 = 0.5. The training algorithm is ADAM with mini-batches of 1024 molecules and max-norm regularisation. The implementation is the in-house GPU-accelerated NeuroChem package (with the AEVLib library for descriptor computation). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : angularCutoff mlips : isHyperparameterOf entity : ANI - smith2017 . mlips : cutoffRadius mlips : isHyperparameterOf entity : ANI - smith2017 . mlips : learningRate mlips : isHyperparameterOf entity : ANI - smith2017 . entity : ANI - smith2017 a mlips : MLIPMethod ; rdfs : label " ANI ␣ ( ANAKIN - ME ) : ␣ atom - type - specific ␣ HDNNP ␣ using ␣ modified ␣ Behler - Parrinello ␣ atomic ␣ environment ␣ vectors ␣ ( AEVs ) " ; mlips : hasDescriptor mlips : ANIDescriptor ; mlips : hasFunctionalForm entity : ani - functional - form - smith2017 ; mlips : hasHyperparameter mlips : angularCutoff , mlips : cutoffRadius , mlips : learningRate , entity :hp - aev - smith2017 , entity : hp - arch - smith2017 ; mlips : hasImplementation entity : impl - neurochem - smith2017 ; mlips : hasLossFunction entity : ani - loss - smith2017 ; mlips : hasTrainingAlgorithm entity : adam - smith2017 . entity : adam - smith2017 a mls : Algorithm ; rdfs : label " ADAM ␣ ( lr =1 e -3 , ␣ beta1 =0.9 , ␣ beta2 =0.999 , ␣ eps =1 e -8) ␣ with ␣ max - norm ␣ regularisation ␣ (3.0) ; ␣ 6 ␣ lr - decay ␣ restarts " . entity : ani - functional - form - smith2017 a mlips : FunctionalForm ; rdfs : label " Total ␣ energy ␣ = ␣ sum ␣ over ␣ atoms ␣ of ␣ element - specific ␣ feed - forward ␣ NN ␣ outputs ␣ taking ␣ modified ␣ BP ␣ atomic ␣ environment ␣ vectors ␣ as ␣ input ␣ ( radial : ␣ shifted ␣ Gaussians ; ␣ angular :␣ shifted - cosine ␣ + ␣ radial - shell ␣ factor ; ␣ atom - type - differentiated ␣ channels ) " . entity : ani - loss - smith2017 a mlips : LossFunction ; rdfs : label " Exponential ␣ cost ␣ C ␣ = ␣ tau ␣ * ␣ exp ((1/ tau ) ␣ * ␣ sum_j ␣ ( E ^ ANI_j ␣ -␣ E ^ DFT_j ) ^2) ,␣ tau ␣=␣ 0.5 ␣( robust ␣ to ␣ outliers ) " . entity :hp - aev - smith2017 a mlips : Hyperparameter ; rdfs : label " ANI ␣ atomic ␣ environment ␣ vector ␣ size " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : string ;

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Hernández et al. mlips : hyperparameterName " aev_size " ; mlips : isHyperparameterOf entity : ANI - smith2017 . entity :hp - arch - smith2017 a mlips : Hyperparameter ; rdfs : label " ANI ␣ per - element ␣ NN ␣ architecture " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : string ; mlips : hyperparameterName " ani_architecture " ; mlips : isHyperparameterOf entity : ANI - smith2017 . entity : impl - neurochem - smith2017 a mlips : Implementation ; mlips : implementedIn mlips : NeuroChem ; mlips : isImplementationOf entity : ANI - smith2017 .

Q8 – Hyperparameter settings. Reported hyperparameter settings: radial cutoff 𝑅𝐶rad = 4.6 Å, ang angular cutoff 𝑅𝐶 = 3.1 Å, AEV with 32 radial shifts and 8 × 8 angular shifts per element pair (768 total elements for 4 atom types), per-element pyramidal NN of architecture 768:128:128:64:1 (∼ 124 033 parameters per element) with Gaussian hidden activations and a linear output; ADAM with initial learning rate 10−3 . @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - aev - smith2017 a mlips : HyperparameterSetting ; rdfs : label " ANI ␣ atomic ␣ environment ␣ vector ␣ size ␣ = ␣ 32 ␣ radial ␣ shifts , ␣ 8 ␣ radial ␣ + ␣ 8 ␣ angular ␣ shifts ␣ ->␣ 768 ␣ AEV ␣ elements ␣ for ␣ 4 ␣ atom ␣ types ␣ for ␣ ANI -1 ␣ training ␣ run ␣ on ␣ the ␣ ANI -1 ␣ dataset " ; mlips : forHyperparameter entity : hp - aev - smith2017 ; mlips : isSettingOf entity : run - ANI1 - smith2017 ; mlips : settingValue " 32 ␣ radial ␣ shifts , ␣ 8 ␣ radial ␣ + ␣ 8 ␣ angular ␣ shifts ␣ ->␣ 768 ␣ AEV ␣ elements ␣ for ␣4␣ atom ␣ types " . entity : setting - arch - smith2017 a mlips : HyperparameterSetting ; rdfs : label " ANI ␣ per - element ␣ NN ␣ architecture ␣ = ␣ Per - atom - type ␣ pyramidal ␣ NN ␣ 768:128:128:64:1 ␣ ( Gaussian ␣ activations , ␣ linear ␣ output ) ; ␣ 124033 ␣ parameters ␣ per ␣ element ␣ for ␣ ANI -1 ␣ training ␣ run ␣ on ␣ the ␣ ANI -1 ␣ dataset " ; mlips : forHyperparameter entity : hp - arch - smith2017 ; mlips : isSettingOf entity : run - ANI1 - smith2017 ; mlips : settingValue " Per - atom - type ␣ pyramidal ␣ NN ␣ 768:128:128:64:1 ␣ ( Gaussian ␣ activations , ␣ linear ␣ output ) ; ␣ 124033 ␣ parameters ␣ per ␣ element " . entity : setting -lr - smith2017 a mlips : HyperparameterSetting ; rdfs : label " learning ␣ rate ␣ = ␣ Initial ␣ learning ␣ rate ␣ 1e -3 ␣ ( mini - batch ␣ size ␣ 1024 ␣ molecules ;␣ 100 - epoch ␣ validation ␣ patience ) ␣ for ␣ ANI -1 ␣ training ␣ run ␣ on ␣ the ␣ ANI -1 ␣ dataset " ; mlips : forHyperparameter mlips : learningRate ; mlips : isSettingOf entity : run - ANI1 - smith2017 ; mlips : settingValue " Initial ␣ learning ␣ rate ␣ 1e -3 ␣ ( mini - batch ␣ size ␣ 1024 ␣ molecules ; ␣ 100 epoch ␣ validation ␣ patience ) " . entity : setting - rcut - ang - smith2017 a mlips : HyperparameterSetting ; rdfs : label " angular ␣ cutoff ␣ = ␣ 3.1 ␣ for ␣ ANI -1 ␣ training ␣ run ␣ on ␣ the ␣ ANI -1 ␣ dataset " ; mlips : forHyperparameter mlips : angularCutoff ; mlips : isSettingOf entity : run - ANI1 - smith2017 ; mlips : settingValue 3.1 . entity : setting - rcut - rad - smith2017 a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 4.6 ␣ for ␣ ANI -1 ␣ training ␣ run ␣ on ␣ the ␣ ANI -1 ␣ dataset " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - ANI1 - smith2017 ; mlips : settingValue 4.6 .

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Q9 – MLIP run and trained model. A single training run produces ANI-1, the flagship potential of the paper. The optimisation iterates 6 lr-decay restarts on top of ADAM. No active-learning, ensembling, or per-element fold-ensemble structure is reported. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - ANI1 - smith2017 a mlips : TrainedModel ; rdfs : label " ANI -1 ␣ potential ␣ ( H / C / N / O ) " . entity : run - ANI1 - smith2017 a mlips : MLIPRun ; rdfs : label " ANI -1 ␣ training ␣ run ␣ on ␣ the ␣ ANI -1 ␣ dataset " ; mlips : appliesMethod entity : ANI - smith2017 ; mlips : hasHyperparameterSetting entity : setting - aev - smith2017 , entity : setting - arch smith2017 , entity : setting - lr - smith2017 , entity : setting - rcut - ang - smith2017 , entity : setting - rcut - rad - smith2017 ; mlips : produces entity : model - ANI1 - smith2017 ; mlips : runsOn entity : ds - ANI1 - smith2017 .

Q10 – Benchmark results. Headline accuracy: total-energy RMSEs (vs. 𝜔B97X/6-31G(d)) of 1.2/1.3/1.3 kcal/mol on the training/validation/held-out test splits, and 1.9 kcal/mol on the GDB-10 transferability test (134 molecules with 10 heavy atoms, outside the training distribution; the per-conformation correlation plot reports 1.8 kcal/mol on 8245 conformations). For relative energies within 30 kcal/mol of the minimum, ANI-1 reaches 0.6 kcal/mol RMSE; semi-empirical baselines DFTB/PM6/AM1 are at 2.4/3.6/4.2. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - rmse - gdb10 - smith2017 a mlips : AccuracyMetric ; rdfs : label " RMSE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 1.9 ␣ [ KiloCAL - PER - MOL ] " , " Total - energy ␣ RMSE ␣ on ␣ the ␣ GDB -10 ␣ transferability ␣ test ␣ (134 ␣ molecules ␣ of ␣ 10 ␣ heavy ␣ atoms ; ␣ molecules ␣ outside ␣ the ␣ training ␣ distribution ) " ; mlips : hasUnit unit : KiloCAL - PER - MOL ; mlips : isMetricOf entity : result - ANI1 - gdb10 - smith2017 ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 1.9 . entity : metric - rmse - test - smith2017 a mlips : AccuracyMetric ; rdfs : label " RMSE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 1.3 ␣ [ KiloCAL - PER - MOL ] " , " Total - energy ␣ RMSE ␣ on ␣ the ␣ ANI -1 ␣ held - out ␣ test ␣ set ␣ ( vs . ␣ wB97X /6 -31 G ( d ) ) " ; mlips : hasUnit unit : KiloCAL - PER - MOL ; mlips : isMetricOf entity : result - ANI1 - test - smith2017 ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 1.3 . entity : metric - rmse - train - smith2017 a mlips : AccuracyMetric ; rdfs : label " RMSE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 1.2 ␣ [ KiloCAL - PER - MOL ] " , " Total - energy ␣ RMSE ␣ on ␣ the ␣ ANI -1 ␣ training ␣ set ␣ ( vs . ␣ wB97X /6 -31 G ( d ) ) " ; mlips : hasUnit unit : KiloCAL - PER - MOL ; mlips : isMetricOf entity : result - ANI1 - train - smith2017 ;

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Hernández et al. mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 1.2 . entity : result - ANI1 - gdb10 - smith2017 a mlips : BenchmarkResult ; rdfs : label " ANI -1 ␣ potential ␣ ( H / C / N / O ) ␣ on ␣ Organic ␣ molecules ␣ (H , ␣C , ␣N , ␣ O ) ␣ in ␣ Smith , ␣ Isayev ,␣ Roitberg ␣ (2017) : ␣ ANI -1 ␣ transferable ␣ NNP ␣ for ␣ H / C / N / O ␣ organics " ; mlips : evaluatesModel entity : model - ANI1 - smith2017 ; mlips : hasAccuracyMetric entity : metric - rmse - gdb10 - smith2017 ; mlips : isResultOf entity : study - smith2017 ; mlips : targetMaterial entity : mat - organic - smith2017 . entity : result - ANI1 - test - smith2017 a mlips : BenchmarkResult ; rdfs : label " ANI -1 ␣ potential ␣ ( H / C / N / O ) ␣ on ␣ Organic ␣ molecules ␣ (H , ␣C , ␣N , ␣ O ) ␣ in ␣ Smith , ␣ Isayev ,␣ Roitberg ␣ (2017) : ␣ ANI -1 ␣ transferable ␣ NNP ␣ for ␣ H / C / N / O ␣ organics " ; mlips : evaluatesModel entity : model - ANI1 - smith2017 ; mlips : hasAccuracyMetric entity : metric - rmse - test - smith2017 ; mlips : isResultOf entity : study - smith2017 ; mlips : targetMaterial entity : mat - organic - smith2017 . entity : result - ANI1 - train - smith2017 a mlips : BenchmarkResult ; rdfs : label " ANI -1 ␣ potential ␣ ( H / C / N / O ) ␣ on ␣ Organic ␣ molecules ␣ (H , ␣C , ␣N , ␣ O ) ␣ in ␣ Smith , ␣ Isayev ,␣ Roitberg ␣ (2017) : ␣ ANI -1 ␣ transferable ␣ NNP ␣ for ␣ H / C / N / O ␣ organics " ; mlips : evaluatesModel entity : model - ANI1 - smith2017 ; mlips : hasAccuracyMetric entity : metric - rmse - train - smith2017 ; mlips : isResultOf entity : study - smith2017 ; mlips : targetMaterial entity : mat - organic - smith2017 . entity : study - smith2017 mlips : hasResult entity : result - ANI1 - gdb10 - smith2017 , entity : result - ANI1 - test - smith2017 , entity : result - ANI1 - train - smith2017 .

Q11 – Computational resources. Not reported quantitatively. The paper states qualitatively that NeuroChem accelerates training, testing, and inference on GPUs via CUBLAS, but it gives no GPU hours, training duration, hardware spec (model number), peak memory, or per-atom inference time. # Q11 - resources : no triples ( paper does not report this ) .

Q12 – Gaps. Beyond Q11 (no quantitative compute metadata), the following ontology-expressible items are not reported: an explicit frozenCore treatment for the all-electron 6-31G(d) reference; the NeuroChem package version; explicit recording of forces among coversProperty (the paper trains on energies only, so this is a true absence rather than an omission); per-element data-set sizes within the 17.2 M total. The “one material per paper” assumption is also stretched here: ANI-1 covers a chemical space, not a single material, so sameAsWikidata is omitted intentionally. K.6

Schütt et al. (2018): SchNet on MD17 small organic molecules

Q1 – Bibliographic identification. Schütt, Sauceda, Kindermans, Tkatchenko, and Müller introduce SchNet, a continuous-filter convolutional deep neural network for molecules and materials. Published in J. Chem. Phys. 148, 241722 (2018); arXiv:1712.06113. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -6091 -3408 > a schema : Person ; schema : affiliation entity : org - FritzHaberInstituteoftheMaxPlanckSociety - schutt2018 ; schema : familyName " Sauceda " ;

An Ontology for Machine Learning Interatomic Potentials schema : givenName " H . ␣ E . " ; schema : identifier < https :// orcid . org /0000 -0001 -6091 -3408 > ; schema : name "H. ␣ E . ␣ Sauceda " . < https :// orcid . org /0000 -0001 -8342 -0964 > a schema : Person ; schema : affiliation mlips : TechnischeUniversitatBerlin ; schema : familyName " Sch ü tt " ; schema : givenName " K . ␣ T . " ; schema : identifier < https :// orcid . org /0000 -0001 -8342 -0964 > ; schema : name "K. ␣ T . ␣ Sch ü tt " . < https :// orcid . org /0000 -0002 -1012 -4854 > a schema : Person ; schema : affiliation entity : org - UniversityofLuxembourg - schutt2018 ; schema : familyName " Tkatchenko " ; schema : givenName " A . " ; schema : identifier < https :// orcid . org /0000 -0002 -1012 -4854 > ; schema : name "A. ␣ Tkatchenko " . entity : article - schutt2018 a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0001 -6091 -3408 > , < https :// orcid . org /0000 -0001 -8342 -0964 > , < https :// orcid . org /0000 -0002 -1012 -4854 > , entity : person Kindermans - schutt2018 , entity : person - Muller - schutt2018 ; schema : datePublished " 2018 " ^^ xsd : gYear ; schema : name " SchNet ␣ --␣ a ␣ deep ␣ learning ␣ architecture ␣ for ␣ molecules ␣ and ␣ materials " ; schema : sameAs < https :// doi . org /10.1063/1.5019779 > . entity : org - FritzHaberInstituteoftheMaxPlanckSociety - schutt2018 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Fritz ␣ Haber ␣ Institute ␣ of ␣ the ␣ Max ␣ Planck ␣ Society " ; schema : identifier < https :// ror . org /03 k9qs827 > ; schema : name " Fritz ␣ Haber ␣ Institute ␣ of ␣ the ␣ Max ␣ Planck ␣ Society " . entity : org - KoreaUniversity - schutt2018 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Korea ␣ University " ; schema : identifier < https :// ror . org /047 dqcg40 > ; schema : name " Korea ␣ University " . entity : org - MaxPlanckInstituteforInformatics - schutt2018 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Max ␣ Planck ␣ Institute ␣ for ␣ Informatics " ; schema : identifier < https :// ror . org /01 w19ak89 > ; schema : name " Max ␣ Planck ␣ Institute ␣ for ␣ Informatics " . entity : org - UniversityofLuxembourg - schutt2018 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " University ␣ of ␣ Luxembourg " ; schema : identifier < https :// ror . org /036 x5ad56 > ; schema : name " University ␣ of ␣ Luxembourg " . entity : person - Kindermans - schutt2018 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " ; schema : affiliation mlips : TechnischeUniversitatBerlin ; schema : familyName " Kindermans " ; schema : givenName " P . - J . " ; schema : name "P. - J . ␣ Kindermans " . entity : person - Muller - schutt2018 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " ; schema : affiliation mlips : TechnischeUniversitatBerlin , entity : org - KoreaUniversity schutt2018 , entity : org - MaxPlanckInstituteforInformatics - schutt2018 ; schema : familyName " M ü ller " ; schema : givenName " K . - R . " ; schema : name "K. - R . ␣ M ü ller " . entity : study - schutt2018 a mlips : BenchmarkStudy ; rdfs : label " Schuett ␣ et ␣ al . ␣ (2018) : ␣ SchNet ␣ on ␣ MD17 ␣ small ␣ organic ␣ molecules " ;

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Hernández et al. mlips : reportedIn entity : article - schutt2018 .

Q2 – Material system. The canonical pass is the MD17 benchmark of eight small organic molecules (benzene, toluene, malonaldehyde, salicylic acid, aspirin, ethanol, uracil, naphthalene) sampled from gas-phase ab initio MD. We model this as one MaterialSystem at the chemical-space level (C/H/N/O small organics). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat - md17 - schutt2018 a mlips : MaterialSystem ; rdfs : comment " Wikidata ␣ Q174211 ␣ ( ' organic ␣ compound ') ␣ is ␣ the ␣ most ␣ generic ␣ appropriate ␣ entry ;␣ MD17 ␣ itself ␣ has ␣ no ␣ Wikidata ␣ entry ␣ as ␣ of ␣ 2026 -04 -28. " ; rdfs : label " MD17 ␣ small ␣ organic ␣ molecules ␣ ( benzene , ␣ toluene , ␣ malonaldehyde , ␣ salicylic ␣ acid ,␣ aspirin , ␣ ethanol , ␣ uracil , ␣ naphthalene ) " ; mlips : chemicalFormula " C / H / N / O ␣ small ␣ organics " ; mlips : materialClass " Molecular : ␣ eight ␣ small ␣ organic ␣ molecules ␣ used ␣ as ␣ MD ␣ trajectories " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q174211 > .

Q3 – Reference calculation method. Reference data come from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - schutt2018 a mlips : DFTCalculation .

Q4 – Reference settings. DFT references are computed with FHI-aims at the PBE+vdW(TS) level (MD17 trajectories). The basis set, k-grid, and convergence parameters are inherited from the published MD17 benchmark and not re-stated in the SchNet paper itself. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - schutt2018 mlips : hasDFTSettings entity : dft - settings - schutt2018 . entity : dft - settings - schutt2018 a mlips : DFTSettings ; rdfs : comment " Tkatchenko - Scheffler ␣ dispersion ␣ correction ␣ ( PBE + vdW - TS ) . " ; mlips : usedDFTCode mlips : FHIaims ; mlips : xcFunctional mlips : PBE .

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Q5 – Training dataset. The MD17 reference set is consumed at 𝑁 = 1,000 and 𝑁 = 50,000 training-set sizes; we record the larger as the canonical numConfigurations. Configurations cover energies and forces. Provenance is published (the dataset is reused as released). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - md17 - schutt2018 a mlips : TrainingDataset ; rdfs : label " MD17 ␣ reference ␣ set , ␣ used ␣ at ␣ N =1000 ␣ and ␣ N =50000 ␣ training ␣ sizes " ; mlips : coversMaterial entity : mat - md17 - schutt2018 ; mlips : coversProperty mlips : Energy , mlips : Forces ; mlips : datasetProvenance mlips : Published ; mlips : hasDFTCalculation entity : dft - schutt2018 ; mlips : numConfigurations 50000 ; mlips : wasRunBy entity : run - schnet - md17 .

Q6 – Sampling strategies. A single sampling strategy applies: ab initio MD trajectories of the eight molecules, randomly sub-sampled. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - md17 - schutt2018 mlips : samplingStrategy entity : md - sampling - schutt2018 . entity :md - sampling - schutt2018 a mlips : SamplingStrategy ; rdfs : comment " MD17 ␣ configurations ␣ are ␣ randomly ␣ sampled ␣ snapshots ␣ from ␣ DFT ␣ MD ␣ trajectories ␣ of ␣ eight ␣ small ␣ organic ␣ molecules . " ; rdfs : label " Ab ␣ initio ␣ MD ␣ trajectories " .

Q7 – MLIP method, components, implementation. SchNet uses atom-type embeddings combined with interaction blocks that compute continuous-filter convolutions over neighbour atoms, mapped to per-atom energy via atom-wise dense layers and summed for the total. The combined energy/force MSE loss balances energy and force MAEs through trade-off 𝜌 = 0.01. Training uses Adam with exponential learning-rate decay; the implementation is the SchNet reference codebase. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : SchNet . mlips : numFeatures mlips : isHyperparameterOf entity : SchNet . mlips : numLayers mlips : isHyperparameterOf entity : SchNet . entity : SchNet a mlips : MLIPMethod ;

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Hernández et al. rdfs : label " SchNet ␣ ( continuous - filter ␣ convolutional ␣ deep ␣ neural ␣ network ) " ; mlips : hasFunctionalForm entity : schnet - functional - form ; mlips : hasHyperparameter mlips : cutoffRadius , mlips : numFeatures , mlips : numLayers , entity :hp - rho ; mlips : hasImplementation entity : schnet - impl ; mlips : hasLossFunction entity : schnet - loss - energy - force ; mlips : hasTrainingAlgorithm entity : adam ; mlips : supportsSimulation mlips : MolecularDynamics , mlips : PhononCalculation . entity : adam a mls : Algorithm ; rdfs : label " ADAM ␣ optimizer ␣ with ␣ mini - batches ␣ of ␣ 32 , ␣ exponential ␣ learning - rate ␣ decay ␣ ( ratio ␣ 0.96 ␣ per ␣ 100 k ␣ steps ) " . entity :hp - rho a mlips : Hyperparameter ; rdfs : label " SchNet ␣ energy / force ␣ loss ␣ trade - off " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : double ; mlips : hyperparameterName " rho " ; mlips : isHyperparameterOf entity : SchNet . entity : schnet - functional - form a mlips : FunctionalForm ; rdfs : label " Atom ␣ embeddings ␣ + ␣ interaction ␣ blocks ␣ with ␣ continuous - filter ␣ convolutions ; ␣ per - atom ␣ energy ␣ via ␣ atom - wise ␣ dense ␣ layers , ␣ summed ␣ for ␣ total ␣ energy " . entity : schnet - impl a mlips : Implementation ; mlips : implementedIn mlips : SchNet ; mlips : isImplementationOf entity : SchNet . entity : schnet - loss - energy - force a mlips : LossFunction ; rdfs : label " Combined ␣ squared - error ␣ loss ␣ on ␣ energies ␣ and ␣ forces ␣ with ␣ trade - off ␣ rho =0.01 " .

Q8 – Hyperparameter settings. Reported settings: 𝑇 = 6 interaction layers, 𝐹 = 64 feature channels, and energy/force loss trade-off 𝜌 = 0.01. The radial-basis cutoff parameter is referenced but not given an explicit numerical setting in the canonical pass. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting -F -64 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ features ␣ = ␣ 64 ␣ for ␣ SchNet ␣ training ␣ run ␣ on ␣ MD17 ␣ ( T =6 , ␣ F =64 , ␣ rho =0.01) " ; mlips : forHyperparameter mlips : numFeatures ; mlips : isSettingOf entity : run - schnet - md17 ; mlips : settingValue 64 . entity : setting -T -6 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ layers ␣ = ␣ 6 ␣ for ␣ SchNet ␣ training ␣ run ␣ on ␣ MD17 ␣ ( T =6 , ␣ F =64 , ␣ rho =0.01) " ; mlips : forHyperparameter mlips : numLayers ; mlips : isSettingOf entity : run - schnet - md17 ; mlips : settingValue 6 . entity : setting - rho -001 a mlips : HyperparameterSetting ; rdfs : label " SchNet ␣ energy / force ␣ loss ␣ trade - off ␣ = ␣ 0.01 ␣ for ␣ SchNet ␣ training ␣ run ␣ on ␣ MD17 ␣ (T =6 , ␣F =64 , ␣ rho =0.01) " ; mlips : forHyperparameter entity : hp - rho ; mlips : isSettingOf entity : run - schnet - md17 ; mlips : settingValue 0.01 .

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Q9 – MLIP run and trained model. A single training run with the combined energy+force loss produces the production SchNet model. The paper also reports separate single-objective runs (energies-only or forces-only); these are recorded as Q12 gaps to keep the canonical run unambiguous. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - schnet - md17 a mlips : TrainedModel ; rdfs : label " SchNet ␣ model ␣ trained ␣ on ␣ MD17 ␣ ( combined ␣ energy + force ␣ loss , ␣ N =50000) " . entity : run - schnet - md17 a mlips : MLIPRun ; rdfs : label " SchNet ␣ training ␣ run ␣ on ␣ MD17 ␣ ( T =6 , ␣ F =64 , ␣ rho =0.01) " ; mlips : appliesMethod entity : SchNet ; mlips : hasHyperparameterSetting entity : setting -F -64 , entity : setting -T -6 , entity : setting - rho -001 ; mlips : produces entity : model - schnet - md17 ; mlips : runsOn entity : ds - md17 - schutt2018 .

Q10 – Benchmark results. For aspirin at 𝑁 = 50,000 we record the MAE of total energy (0.12 kcal/mol) and the MAE of atomic forces (0.33 kcal/mol/Å). Per-molecule numbers for the other seven species and at the smaller 𝑁 = 1,000 regime are given in the paper and are not enumerated here as separate BenchmarkResult instances. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - mae - md17 - energy a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 0.12 ␣ [ KiloCAL - PER - MOL ] " , " MAE ␣ of ␣ total ␣ energy ␣ on ␣ MD17 ␣ aspirin ␣ ( N =50000 , ␣ energy + forces ␣ loss ) " ; mlips : hasUnit unit : KiloCAL - PER - MOL ; mlips : isMetricOf entity : result - md17 - energy ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 0.12 . entity : metric - mae - md17 - forces a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Force ␣ = ␣ 0.33 ␣ [ kilocalorie ␣ per ␣ mole ␣ per ␣ angstrom ] " , " MAE ␣ of ␣ atomic ␣ forces ␣ on ␣ MD17 ␣ aspirin ␣ ( N =50000 , ␣ energy + forces ␣ loss ) " ; mlips : hasUnit mlips : KiloCAL - PER - MOL - ANGSTROM ; mlips : isMetricOf entity : result - md17 - forces ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 0.33 . entity : result - md17 - energy a mlips : BenchmarkResult ; rdfs : label " SchNet ␣ model ␣ trained ␣ on ␣ MD17 ␣ ( combined ␣ energy + force ␣ loss , ␣ N =50000) ␣ on ␣ MD17 ␣ small ␣ organic ␣ molecules ␣ ( benzene , ␣ toluene , ␣ malonaldehyde , ␣ salicylic ␣ acid , ␣ aspirin ,␣ ethanol , ␣ uracil , ␣ naphthalene ) ␣ in ␣ Schuett ␣ et ␣ al . ␣ (2018) : ␣ SchNet ␣ on ␣ MD17 ␣ small ␣ organic ␣ molecules " ; mlips : evaluatesModel entity : model - schnet - md17 ; mlips : hasAccuracyMetric entity : metric - mae - md17 - energy ; mlips : isResultOf entity : study - schutt2018 ;

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Hernández et al. mlips : targetMaterial entity : mat - md17 - schutt2018 . entity : result - md17 - forces a mlips : BenchmarkResult ; rdfs : label " SchNet ␣ model ␣ trained ␣ on ␣ MD17 ␣ ( combined ␣ energy + force ␣ loss , ␣ N =50000) ␣ on ␣ MD17 ␣ small ␣ organic ␣ molecules ␣ ( benzene , ␣ toluene , ␣ malonaldehyde , ␣ salicylic ␣ acid , ␣ aspirin ,␣ ethanol , ␣ uracil , ␣ naphthalene ) ␣ in ␣ Schuett ␣ et ␣ al . ␣ (2018) : ␣ SchNet ␣ on ␣ MD17 ␣ small ␣ organic ␣ molecules " ; mlips : evaluatesModel entity : model - schnet - md17 ; mlips : hasAccuracyMetric entity : metric - mae - md17 - forces ; mlips : isResultOf entity : study - schutt2018 ; mlips : targetMaterial entity : mat - md17 - schutt2018 . entity : study - schutt2018 mlips : hasResult entity : result - md17 - energy , entity : result - md17 - forces .

Q11 – Computational resources. Not reported for the canonical MD17 SchNet training. The paper reports a separately trained C20 -fullerene SchNet inference speedup (∼11 s on 32 CPU cores vs. ∼10 ms on a single GTX 1080), but for an auxiliary model not encoded here. # Q11 - resources : no triples ( paper does not report this ) .

Q12 – Gaps. Beyond Q11, the paper does not report: training duration or GPU hours for the canonical MD17 run; training hardware; peak memory. SchNet’s auxiliary applications (QM9 single-property prediction with 𝑁 =50k/110k, Materials Project formation-energy regression, and the PIMD/anharmonicity study on C20 -fullerene at PBE+vdW(TS)) are not encoded as separate MLIPRun instances; the ontology can express each as a sibling run, but doing so would multiply the canonical-file size without adding new ontology coverage. K.7

Bartók et al. (2018): general-purpose GAP for silicon

Q1 – Bibliographic identification. Bartók, Kermode, Bernstein, and Csányi train a single generalpurpose Gaussian Approximation Potential covering crystalline, liquid, amorphous, surface, defect, and crack-tip silicon configurations. Published in Phys. Rev. X 8, 041048 (2018); arXiv:1805.01568. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -6755 -6271 > a schema : Person ; schema : affiliation mlips : RutherfordAppletonLaboratory , mlips : ScienceandTechnologyFacilitiesCouncil ; schema : familyName " Kermode " ; schema : givenName " James " ; schema : identifier < https :// orcid . org /0000 -0001 -6755 -6271 > ; schema : name " James ␣ Kermode " . < https :// orcid . org /0000 -0002 -4347 -8819 > schema : affiliation mlips : RutherfordAppletonLaboratory , mlips : ScienceandTechnologyFacilitiesCouncil . < https :// orcid . org /0000 -0002 -6532 -1337 > a schema : Person ; schema : affiliation mlips : RutherfordAppletonLaboratory , mlips : ScienceandTechnologyFacilitiesCouncil ; schema : familyName " Bernstein " ; schema : givenName " Noam " ; schema : identifier < https :// orcid . org /0000 -0002 -6532 -1337 > ; schema : name " Noam ␣ Bernstein " . entity : article - bartok2018si a schema : ScholarlyArticle ;

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schema : author < https :// orcid . org /0000 -0001 -6755 -6271 > , < https :// orcid . org /0000 -0002 -4347 -8819 > , < https :// orcid . org /0000 -0002 -6532 -1337 > , entity : person Csanyi - bartok2018si ; schema : datePublished " 2018 " ^^ xsd : gYear ; schema : name " Machine ␣ learning ␣ a ␣ general ␣ purpose ␣ interatomic ␣ potential ␣ for ␣ silicon " ; schema : sameAs < https :// doi . org /10.1103/ PhysRevX .8.041048 > . entity : person - Csanyi - bartok2018si a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " ; schema : affiliation mlips : RutherfordAppletonLaboratory , mlips : ScienceandTechnologyFacilitiesCouncil ; schema : familyName " Cs á nyi " ; schema : givenName " G á bor " ; schema : name "Gá bor ␣ Cs á nyi " . entity : study - bartok2018si a mlips : BenchmarkStudy ; rdfs : label " Bartok ␣ et ␣ al . ␣ (2018) : ␣ general - purpose ␣ GAP ␣ for ␣ silicon " ; mlips : reportedIn entity : article - bartok2018si .

Q2 – Material system. Bulk silicon is encoded as a single MaterialSystem; the broad configurational coverage (diamond, 𝛽-Sn, simple-hexagonal, hex-diamond, bcc, bc8, fcc, hcp, st12, liquid, amorphous, surfaces, point defects, crack tips) is recorded as materialClass text and as the eight sampling strategies in Q6. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat -Si - bartok2018 a mlips : MaterialSystem ; rdfs : label " Silicon ␣ ( general - purpose : ␣ crystal , ␣ liquid , ␣ amorphous , ␣ defective ) " ; mlips : chemicalFormula " Si " ; mlips : materialClass " Single - element ␣ semiconductor ; ␣ benchmarked ␣ on ␣ diamond , ␣ beta - Sn , ␣ simple ␣ hexagonal , ␣ hex - diamond , ␣ bcc , ␣ bc8 , ␣ fcc , ␣ hcp , ␣ st12 , ␣ liquid , ␣ amorphous , ␣ surfaces ,␣ point ␣ defects , ␣ crack ␣ tips " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q670 > .

Q3 – Reference calculation method. Reference data come from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - bartok2018si a mlips : DFTCalculation .

Q4 – Reference settings. DFT is performed with CASTEP using the PW91 functional, ultrasoft pseudopotentials, a 250 eV plane-wave cutoff, and Monkhorst–Pack k-point meshes with 0.03 Å−1 spacing for production (with 0.05 eV electronic smearing); 0.015 Å−1 for 𝐸 (𝑉 ) testing curves; 0.07 Å−1 for amorphous re-optimisation. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > .

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Hernández et al. @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - bartok2018si mlips : hasDFTSettings entity : dft - settings - bartok2018si . entity : dft - settings - bartok2018si a mlips : DFTSettings ; mlips : energyCutoff 250 ; mlips : kPointMesh " Monkhorst - Pack ␣ with ␣ 0.03 ␣ Ang ^ -1 ␣ spacing ␣ ( with ␣ 0.05 ␣ eV ␣ electronic ␣ smearing ); ␣ 0.015 ␣ Ang ^ -1 ␣ for ␣ E ( V ) ␣ testing ␣ curves ; ␣ 0.07 ␣ Ang ^ -1 ␣ for ␣ amorphous ␣ re optimization " ; mlips : pseudopotentialType mlips : Ultrasoft ; mlips : usedDFTCode mlips : CASTEP ; mlips : xcFunctional mlips : PW91 .

Q5 – Training dataset. The fitting database has 2,475 unit cells contributing 171,815 atomic environments and 531,710 pieces of electronic-structure data (energies, forces, virials). Provenance is in-house (the database was assembled by the authors specifically for this work). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds -Si - bartok2018 a mlips : TrainingDataset ; rdfs : label " Si ␣ general - purpose ␣ GAP ␣ fitting ␣ database ␣ (2475 ␣ unit ␣ cells , ␣ 171 ,815 ␣ atomic ␣ environments , ␣ 531 ,710 ␣ pieces ␣ of ␣ electronic - structure ␣ data ) " ; mlips : coversMaterial entity : mat - Si - bartok2018 ; mlips : coversProperty mlips : Energy , mlips : Forces , mlips : Virials ; mlips : datasetProvenance mlips : InHouse ; mlips : hasDFTCalculation entity : dft - bartok2018si ; mlips : numConfigurations 2475 ; mlips : wasRunBy entity : run - gap - Si .

Q6 – Sampling strategies. Eight strategies were combined: crystal-phase enumeration with strain perturbations; surface enumeration including reconstructions and decohesion paths; vacancy/divacancy/interstitial point-defect enumeration; liquid-phase MD; quenched-melt amorphous trajectories; crack-tip geometries with bond breaking; screw-dislocation cores; and a single isolated-atom anchor for the cohesive-energy zero. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : amorphous - sampling - bartok2018si a mlips : SamplingStrategy ; rdfs : comment " Configurations ␣ from ␣ quenched - melt ␣ amorphous - Si ␣ trajectories ␣ in ␣ 64 - ␣ and ␣ 216 - atom ␣ cells . " ; rdfs : label " Amorphous - phase ␣ quench ␣ sampling " . entity : crack - sampling - bartok2018si a mlips : SamplingStrategy ; rdfs : comment " Small ␣ (110) ␣ and ␣ (111) ␣ crack - tip ␣ geometries ␣ with ␣ bond - breaking ␣ environments . " ; rdfs : label " Crack - tip ␣ sampling " .

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entity : defect - sampling - bartok2018si a mlips : SamplingStrategy ; rdfs : comment " Vacancy , ␣ divacancy , ␣ and ␣ interstitial ␣ ( hexagonal , ␣ tetrahedral , ␣ dumbbell ) ␣ configurations ␣ in ␣ diamond ␣ Si , ␣ sampled ␣ by ␣ DFT ␣ MD ␣ around ␣ the ␣ defect . " ; rdfs : label " Point - defect ␣ enumeration " . entity : dislocation - sampling - bartok2018si a mlips : SamplingStrategy ; rdfs : comment " Screw - dislocation ␣ core ␣ configurations ␣ in ␣ 144 - atom ␣ periodic ␣ cells . " ; rdfs : label " Screw - dislocation ␣ core ␣ sampling " . entity :ds -Si - bartok2018 mlips : samplingStrategy entity : amorphous - sampling - bartok2018si , entity : crack - sampling bartok2018si , entity : defect - sampling - bartok2018si , entity : dislocation - sampling bartok2018si , entity : isolated - atom - sampling - bartok2018si , entity : liquid - sampling bartok2018si , entity : phase - sampling - bartok2018si , entity : surface - sampling bartok2018si . entity : isolated - atom - sampling - bartok2018si a mlips : SamplingStrategy ; rdfs : comment " A ␣ single ␣ isolated ␣ Si ␣ atom ␣ is ␣ included ␣ to ␣ anchor ␣ the ␣ cohesive - energy ␣ zero ." ; rdfs : label " Isolated - atom ␣ anchor " . entity : liquid - sampling - bartok2018si a mlips : SamplingStrategy ; rdfs : comment " Snapshots ␣ from ␣ DFT ␣ MD ␣ trajectories ␣ of ␣ molten ␣ silicon ␣ at ␣ high ␣ temperature ␣ in ␣ 64 - ␣ and ␣ 128 - atom ␣ supercells . " ; rdfs : label " Liquid - phase ␣ MD ␣ sampling " . entity : phase - sampling - bartok2018si a mlips : SamplingStrategy ; rdfs : comment " Configurations ␣ covering ␣ diamond , ␣ beta - Sn , ␣ simple ␣ hexagonal , ␣ hex - diamond , ␣ bcc ,␣ bc8 , ␣ fcc , ␣ hcp , ␣ st12 ␣ across ␣ a ␣ range ␣ of ␣ unit - cell ␣ sizes ␣ and ␣ lattice ␣ strains . " ; rdfs : label " Crystal - phase ␣ enumeration ␣ with ␣ strain ␣ perturbations " . entity : surface - sampling - bartok2018si a mlips : SamplingStrategy ; rdfs : comment " Diamond ␣ (001) ,␣ (110) ,␣ (111) ␣ surfaces ␣ with ␣ unreconstructed , ␣ adatom , ␣ and ␣ Pandey / DAS ␣ reconstructions , ␣ plus ␣ decohesion ␣ separation ␣ paths ␣ along ␣ (100) ,␣ (110) ,␣ (111) ." ; rdfs : label " Surface ␣ enumeration ␣ including ␣ reconstructions ␣ and ␣ decohesion ␣ paths " .

Q7 – MLIP method, components, implementation. The method combines a cubic-spline pairpotential repulsive term with a many-body SOAP-kernel Gaussian-process regression. Training uses sparse GPR with CUR-selected representative environments. The implementation is QUIP with the GAP plug-in. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : GAP . mlips : numAngularBasis mlips : isHyperparameterOf entity : GAP . mlips : numRadialBasis mlips : isHyperparameterOf entity : GAP . mlips : numSparseConfigs mlips : isHyperparameterOf entity : GAP . entity : GAP a mlips : MLIPMethod ; rdfs : label " Gaussian ␣ Approximation ␣ Potential ␣ with ␣ SOAP ␣ kernel " ; mlips : hasDescriptor mlips : SOAPDescriptor ; mlips : hasFunctionalForm entity : gap - functional - form ; mlips : hasHyperparameter mlips : cutoffRadius , mlips : numAngularBasis , mlips : numRadialBasis , mlips : numSparseConfigs , entity : hp - delta , entity : hp - sigma - atom , entity :hp - zeta ; mlips : hasImplementation entity : quip - impl ;

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Hernández et al. mlips : hasLossFunction entity : gap - loss - bartok2018si ; mlips : hasTrainingAlgorithm entity : gpr - bartok2018si ; mlips : supportsSimulation mlips : GeometryOptimization , mlips : MolecularDynamics , mlips : NudgedElasticBand , mlips : PhononCalculation . entity : gap - functional - form a mlips : FunctionalForm ; rdfs : label " Pair ␣ potential ␣ ( cubic - spline ␣ repulsive ) ␣ plus ␣ SOAP - kernel ␣ many - body ␣ Gaussian - process ␣ regression " . entity : gap - loss - bartok2018si a mlips : LossFunction ; rdfs : label " Regularised ␣ least ␣ squares ␣ on ␣ energies , ␣ forces , ␣ virials ␣ with ␣ per - class ␣ regularisation ␣ ( sigma_E , ␣ sigma_F , ␣ sigma_V ) " . entity : gpr - bartok2018si a mls : Algorithm ; rdfs : label " Sparse ␣ Gaussian - process ␣ regression ␣ with ␣ CUR - selected ␣ representative ␣ environments " . entity :hp - delta a mlips : Hyperparameter ; rdfs : label " SOAP ␣ / ␣ Huber ␣ delta " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : double ; mlips : hyperparameterName " delta " ; mlips : isHyperparameterOf entity : GAP . entity :hp - sigma - atom a mlips : Hyperparameter ; rdfs : label " SOAP ␣ atomic ␣ Gaussian ␣ width " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : double ; mlips : hyperparameterName " sigma_atom " ; mlips : isHyperparameterOf entity : GAP . entity :hp - zeta a mlips : Hyperparameter ; rdfs : label " SOAP ␣ kernel ␣ polynomial ␣ power " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : integer ; mlips : hyperparameterName " zeta " ; mlips : isHyperparameterOf entity : GAP . entity : quip - impl a mlips : Implementation ; mlips : implementedIn mlips : QUIP ; mlips : isImplementationOf entity : GAP .

Q8 – Hyperparameter settings. Reported settings: SOAP cutoff 𝑟𝑐 = 5.0 Å, atomic-Gaussian width 𝜎atom = 0.5 Å, kernel polynomial power 𝜁 = 4, energy-scale parameter 𝛿 = 3 eV, and 𝑀 = 9,000 representative environments. Per-class regularisations 𝜎𝐸 , 𝜎𝐹 , 𝜎𝑉 are also tuned but not enumerated as HyperparameterSetting instances. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting -M -9000 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ sparse ␣ configurations ␣ = ␣ 9000 ␣ for ␣ GAP ␣ training ␣ run ␣ on ␣ the ␣ general - purpose ␣ Si ␣ database " ; mlips : forHyperparameter mlips : numSparseConfigs ; mlips : isSettingOf entity : run - gap - Si ; mlips : settingValue 9000 . entity : setting - delta -3 a mlips : HyperparameterSetting ; rdfs : label " SOAP ␣ / ␣ Huber ␣ delta ␣ = ␣ 3 ␣ for ␣ GAP ␣ training ␣ run ␣ on ␣ the ␣ general - purpose ␣ Si ␣ database " ; mlips : forHyperparameter entity : hp - delta ; mlips : isSettingOf entity : run - gap - Si ;

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mlips : settingValue 3 . entity : setting - rcut -5 - bartok2018si a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 5 ␣ for ␣ GAP ␣ training ␣ run ␣ on ␣ the ␣ general - purpose ␣ Si ␣ database " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - gap - Si ; mlips : settingValue 5 . entity : setting - sigma - atom -05 a mlips : HyperparameterSetting ; rdfs : label " SOAP ␣ atomic ␣ Gaussian ␣ width ␣ = ␣ 0.5 ␣ for ␣ GAP ␣ training ␣ run ␣ on ␣ the ␣ general purpose ␣ Si ␣ database " ; mlips : forHyperparameter entity : hp - sigma - atom ; mlips : isSettingOf entity : run - gap - Si ; mlips : settingValue 0.5 . entity : setting - zeta -4 a mlips : HyperparameterSetting ; rdfs : label " SOAP ␣ kernel ␣ polynomial ␣ power ␣ = ␣ 4 ␣ for ␣ GAP ␣ training ␣ run ␣ on ␣ the ␣ general purpose ␣ Si ␣ database " ; mlips : forHyperparameter entity : hp - zeta ; mlips : isSettingOf entity : run - gap - Si ; mlips : settingValue 4 .

Q9 – MLIP run and trained model. A single GPR fit produces the GAP-6 silicon potential. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - gap - Si a mlips : TrainedModel ; rdfs : label " GAP -6 ␣ silicon ␣ potential " . entity : run - gap - Si a mlips : MLIPRun ; rdfs : label " GAP ␣ training ␣ run ␣ on ␣ the ␣ general - purpose ␣ Si ␣ database " ; mlips : appliesMethod entity : GAP ; mlips : hasHyperparameterSetting entity : setting -M -9000 , entity : setting - delta -3 , entity : setting - rcut -5 - bartok2018si , entity : setting - sigma - atom -05 , entity : setting - zeta -4 ; mlips : produces entity : model - gap - Si ; mlips : runsOn entity : ds - Si - bartok2018 .

Q10 – Benchmark results. The headline accuracy figure is the median absolute force-component error on the held-out testing set (grain-boundary, di-interstitial, GSF-path, amorphous configurations): 0.025 eV/Å. The paper reports many additional per-property and per-phase comparisons (lattice constants, elastic moduli, surface energies, defect formation energies, EOS curves) but in derived form rather than as separate BenchmarkResult instances. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - gap -si - forces - median a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Force ␣ = ␣ 0.025 ␣ [ EV - PER - ANGSTROM ] " , " Median ␣ absolute ␣ force - component ␣ error ␣ on ␣ the ␣ testing ␣ database ␣ ( held - out ␣ grain ␣ boundary , ␣ di - interstitials , ␣ GSF ␣ paths ,␣ amorphous ) " ; mlips : hasUnit unit : EV - PER - ANGSTROM ;

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Hernández et al. mlips : isMetricOf entity : result - gap - si - forces ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 0.025 . entity : result - gap -si - forces a mlips : BenchmarkResult ; rdfs : label " GAP -6 ␣ silicon ␣ potential ␣ on ␣ Silicon ␣ ( general - purpose : ␣ crystal , ␣ liquid , ␣ amorphous , ␣ defective ) ␣ in ␣ Bartok ␣ et ␣ al . ␣ (2018) : ␣ general - purpose ␣ GAP ␣ for ␣ silicon " ; mlips : evaluatesModel entity : model - gap - Si ; mlips : hasAccuracyMetric entity : metric - gap - si - forces - median ; mlips : isResultOf entity : study - bartok2018si ; mlips : targetMaterial entity : mat - Si - bartok2018 . entity : study - bartok2018si mlips : hasResult entity : result - gap - si - forces .

Q11 – Computational resources. Not reported. # Q11 - resources : no triples ( paper does not report this ) .

Q12 – Gaps. Beyond Q11, the paper does not record explicit values for: the per-class force/virial regularisations 𝜎𝐹 , 𝜎𝑉 (only their existence and qualitative role); the SOAP 𝑙 max and 𝑛 max basis indices that are referenced under hasHyperparameter but lack HyperparameterSetting instances; and any frozenCore treatment beyond the ultrasoft pseudopotential. The paper also sketches several downstream applications (crack tip propagation, amorphous-Si melt-quench MD, recrystallisation kinetics) which are not encoded as separate MLIPRun instances. K.8

Wang et al. (2018): DeePMD-kit, water demonstration

Q1 – Bibliographic identification. Wang, Zhang, Han, and E document DeePMD-kit, a TensorFlowbased deep learning package for many-body potential energy representation and molecular dynamics. Published in Comput. Phys. Commun. 228, 178–184 (2018); arXiv:1712.03641. We exercise the protocol on the single liquid-water demonstration in §IV; the package’s broader multi-system, multi-method capabilities are flagged as the central gap in Q12. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0002 -3553 -7313 > a schema : Person ; schema : affiliation mlips : PrincetonUniversity ; schema : familyName " Han " ; schema : givenName " Jiequn " ; schema : identifier < https :// orcid . org /0000 -0002 -3553 -7313 > ; schema : name " Jiequn ␣ Han " . < https :// orcid . org /0000 -0002 -4302 -1886 > a schema : Person ; schema : affiliation entity : org - InstituteofAppliedPhysicsandComputationalMathematics wang2018dpkit , entity : org - NumericalMethodChina - wang2018dpkit ; schema : familyName " Wang " ; schema : givenName " Han " ; schema : identifier < https :// orcid . org /0000 -0002 -4302 -1886 > ; schema : name " Han ␣ Wang " . < https :// orcid . org /0000 -0002 -8470 -5846 > a schema : Person ; schema : affiliation mlips : PrincetonUniversity ; schema : familyName " Zhang " ; schema : givenName " Linfeng " ; schema : identifier < https :// orcid . org /0000 -0002 -8470 -5846 > ;

An Ontology for Machine Learning Interatomic Potentials schema : name " Linfeng ␣ Zhang " . entity : article - wang2018dpkit a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0002 -3553 -7313 > , < https :// orcid . org /0000 -0002 -4302 -1886 > , < https :// orcid . org /0000 -0002 -8470 -5846 > , entity : person -E wang2018dpkit ; schema : datePublished " 2018 " ^^ xsd : gYear ; schema : name " DeePMD - kit : ␣ A ␣ deep ␣ learning ␣ package ␣ for ␣ many - body ␣ potential ␣ energy ␣ representation ␣ and ␣ molecular ␣ dynamics " ; schema : sameAs < https :// doi . org /10.1016/ j . cpc .2018.03.016 > . entity : org - InstituteofAppliedPhysicsandComputationalMathematics - wang2018dpkit a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Institute ␣ of ␣ Applied ␣ Physics ␣ and ␣ Computational ␣ Mathematics " ; schema : identifier < https :// ror . org /03 sxpbt26 > ; schema : name " Institute ␣ of ␣ Applied ␣ Physics ␣ and ␣ Computational ␣ Mathematics " . entity : org - NumericalMethodChina - wang2018dpkit a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Numerical ␣ Method ␣ ( China ) " ; schema : identifier < https :// ror . org /02 ns8zp42 > ; schema : name " Numerical ␣ Method ␣ ( China ) " . entity : person -E - wang2018dpkit a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " ; schema : familyName " E " ; schema : givenName " Weinan " ; schema : name " Weinan ␣ E " . entity : study - wang2018dpkit a mlips : BenchmarkStudy ; rdfs : label " Wang ␣ et ␣ al . ␣ (2018) : ␣ DeePMD - kit ␣ software , ␣ water ␣ demonstration " ; mlips : reportedIn entity : article - wang2018dpkit .

Q2 – Material system. The demonstration system is liquid water (64 H2 O molecules under periodic boundary conditions, ∼330 K). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat - water - wang2018 a mlips : MaterialSystem ; rdfs : label " Liquid ␣ water ␣ (64 ␣ H2O ␣ molecules , ␣ PBC , ␣ ~330 ␣ K ) " ; mlips : chemicalFormula " H2O " ; mlips : materialClass " Molecular ␣ liquid ␣ ( bulk ␣ water ␣ under ␣ periodic ␣ boundary ␣ conditions ) " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q283 > .

Q3 – Reference calculation method. Reference data come from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - wang2018dpkit a mlips : DFTCalculation .

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Q4 – Reference settings. The functional is PBE0+TS (hybrid PBE0 with Tkatchenko–Scheffler dispersion). Other DFT settings (engine, plane-wave or basis-set choice, k-mesh) are not stated in the demonstration section. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - settings - wang2018dpkit a mlips : DFTSettings ; rdfs : comment " Tkatchenko - Scheffler ␣ dispersion ␣ correction ␣ ( PBE0 + TS ) . " ; mlips : xcFunctional mlips : PBE0 . entity : dft - wang2018dpkit mlips : hasDFTSettings entity : dft - settings - wang2018dpkit .

Q5 – Training dataset. The reference set is 40,000 frames from a 20 ps NVT AIMD trajectory of 64 water molecules at 330 K (38,000 train + 2,000 test). Energies and forces are covered. Provenance is published (reused from the underlying AIMD work). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - water - wang2018 a mlips : TrainingDataset ; rdfs : label " Liquid - water ␣ reference ␣ set : ␣ 40000 ␣ frames ␣ from ␣ a ␣ 20 ␣ ps ␣ NVT ␣ AIMD ␣ trajectory ␣ at ␣ 330 ␣K␣ of ␣ 64 ␣ H2O ␣ molecules ␣ (38000 ␣ train ␣ + ␣ 2000 ␣ test ) " ; mlips : coversMaterial entity : mat - water - wang2018 ; mlips : coversProperty mlips : Energy , mlips : Forces ; mlips : datasetProvenance mlips : Published ; mlips : hasDFTCalculation entity : dft - wang2018dpkit ; mlips : numConfigurations 40000 ; mlips : wasRunBy entity : run - deepmd - water .

Q6 – Sampling strategies. A single sampling strategy applies: vibrational sampling via NVT AIMD with a 0.0005 ps stride. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : aimd - sampling - wang2018 a mlips : SamplingStrategy ; rdfs : comment " Configurations ␣ are ␣ recorded ␣ every ␣ 0.0005 ␣ ps ␣ along ␣ a ␣ 20 ␣ ps ␣ NVT ␣ AIMD ␣ trajectory ␣ of ␣ 64 ␣ water ␣ molecules ␣ at ␣ 330 ␣ K . " ; rdfs : label " Vibrational ␣ sampling ␣ ( NVT ␣ AIMD ) " . entity :ds - water - wang2018 mlips : samplingStrategy entity : aimd - sampling - wang2018 .

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Q7 – MLIP method, components, implementation. The method is Deep Potential Molecular Dynamics (DeePMD): a per-atom DNN over local-frame radial+angular descriptors (1/R, x/R, y/R, z/R) sorted by chemical species, with five hidden layers (240, 120, 60, 30, 10) and tanh activations. Loss is a weighted MSE on energy and force (no virial) with annealed prefactors. Optimisation is Adam with exponential learning-rate decay. The implementation is DeePMD-kit v0.1 (Python/C++ on TensorFlow), with LAMMPS pair-style deepmd and i-PI dp_ipi clients shipping in the package. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : DeePMD . mlips : learningRate mlips : isHyperparameterOf entity : DeePMD . entity : DeePMD a mlips : MLIPMethod ; rdfs : label " Deep ␣ Potential ␣ Molecular ␣ Dynamics ␣ ( DeePMD ) " ; mlips : hasDescriptor mlips : DeepPotentialDescriptor ; mlips : hasFunctionalForm entity : deepmd - functional - form ; mlips : hasHyperparameter mlips : cutoffRadius , mlips : learningRate , entity : hp - decay - rate deepmd , entity : hp - decay - steps - deepmd , entity : hp - hidden - deepmd ; mlips : hasImplementation entity : deepmd - kit - impl ; mlips : hasLossFunction entity : deepmd - loss - wang2018 ; mlips : hasTrainingAlgorithm entity : adam - deepmd ; mlips : supportsSimulation mlips : MolecularDynamics . entity : adam - deepmd a mls : Algorithm ; rdfs : label " Adam ␣ stochastic ␣ gradient ␣ descent ␣ with ␣ exponentially ␣ decaying ␣ learning ␣ rate ␣( start ␣1e -3 , ␣ decay ␣ rate ␣ 0.95 ␣ every ␣ 5000 ␣ steps ) " . entity : deepmd - functional - form a mlips : FunctionalForm ; rdfs : label " Per - atom ␣ DNN ␣ over ␣ local - frame ␣ radial + angular ␣ descriptors ␣ (1/ R , ␣ x /R , ␣ y /R , ␣ z /R)␣ sorted ␣ by ␣ chemical ␣ species , ␣ 5 ␣ hidden ␣ layers ␣ (240 , ␣ 120 , ␣ 60 , ␣ 30 , ␣ 10) ␣ with ␣ tanh ␣ activations " . entity : deepmd - kit - impl a mlips : Implementation ; mlips : implementedIn mlips : DeePMDkit ; mlips : isImplementationOf entity : DeePMD ; mlips : version " 0.1 " . entity : deepmd - loss - wang2018 a mlips : LossFunction ; rdfs : label " Weighted ␣ MSE ␣ on ␣ energy ␣ and ␣ force ␣ ( no ␣ virial ) ,␣ with ␣ annealed ␣ prefactors ␣ ( p_e :␣ 0.02 ␣ ->␣ 8; ␣ p_f : ␣ 1000 ␣ ->␣ 1; ␣ p_v : ␣ 0) " . entity :hp - decay - rate - deepmd a mlips : Hyperparameter ; rdfs : label " DeePMD ␣ learning - rate ␣ decay ␣ rate " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : double ; mlips : hyperparameterName " decay_rate " ; mlips : isHyperparameterOf entity : DeePMD . entity :hp - decay - steps - deepmd a mlips : Hyperparameter ; rdfs : label " DeePMD ␣ learning - rate ␣ decay ␣ steps " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : integer ; mlips : hyperparameterName " decay_steps " ; mlips : isHyperparameterOf entity : DeePMD . entity :hp - hidden - deepmd a mlips : Hyperparameter ; rdfs : label " DeePMD ␣ per - atom ␣ hidden ␣ layer ␣ architecture " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : string ; mlips : hyperparameterName " hidden_layers " ;

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Q8 – Hyperparameter settings. Reported settings: cutoff radius 𝑟𝑐 = 6.0 Å; per-atom hidden architecture (240, 120, 60, 30, 10); initial learning rate 10−3 ; learning-rate decay rate 0.95; decay applied every 5,000 steps. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - decay - rate - deepmd a mlips : HyperparameterSetting ; rdfs : label " DeePMD ␣ learning - rate ␣ decay ␣ rate ␣ = ␣ 0.95 ␣ for ␣ DeePMD - kit ␣ demonstration ␣ training ␣ run ␣ on ␣ the ␣ liquid - water ␣ dataset ␣ (10^6 ␣ batches , ␣ batch ␣ size ␣ 4) " ; mlips : forHyperparameter entity : hp - decay - rate - deepmd ; mlips : isSettingOf entity : run - deepmd - water ; mlips : settingValue 0.95 . entity : setting - decay - steps - deepmd a mlips : HyperparameterSetting ; rdfs : label " DeePMD ␣ learning - rate ␣ decay ␣ steps ␣ = ␣ 5000 ␣ for ␣ DeePMD - kit ␣ demonstration ␣ training ␣ run ␣ on ␣ the ␣ liquid - water ␣ dataset ␣ (10^6 ␣ batches , ␣ batch ␣ size ␣ 4) " ; mlips : forHyperparameter entity : hp - decay - steps - deepmd ; mlips : isSettingOf entity : run - deepmd - water ; mlips : settingValue 5000 . entity : setting - hidden - deepmd a mlips : HyperparameterSetting ; rdfs : label " DeePMD ␣ per - atom ␣ hidden ␣ layer ␣ architecture ␣ = ␣ (240 , ␣ 120 , ␣ 60 , ␣ 30 , ␣ 10) ␣ for ␣ DeePMD - kit ␣ demonstration ␣ training ␣ run ␣ on ␣ the ␣ liquid - water ␣ dataset ␣ (10^6 ␣ batches , ␣ batch ␣ size ␣ 4) " ; mlips : forHyperparameter entity : hp - hidden - deepmd ; mlips : isSettingOf entity : run - deepmd - water ; mlips : settingValue " (240 , ␣ 120 , ␣ 60 , ␣ 30 , ␣ 10) " . entity : setting - lr0 - deepmd a mlips : HyperparameterSetting ; rdfs : label " learning ␣ rate ␣ = ␣ 0.001 ␣ for ␣ DeePMD - kit ␣ demonstration ␣ training ␣ run ␣ on ␣ the ␣ liquid - water ␣ dataset ␣ (10^6 ␣ batches , ␣ batch ␣ size ␣ 4) " ; mlips : forHyperparameter mlips : learningRate ; mlips : isSettingOf entity : run - deepmd - water ; mlips : settingValue 0.001 . entity : setting - rcut -60 - wang2018 a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 6 ␣ for ␣ DeePMD - kit ␣ demonstration ␣ training ␣ run ␣ on ␣ the ␣ liquid water ␣ dataset ␣ (10^6 ␣ batches , ␣ batch ␣ size ␣ 4) " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - deepmd - water ; mlips : settingValue 6 .

Q9 – MLIP run and trained model. A single run of 106 batches at batch size 4 produces the demonstration DeePMD water model. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - deepmd - water a mlips : TrainedModel ; rdfs : label " DeePMD ␣ water ␣ model ␣ ( PBE0 + TS ␣ reference , ␣ demonstration ␣ of ␣ DeePMD - kit ) " . entity : run - deepmd - water

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a mlips : MLIPRun ; rdfs : label " DeePMD - kit ␣ demonstration ␣ training ␣ run ␣ on ␣ the ␣ liquid - water ␣ dataset ␣ (10^6 ␣ batches ,␣ batch ␣ size ␣ 4) " ; mlips : appliesMethod entity : DeePMD ; mlips : hasHyperparameterSetting entity : setting - decay - rate - deepmd , entity : setting - decay steps - deepmd , entity : setting - hidden - deepmd , entity : setting - lr0 - deepmd , entity : setting - rcut -60 - wang2018 ; mlips : produces entity : model - deepmd - water ; mlips : runsOn entity : ds - water - wang2018 .

Q10 – Benchmark results. Test-set RMSEs: 0.028 eV on the 64-water-cell total energy and 0.024 eV/Å on atomic-force components. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - rmse - water - energy a mlips : AccuracyMetric ; rdfs : label " RMSE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 0.028 ␣ [ EV ] " , " Test - set ␣ RMSE ␣ on ␣ total ␣ energy ␣ of ␣ the ␣ 64 - water ␣ cell ␣ ( DeePMD ␣ vs ␣ PBE0 + TS ␣ DFT ) " ; mlips : hasUnit unit : EV ; mlips : isMetricOf entity : result - deepmd - water - energy ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 0.028 . entity : metric - rmse - water - forces a mlips : AccuracyMetric ; rdfs : label " RMSE ␣ of ␣ Force ␣ = ␣ 0.024 ␣ [ EV - PER - ANGSTROM ] " , " Test - set ␣ RMSE ␣ on ␣ atomic ␣ force ␣ components ␣ ( DeePMD ␣ vs ␣ PBE0 + TS ␣ DFT ) " ; mlips : hasUnit unit : EV - PER - ANGSTROM ; mlips : isMetricOf entity : result - deepmd - water - forces ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 0.024 . entity : result - deepmd - water - energy a mlips : BenchmarkResult ; rdfs : label " DeePMD ␣ water ␣ model ␣ ( PBE0 + TS ␣ reference , ␣ demonstration ␣ of ␣ DeePMD - kit ) ␣ on ␣ Liquid ␣ water ␣ (64 ␣ H2O ␣ molecules , ␣ PBC , ␣ ~330 ␣ K ) ␣ in ␣ Wang ␣ et ␣ al . ␣ (2018) : ␣ DeePMD - kit ␣ software ,␣ water ␣ demonstration " ; mlips : evaluatesModel entity : model - deepmd - water ; mlips : hasAccuracyMetric entity : metric - rmse - water - energy ; mlips : isResultOf entity : study - wang2018dpkit ; mlips : targetMaterial entity : mat - water - wang2018 . entity : result - deepmd - water - forces a mlips : BenchmarkResult ; rdfs : label " DeePMD ␣ water ␣ model ␣ ( PBE0 + TS ␣ reference , ␣ demonstration ␣ of ␣ DeePMD - kit ) ␣ on ␣ Liquid ␣ water ␣ (64 ␣ H2O ␣ molecules , ␣ PBC , ␣ ~330 ␣ K ) ␣ in ␣ Wang ␣ et ␣ al . ␣ (2018) : ␣ DeePMD - kit ␣ software ,␣ water ␣ demonstration " ; mlips : evaluatesModel entity : model - deepmd - water ; mlips : hasAccuracyMetric entity : metric - rmse - water - forces ; mlips : isResultOf entity : study - wang2018dpkit ; mlips : targetMaterial entity : mat - water - wang2018 . entity : study - wang2018dpkit mlips : hasResult entity : result - deepmd - water - energy , entity : result - deepmd - water - forces .

Q11 – Computational resources. The paper records training duration of approximately 16 hours on an Intel Core i7-3770 CPU with 32 GB RAM and 4 OpenMP threads. GPU hours, peak memory, and per-atom inference time are not recorded. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > .

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@prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : run - deepmd - water mlips : trainingDuration " 16 ␣ hours " ; mlips : trainingHardware " Intel ␣ Core ␣ i7 -3770 ␣ CPU ␣ with ␣ 32 ␣ GB ␣ RAM , ␣ 4 ␣ OpenMP ␣ threads " .

Q12 – Gaps. The central gap is one of scope: this is a software paper, and the protocol’s "one paper ≡ one method × one material system" framing captures only the demonstration example. The package’s multi-system support, alternate descriptor choices, ensemble training, and downstream MD/i-PI tooling are not encoded. The demonstration’s DFT settings (engine, k-mesh, energy cutoff) are also not surfaced beyond the functional choice; and inference-time data are not reported even though the paper benchmarks DeePMD-LAMMPS performance qualitatively. K.9

Lysogorskiy et al. (2021): PACE applied to Cu and Si

Q1 – Bibliographic identification. Lysogorskiy, van der Oord, Bochkarev, Menon, Rinaldi, Hammerschmidt, Mrovec, Thompson, Csányi, Ortner, and Drautz introduce PACE, a performant C++ implementation of the Atomic Cluster Expansion ([17]) released as a LAMMPS pair-style. Production parameterisations are presented for fcc copper and diamond silicon. Published in npj Computational Materials 7, 97 (2021); doi:10.1038/s41524-021-00559-9. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -7101 -8804 > a schema : Person ; schema : affiliation mlips : RuhrUniversityBochum ; schema : familyName " Drautz " ; schema : givenName " Ralf " ; schema : identifier < https :// orcid . org /0000 -0001 -7101 -8804 > ; schema : name " Ralf ␣ Drautz " . < https :// orcid . org /0000 -0001 -7229 -5758 > a schema : Person ; schema : affiliation mlips : RuhrUniversityBochum ; schema : familyName " Bochkarev " ; schema : givenName " Anton " ; schema : identifier < https :// orcid . org /0000 -0001 -7229 -5758 > ; schema : name " Anton ␣ Bochkarev " . < https :// orcid . org /0000 -0001 -8216 -2254 > a schema : Person ; schema : affiliation mlips : RuhrUniversityBochum ; schema : familyName " Mrovec " ; schema : givenName " Matous " ; schema : identifier < https :// orcid . org /0000 -0001 -8216 -2254 > ; schema : name " Matous ␣ Mrovec " . < https :// orcid . org /0000 -0001 -9837 -8383 > a schema : Person ; schema : affiliation mlips : RuhrUniversityBochum ; schema : familyName " Rinaldi " ; schema : givenName " Matteo " ; schema : identifier < https :// orcid . org /0000 -0001 -9837 -8383 > ; schema : name " Matteo ␣ Rinaldi " . < https :// orcid . org /0000 -0002 -0324 -9114 > a schema : Person ; schema : affiliation entity : org - SandiaNationalLaboratories - lysogorskiy2021ace ; schema : familyName " Thompson " ;

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schema : givenName " Aidan " ; schema : identifier < https :// orcid . org /0000 -0002 -0324 -9114 > ; schema : name " Aidan ␣ Thompson " . < https :// orcid . org /0000 -0002 -2270 -4469 > a schema : Person ; schema : affiliation mlips : RuhrUniversityBochum ; schema : familyName " Hammerschmidt " ; schema : givenName " Thomas " ; schema : identifier < https :// orcid . org /0000 -0002 -2270 -4469 > ; schema : name " Thomas ␣ Hammerschmidt " . < https :// orcid . org /0000 -0002 -6776 -1213 > a schema : Person ; schema : affiliation mlips : RuhrUniversityBochum ; schema : familyName " Menon " ; schema : givenName " Sarath " ; schema : identifier < https :// orcid . org /0000 -0002 -6776 -1213 > ; schema : name " Sarath ␣ Menon " . < https :// orcid . org /0000 -0002 -8180 -2034 > schema : affiliation mlips : UniversityofCambridge . < https :// orcid . org /0000 -0003 -1498 -8120 > a schema : Person ; schema : affiliation entity : org - UniversityofBritishColumbia - lysogorskiy2021ace ; schema : familyName " Ortner " ; schema : givenName " Christoph " ; schema : identifier < https :// orcid . org /0000 -0003 -1498 -8120 > ; schema : name " Christoph ␣ Ortner " . < https :// orcid . org /0000 -0003 -1845 -0387 > a schema : Person ; schema : affiliation mlips : UniversityofCambridge ; schema : familyName " Oord " ; schema : givenName " Cas ␣ van ␣ der " ; schema : identifier < https :// orcid . org /0000 -0003 -1845 -0387 > ; schema : name " Cas ␣ van ␣ der ␣ Oord " . < https :// orcid . org /0000 -0003 -4617 -3188 > a schema : Person ; schema : affiliation mlips : RuhrUniversityBochum ; schema : familyName " Lysogorskiy " ; schema : givenName " Yury " ; schema : identifier < https :// orcid . org /0000 -0003 -4617 -3188 > ; schema : name " Yury ␣ Lysogorskiy " . entity : article - lysogorskiy2021ace a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0001 -7101 -8804 > , < https :// orcid . org /0000 -0001 -7229 -5758 > , < https :// orcid . org /0000 -0001 -8216 -2254 > , < https :// orcid . org /0000 -0001 -9837 -8383 > , < https :// orcid . org /0000 -0002 -0324 -9114 > , < https :// orcid . org /0000 -0002 -2270 -4469 > , < https :// orcid . org /0000 -0002 -6776 -1213 > , < https :// orcid . org /0000 -0002 -8180 -2034 > , < https :// orcid . org /0000 -0003 -1498 -8120 > , < https :// orcid . org /0000 -0003 -1845 -0387 > , < https :// orcid . org /0000 -0003 -4617 -3188 > ; schema : datePublished " 2021 " ^^ xsd : gYear ; schema : name " Performant ␣ implementation ␣ of ␣ the ␣ atomic ␣ cluster ␣ expansion ␣ ( PACE ) ␣ and ␣ application ␣ to ␣ copper ␣ and ␣ silicon " ; schema : sameAs < https :// doi . org /10.1038/ s41524 -021 -00559 -9 > . entity : org - SandiaNationalLaboratories - lysogorskiy2021ace a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Sandia ␣ National ␣ Laboratories " ; schema : identifier < https :// ror . org /01 apwpt12 > ; schema : name " Sandia ␣ National ␣ Laboratories " . entity : org - UniversityofBritishColumbia - lysogorskiy2021ace a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " University ␣ of ␣ British ␣ Columbia " ; schema : identifier < https :// ror . org /03 rmrcq20 > ; schema : name " University ␣ of ␣ British ␣ Columbia " . entity : study - lysogorskiy2021ace a mlips : BenchmarkStudy ; rdfs : label " Lysogorskiy ␣ et ␣ al . ␣ (2021) : ␣ PACE ␣ applied ␣ to ␣ Cu ␣ and ␣ Si " ; mlips : reportedIn entity : article - lysogorskiy2021ace .

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Q2 – Material system. Two single-element systems are encoded as separate MaterialSystem instances: copper (fcc, with bcc/dhcp/hcp polymorphs and surfaces/defects in the reference set) and silicon (diamond cubic, with reference data from the GAP-Si general-purpose database of Bartók et al. 2018). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat -Cu - lysogorskiy2021ace a mlips : MaterialSystem ; rdfs : label " Copper ␣ ( fcc , ␣ with ␣ bcc / hcp / dhcp ␣ polymorphs ␣ and ␣ surfaces / defects ␣ in ␣ the ␣ reference ␣ set ) " ; mlips : chemicalFormula " Cu " ; mlips : materialClass " Elemental ␣ metal ; ␣ fcc ␣ ground ␣ state , ␣ validated ␣ across ␣ fcc / bcc / dhcp / hcp ␣ polymorphs , ␣ surfaces , ␣ and ␣ clusters " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q753 > . entity : mat -Si - lysogorskiy2021ace a mlips : MaterialSystem ; rdfs : label " Silicon ␣ ( diamond ␣ cubic , ␣ plus ␣ surfaces , ␣ vacancies , ␣ interstitials , ␣ and ␣ liquid )" ; mlips : chemicalFormula " Si " ; mlips : materialClass " Elemental ␣ semiconductor ; ␣ diamond - cubic ␣ ground ␣ state . ␣ Reference ␣ data ␣ is ␣ the ␣ GAP ␣ general - purpose ␣ Si ␣ database ␣ of ␣ Bartok ␣ et ␣ al . ␣ 2018 " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q670 > .

Q3 – Reference calculation method. Both reference datasets come from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft -Cu - lysogorskiy2021ace a mlips : DFTCalculation . entity : dft -Si - lysogorskiy2021ace a mlips : DFTCalculation .

Q4 – Reference settings. Cu reference data are produced with FHI-aims at the PBE level (small clusters, bulk phases, surfaces and slabs, configurations with displaced or missing atoms), partly assembled with the pyiron workflow framework. Si reference data are the published GAP-Si general-purpose fitting database from CASTEP (PW91 inherited from Bartók et al. 2018). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft -Cu - lysogorskiy2021ace mlips : hasDFTSettings entity : dft - settings - Cu - lysogorskiy2021ace . entity : dft -Si - lysogorskiy2021ace mlips : hasDFTSettings entity : dft - settings - Si - lysogorskiy2021ace . entity : dft - settings - Cu - lysogorskiy2021ace a mlips : DFTSettings ; mlips : usedDFTCode mlips : FHIaims ; mlips : xcFunctional mlips : PBE . entity : dft - settings - Si - lysogorskiy2021ace

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a mlips : DFTSettings ; rdfs : comment " Inherited ␣ from ␣ the ␣ Bartok ␣ et ␣ al . ␣ 2018 ␣ GAP - Si ␣ reference ␣ database . " ; mlips : usedDFTCode mlips : CASTEP ; mlips : xcFunctional mlips : PW91 .

Q5 – Training dataset. Cu: in-house FHI-aims set covering clusters, bulk polymorphs, surfaces, slabs, and defects (configuration count not enumerated in the main text). Si: the published Bartók-2018 GAP-Si database of 2,475 configurations covering crystal phases, surfaces, vacancies, interstitials, and liquid Si. Cu covers energies+forces; Si additionally covers virials. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds -Cu - lysogorskiy2021ace a mlips : TrainingDataset ; rdfs : label " PACE - Cu ␣ reference ␣ data : ␣ small ␣ clusters , ␣ bulk ␣ phases , ␣ surfaces , ␣ slabs , ␣ and ␣ defective ␣ configurations ␣ of ␣ copper , ␣ generated ␣ with ␣ FHI - aims ; ␣ assembled ␣ in ␣ part ␣ with ␣ the ␣ pyiron ␣ workflow ␣ framework " ; mlips : coversMaterial entity : mat - Cu - lysogorskiy2021ace ; mlips : coversProperty mlips : Energy , mlips : Forces ; mlips : datasetProvenance mlips : InHouse ; mlips : hasDFTCalculation entity : dft - Cu - lysogorskiy2021ace ; mlips : wasRunBy entity : run - ace - Cu - lysogorskiy2021ace . entity :ds -Si - lysogorskiy2021ace a mlips : TrainingDataset ; rdfs : label " PACE - Si ␣ reference ␣ data : ␣ the ␣ published ␣ Bartok -2018 ␣ general - purpose ␣ Si ␣ GAP ␣ fitting ␣ database ␣ (2475 ␣ configurations ␣ covering ␣ crystal ␣ phases , ␣ surfaces , ␣ vacancies ,␣ interstitials , ␣ and ␣ liquid ) " ; mlips : coversMaterial entity : mat - Si - lysogorskiy2021ace ; mlips : coversProperty mlips : Energy , mlips : Forces , mlips : Virials ; mlips : datasetProvenance mlips : Published ; mlips : hasDFTCalculation entity : dft - Si - lysogorskiy2021ace ; mlips : numConfigurations 2475 ; mlips : wasRunBy entity : run - ace - Si - lysogorskiy2021ace .

Q6 – Sampling strategies. Cu: configurational coverage of clusters, polymorphs, surfaces, and defective structures. Si: reuse of the published GAP-Si database’s sampling strategy. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :cu - sampling - lysogorskiy2021ace a mlips : SamplingStrategy ; rdfs : comment " The ␣ Cu ␣ reference ␣ data ␣ is ␣ partly ␣ described ␣ in ␣ Drautz ␣ 2019 ␣ ref ␣ [1] ␣ and ␣ extended ␣ for ␣ this ␣ work ; ␣ it ␣ includes ␣ small ␣ clusters , ␣ bulk ␣ Cu ␣ polymorphs , ␣ surfaces ␣ and ␣ slabs , ␣ and ␣ configurations ␣ with ␣ slightly ␣ displaced ␣ or ␣ missing ␣ atoms . ␣ Part ␣ of ␣ the ␣ data ␣ was ␣ assembled ␣ with ␣ the ␣ pyiron ␣ workflow ␣ framework . " ; rdfs : label " Cu ␣ reference - set ␣ construction ␣ ( clusters , ␣ polymorphs , ␣ surfaces , ␣ defects ) " . entity :ds -Cu - lysogorskiy2021ace mlips : samplingStrategy entity : cu - sampling - lysogorskiy2021ace . entity :ds -Si - lysogorskiy2021ace mlips : samplingStrategy entity : si - sampling - lysogorskiy2021ace . entity :si - sampling - lysogorskiy2021ace a mlips : SamplingStrategy ; rdfs : comment " The ␣ Si ␣ reference ␣ data ␣ is ␣ the ␣ published ␣ GAP - Si ␣ fitting ␣ database ␣ ( Bartok ␣ et ␣ al .␣ 2018) ,␣ which ␣ covers ␣ a ␣ wide ␣ range ␣ of ␣ bulk ␣ crystal ␣ phases , ␣ surfaces , ␣ vacancies , ␣ interstitials , ␣ and ␣ liquid ␣ silicon ␣ configurations . " ;

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Hernández et al. rdfs : label " Si ␣ reference - set ␣ reuse ␣ from ␣ the ␣ GAP - Si ␣ general - purpose ␣ database " .

Q7 – MLIP method, components, implementation. The method is the Atomic Cluster Expansion of Drautz 2019: per-atom property 𝜑𝑖 expanded over body-ordered multi-atom basis functions, with truncation at body order 𝜈 max and total energy as a sum over per-atom embeddings. The Cu fit uses a nonlinear two-density Finnis–Sinclair embedding; the Si fit uses a linear embedding at 𝜈 max = 4. Implementation: PACE (C++ LAMMPS pair_style). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : bodyOrder mlips : isHyperparameterOf entity : ACE - lysogorskiy2021ace . mlips : cutoffRadius mlips : isHyperparameterOf entity : ACE - lysogorskiy2021ace . entity : ACE - lysogorskiy2021ace a mlips : MLIPMethod ; rdfs : label " Atomic ␣ Cluster ␣ Expansion ␣ ( ACE ) ␣ of ␣ Drautz ␣ 2019 , ␣ in ␣ the ␣ PACE ␣ formulation " ; mlips : hasDescriptor mlips : AtomicClusterExpansionDescriptor ; mlips : hasFunctionalForm entity : ace - functional - form - lysogorskiy2021ace ; mlips : hasHyperparameter mlips : bodyOrder , mlips : cutoffRadius , entity : hp - nbasis lysogorskiy2021ace ; mlips : hasImplementation entity : pace - impl - lysogorskiy2021ace ; mlips : hasLossFunction entity : ace - loss - lysogorskiy2021ace ; mlips : supportsSimulation mlips : GeometryOptimization , mlips : MolecularDynamics , mlips : PhononCalculation , mlips : ThermodynamicIntegration . entity : ace - functional - form - lysogorskiy2021ace a mlips : FunctionalForm ; rdfs : label " Linear ␣ ( or ␣ Finnis - Sinclair - style ␣ nonlinear ) ␣ embedding ␣ of ␣ body - ordered ␣ ACE ␣ basis ␣ functions ; ␣ per - atom ␣ property ␣ phi_i ␣ is ␣ expanded ␣ over ␣ multi - atom ␣ basis ␣ terms ␣ with ␣ truncation ␣ at ␣ body ␣ order ␣ nu_max ; ␣ total ␣ energy ␣ is ␣ the ␣ sum ␣ of ␣ per - atom ␣ embeddings " . entity : ace - loss - lysogorskiy2021ace a mlips : LossFunction ; rdfs : label " Weighted ␣ least - squares ␣ on ␣ energies ␣ and ␣ forces ␣ ( linear ␣ regression ␣ for ␣ Si ; ␣ nonlinear ␣ two - density ␣ Finnis - Sinclair ␣ embedding ␣ optimisation ␣ for ␣ Cu ) " . entity :hp - nbasis - lysogorskiy2021ace a mlips : Hyperparameter ; rdfs : label " PACE ␣ total ␣ linear ␣ basis ␣ size " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : integer ; mlips : hyperparameterName " num_basis_functions " ; mlips : isHyperparameterOf entity : ACE - lysogorskiy2021ace . entity : pace - impl - lysogorskiy2021ace a mlips : Implementation ; mlips : implementedIn mlips : PACE ; mlips : isImplementationOf entity : ACE - lysogorskiy2021ace ; mlips : version " PACE ␣ C ++ ␣ ( LAMMPS ␣ pair_style ) " .

Q8 – Hyperparameter settings. Reported settings: Cu cutoff radius 𝑟𝑐 = 7.4 Å; Cu basis size 2,072 parameters (756 expansion coefficients per atomic density × 2 densities + 560 radial-function parameters); Si linear basis size 6,827 functions at body order 𝜈 max = 4. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > .

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entity : setting - bodyorder - Si - lysogorskiy2021ace a mlips : HyperparameterSetting ; rdfs : label " body ␣ order ␣ = ␣ 4 ␣ ( Si ␣ linear ␣ ACE ; ␣ Cu ␣ Finnis - Sinclair ␣ embedding ␣ uses ␣ two ␣ atomic ␣ densities ) ␣ for ␣ PACE - Si ␣ fitting ␣ run ␣ ( linear ␣ ACE , ␣ nu_max =4) " ; mlips : forHyperparameter mlips : bodyOrder ; mlips : isSettingOf entity : run - ace - Si - lysogorskiy2021ace ; mlips : settingValue " 4 ␣ ( Si ␣ linear ␣ ACE ; ␣ Cu ␣ Finnis - Sinclair ␣ embedding ␣ uses ␣ two ␣ atomic ␣ densities ) " . entity : setting - nbasis - Cu - lysogorskiy2021ace a mlips : HyperparameterSetting ; rdfs : label " PACE ␣ total ␣ linear ␣ basis ␣ size ␣ = ␣ 2072 ␣ ( Cu : ␣ 756 ␣ expansion ␣ coefficients ␣ per ␣ atomic ␣ density ␣ x ␣ 2 ␣ densities ␣ + ␣ 560 ␣ radial - function ␣ parameters ) ␣ for ␣ PACE - Cu ␣ fitting ␣ run ␣( nonlinear ␣ two - density ␣ Finnis - Sinclair ␣ embedding ) " ; mlips : forHyperparameter entity : hp - nbasis - lysogorskiy2021ace ; mlips : isSettingOf entity : run - ace - Cu - lysogorskiy2021ace ; mlips : settingValue " 2072 ␣ ( Cu : ␣ 756 ␣ expansion ␣ coefficients ␣ per ␣ atomic ␣ density ␣ x ␣ 2 ␣ densities ␣ + ␣ 560 ␣ radial - function ␣ parameters ) " . entity : setting - nbasis - Si - lysogorskiy2021ace a mlips : HyperparameterSetting ; rdfs : label " PACE ␣ total ␣ linear ␣ basis ␣ size ␣ = ␣ 6827 ␣ ( Si ␣ linear ␣ basis ␣ functions ) ␣ for ␣ PACE Si ␣ fitting ␣ run ␣ ( linear ␣ ACE , ␣ nu_max =4) " ; mlips : forHyperparameter entity : hp - nbasis - lysogorskiy2021ace ; mlips : isSettingOf entity : run - ace - Si - lysogorskiy2021ace ; mlips : settingValue " 6827 ␣ ( Si ␣ linear ␣ basis ␣ functions ) " . entity : setting - rcut - Cu - lysogorskiy2021ace a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 7.4 ␣ ( Cu ) ␣ for ␣ PACE - Cu ␣ fitting ␣ run ␣ ( nonlinear ␣ two - density ␣ Finnis - Sinclair ␣ embedding ) " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - ace - Cu - lysogorskiy2021ace ; mlips : settingValue " 7.4 ␣ ( Cu ) " .

Q9 – MLIP run and trained model. Two training runs are encoded: one for PACE-Cu (nonlinear Finnis–Sinclair embedding) and one for PACE-Si (linear ACE, 𝜈 max = 4). Both produce a single TrainedModel with a recorded per-atom inference time (inferenceTimePerAtom = 0.00032 s/atom for Cu, 0.0008 s/atom for Si). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - ace -Cu - lysogorskiy2021ace a mlips : TrainedModel ; rdfs : label " PACE - Cu ␣ ( general - purpose ␣ ACE ␣ for ␣ fcc ␣ copper ) " . entity : model - ace -Si - lysogorskiy2021ace a mlips : TrainedModel ; rdfs : label " PACE - Si ␣ ( linear ␣ ACE ␣ matching ␣ GAP - Si ␣ accuracy ) " . entity : run - ace -Cu - lysogorskiy2021ace a mlips : MLIPRun ; rdfs : label " PACE - Cu ␣ fitting ␣ run ␣ ( nonlinear ␣ two - density ␣ Finnis - Sinclair ␣ embedding ) " ; mlips : appliesMethod entity : ACE - lysogorskiy2021ace ; mlips : hasHyperparameterSetting entity : setting - nbasis - Cu - lysogorskiy2021ace , entity : setting - rcut - Cu - lysogorskiy2021ace ; mlips : produces entity : model - ace - Cu - lysogorskiy2021ace ; mlips : runsOn entity : ds - Cu - lysogorskiy2021ace . entity : run - ace -Si - lysogorskiy2021ace a mlips : MLIPRun ; rdfs : label " PACE - Si ␣ fitting ␣ run ␣ ( linear ␣ ACE , ␣ nu_max =4) " ; mlips : appliesMethod entity : ACE - lysogorskiy2021ace ; mlips : hasHyperparameterSetting entity : setting - bodyorder - Si - lysogorskiy2021ace , entity : setting - nbasis - Si - lysogorskiy2021ace ; mlips : produces entity : model - ace - Si - lysogorskiy2021ace ; mlips : runsOn entity : ds - Si - lysogorskiy2021ace .

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Q10 – Benchmark results. PACE-Cu attains a final fit error of 2.9 meV/atom on structures within 1 eV of the ground state (after ground-state fine-tuning), with force errors near 15 meV/Å on higher-energy structures. PACE-Si matches GAP-Si accuracy on the Bartók-2018 database with energy MAE 1.81 meV/atom and force MAE 82 meV/Å. Three BenchmarkResult instances cover these. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - ace -Cu - fit - lysogorskiy2021ace a mlips : AccuracyMetric ; rdfs : label " Final ␣ fit ␣ error ␣ on ␣ Cu ␣ reference ␣ data ␣ within ␣ 1 ␣ eV ␣ of ␣ the ␣ ground ␣ state ␣ ( after ␣ ground - state ␣ fine - tuning ) " , " RMSE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 2.9 ␣ [ millielectronvolt ␣ per ␣ atom ] " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - ace - Cu - fit - lysogorskiy2021ace ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 2.9 . entity : metric - ace -Si - energy - lysogorskiy2021ace a mlips : AccuracyMetric ; rdfs : label " Energy ␣ error ␣ on ␣ the ␣ Bartok -2018 ␣ GAP - Si ␣ database ␣ ( PACE - Si ␣ linear ␣ ACE ) " , " MAE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 1.81 ␣ [ millielectronvolt ␣ per ␣ atom ] " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - ace - Si - energy - lysogorskiy2021ace ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 1.81 . entity : metric - ace -Si - forces - lysogorskiy2021ace a mlips : AccuracyMetric ; rdfs : label " Force - component ␣ error ␣ on ␣ the ␣ Bartok -2018 ␣ GAP - Si ␣ database ␣ ( PACE - Si ␣ linear ␣ ACE )" , " MAE ␣ of ␣ Force ␣ = ␣ 82 ␣ [ millielectronvolt ␣ per ␣ angstrom ] " ; mlips : hasUnit mlips : MilliEV - PER - ANGSTROM ; mlips : isMetricOf entity : result - ace - Si - forces - lysogorskiy2021ace ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 82 . entity : result - ace -Cu - fit - lysogorskiy2021ace a mlips : BenchmarkResult ; rdfs : label " PACE - Cu ␣ ( general - purpose ␣ ACE ␣ for ␣ fcc ␣ copper ) ␣ on ␣ Copper ␣ ( fcc , ␣ with ␣ bcc / hcp / dhcp ␣ polymorphs ␣ and ␣ surfaces / defects ␣ in ␣ the ␣ reference ␣ set ) ␣ in ␣ Lysogorskiy ␣ et ␣ al . ␣ (2021) :␣ PACE ␣ applied ␣ to ␣ Cu ␣ and ␣ Si " ; mlips : evaluatesModel entity : model - ace - Cu - lysogorskiy2021ace ; mlips : hasAccuracyMetric entity : metric - ace - Cu - fit - lysogorskiy2021ace ; mlips : isResultOf entity : study - lysogorskiy2021ace ; mlips : targetMaterial entity : mat - Cu - lysogorskiy2021ace . entity : result - ace -Si - energy - lysogorskiy2021ace a mlips : BenchmarkResult ; rdfs : label " PACE - Si ␣ ( linear ␣ ACE ␣ matching ␣ GAP - Si ␣ accuracy ) ␣ on ␣ Silicon ␣ ( diamond ␣ cubic , ␣ plus ␣ surfaces , ␣ vacancies , ␣ interstitials , ␣ and ␣ liquid ) ␣ in ␣ Lysogorskiy ␣ et ␣ al . ␣ (2021) : ␣ PACE ␣ applied ␣ to ␣ Cu ␣ and ␣ Si " ; mlips : evaluatesModel entity : model - ace - Si - lysogorskiy2021ace ; mlips : hasAccuracyMetric entity : metric - ace - Si - energy - lysogorskiy2021ace ; mlips : isResultOf entity : study - lysogorskiy2021ace ; mlips : targetMaterial entity : mat - Si - lysogorskiy2021ace . entity : result - ace -Si - forces - lysogorskiy2021ace a mlips : BenchmarkResult ; rdfs : label " PACE - Si ␣ ( linear ␣ ACE ␣ matching ␣ GAP - Si ␣ accuracy ) ␣ on ␣ Silicon ␣ ( diamond ␣ cubic , ␣ plus ␣ surfaces , ␣ vacancies , ␣ interstitials , ␣ and ␣ liquid ) ␣ in ␣ Lysogorskiy ␣ et ␣ al . ␣ (2021) : ␣ PACE ␣ applied ␣ to ␣ Cu ␣ and ␣ Si " ; mlips : evaluatesModel entity : model - ace - Si - lysogorskiy2021ace ; mlips : hasAccuracyMetric entity : metric - ace - Si - forces - lysogorskiy2021ace ; mlips : isResultOf entity : study - lysogorskiy2021ace ; mlips : targetMaterial entity : mat - Si - lysogorskiy2021ace .

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entity : study - lysogorskiy2021ace mlips : hasResult entity : result - ace - Cu - fit - lysogorskiy2021ace , entity : result - ace - Si energy - lysogorskiy2021ace , entity : result - ace - Si - forces - lysogorskiy2021ace .

Q11 – Computational resources. The headline claim is computational performance: PACE shifts the accuracy/cost Pareto front for ML interatomic potentials. We capture the per-atom inference times on the trained models in Q9 (0.32 ms/atom for Cu, 0.80 ms/atom for Si on a single force call). Training duration, GPU/CPU hours, training hardware, and peak memory are not reported. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - ace -Cu - lysogorskiy2021ace mlips : inferenceTimePerAtom 0.00032 . entity : model - ace -Si - lysogorskiy2021ace mlips : inferenceTimePerAtom 0.0008 .

Q12 – Gaps. The protocol’s "one paper ≡ one method × one material" framing is mildly stretched: the paper trains two ACE parameterisations (Cu and Si) and we encode both within one lysogorskiy2021ace.ttl via two MaterialSystem, two MLIPRun, and two TrainedModel instances rather than splitting into sibling files. Other unreported items: explicit DFT settings on the Cu side beyond engine and functional (energy cutoff, k-mesh, pseudopotential / NAO basis); explicit numConfigurations for the Cu reference set; the Pareto benchmark is reported as a derived figure rather than an AccuracyMetric across all five models compared (ACE, EAM, SNAP, GTINV, GAP); training-cost metadata. K.10

Smith et al. (2019): ANI-1ccx via DFT→CCSD(T) transfer learning

Q1 – Bibliographic identification. Smith, Nebgen, Zubatyuk, Lubbers, Devereux, Barros, Tretiak, Isayev, and Roitberg present ANI-1ccx, a neural network potential pretrained on a large DFT dataset (ANI-1x) and fine-tuned by transfer learning on a much smaller DLPNO-CCSD(T)/CBS dataset, achieving coupled-cluster accuracy on H/C/N/O organic molecules. Published in Nat. Commun. 10, 2903 (2019); arXiv:1903.10405. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -5310 -3263 > a schema : Person ; schema : affiliation mlips : LosAlamosNationalLaboratory , entity : org CenterforIntegratedNanotechnologies - smith2019ccx ; schema : familyName " Nebgen " ; schema : givenName " Benjamin ␣ T . " ; schema : identifier < https :// orcid . org /0000 -0001 -5310 -3263 > ; schema : name " Benjamin ␣ T . ␣ Nebgen " . < https :// orcid . org /0000 -0001 -5547 -3647 > a schema : Person ; schema : affiliation mlips : LosAlamosNationalLaboratory , entity : org CenterforIntegratedNanotechnologies - smith2019ccx , entity : org LosAlamosNationalSecurityUnitedStates - smith2019ccx ; schema : familyName " Tretiak " ;

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schema : givenName " Sergei " ; schema : identifier < https :// orcid . org /0000 -0001 -5547 -3647 > ; schema : name " Sergei ␣ Tretiak " . < https :// orcid . org /0000 -0001 -7314 -7896 > schema : affiliation mlips : LosAlamosNationalLaboratory , mlips : UniversityofFlorida . < https :// orcid . org /0000 -0001 -7581 -8497 > a schema : Person ; schema : affiliation entity : org - UniversityofNorthCarolinaatChapelHill - smith2019ccx ; schema : familyName " Isayev " ; schema : givenName " Olexandr " ; schema : identifier < https :// orcid . org /0000 -0001 -7581 -8497 > ; schema : name " Olexandr ␣ Isayev " . < https :// orcid . org /0000 -0002 -1333 -5972 > a schema : Person ; schema : affiliation mlips : LosAlamosNationalLaboratory ; schema : familyName " Barros " ; schema : givenName " Kipton " ; schema : identifier < https :// orcid . org /0000 -0002 -1333 -5972 > ; schema : name " Kipton ␣ Barros " . < https :// orcid . org /0000 -0002 -7285 -9389 > a schema : Person ; schema : affiliation mlips : LosAlamosNationalLaboratory , entity : org JacksonStateUniversity - smith2019ccx ; schema : familyName " Zubatyuk " ; schema : givenName " Roman " ; schema : identifier < https :// orcid . org /0000 -0002 -7285 -9389 > ; schema : name " Roman ␣ Zubatyuk " . < https :// orcid . org /0000 -0002 -9001 -9973 > a schema : Person ; schema : affiliation mlips : LosAlamosNationalLaboratory ; schema : familyName " Lubbers " ; schema : givenName " Nicholas " ; schema : identifier < https :// orcid . org /0000 -0002 -9001 -9973 > ; schema : name " Nicholas ␣ Lubbers " . < https :// orcid . org /0000 -0003 -3963 -8784 > schema : affiliation mlips : UniversityofFlorida . entity : article - smith2019ccx a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0001 -5310 -3263 > , < https :// orcid . org /0000 -0001 -5547 -3647 > , < https :// orcid . org /0000 -0001 -7314 -7896 > , < https :// orcid . org /0000 -0001 -7581 -8497 > , < https :// orcid . org /0000 -0002 -1333 -5972 > , < https :// orcid . org /0000 -0002 -7285 -9389 > , < https :// orcid . org /0000 -0002 -9001 -9973 > , < https :// orcid . org /0000 -0003 -3963 -8784 > , entity : person - Devereux - smith2019ccx ; schema : datePublished " 2019 " ^^ xsd : gYear ; schema : name " Approaching ␣ coupled ␣ cluster ␣ accuracy ␣ with ␣ a ␣ general - purpose ␣ neural ␣ network ␣ potential ␣ through ␣ transfer ␣ learning " ; schema : sameAs < https :// doi . org /10.1038/ s41467 -019 -10827 -4 > . entity : org - CenterforIntegratedNanotechnologies - smith2019ccx a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Center ␣ for ␣ Integrated ␣ Nanotechnologies " ; schema : identifier < https :// ror . org /031 yh0y38 > ; schema : name " Center ␣ for ␣ Integrated ␣ Nanotechnologies " . entity : org - JacksonStateUniversity - smith2019ccx a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Jackson ␣ State ␣ University " ; schema : identifier < https :// ror . org /01 ecnnp60 > ; schema : name " Jackson ␣ State ␣ University " . entity : org - LosAlamosNationalSecurityUnitedStates - smith2019ccx a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Los ␣ Alamos ␣ National ␣ Security ␣ ( United ␣ States ) " ; schema : identifier < https :// ror . org /037 ddaj94 > ; schema : name " Los ␣ Alamos ␣ National ␣ Security ␣ ( United ␣ States ) " . entity : org - UniversityofNorthCarolinaatChapelHill - smith2019ccx a schema : Organization ;

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rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " University ␣ of ␣ North ␣ Carolina ␣ at ␣ Chapel ␣ Hill " ; schema : identifier < https :// ror . org /0130 frc33 > ; schema : name " University ␣ of ␣ North ␣ Carolina ␣ at ␣ Chapel ␣ Hill " . entity : person - Devereux - smith2019ccx a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " ; schema : affiliation mlips : UniversityofFlorida ; schema : familyName " Devereux " ; schema : givenName " Christian " ; schema : name " Christian ␣ Devereux " . entity : study - smith2019ccx a mlips : BenchmarkStudy ; rdfs : label " Smith ␣ et ␣ al . ␣ (2019) : ␣ ANI -1 ccx ␣ via ␣ transfer ␣ learning ␣ to ␣ CCSD ( T ) " ; mlips : reportedIn entity : article - smith2019ccx .

Q2 – Material system. The MLIP covers the H/C/N/O chemical space of small organic molecules (drug-like and reaction-relevant species, average ∼15 atoms per molecule, primarily from the GDB11 universe of ∼57k distinct species). We model this as one MaterialSystem at the chemical-space level rather than enumerating individual molecules. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat - organics - HCNO - smith2019ccx a mlips : MaterialSystem ; rdfs : comment " Wikidata ␣ Q174211 ␣ ( ' organic ␣ compound ') ␣ is ␣ the ␣ most ␣ generic ␣ appropriate ␣ entry ;␣ the ␣ H / C / N / O ␣ chemical - space ␣ slice ␣ has ␣ no ␣ dedicated ␣ Wikidata ␣ entry ␣ as ␣ of ␣ 2026 -04 -28. " ; rdfs : label " Organic ␣ molecules ␣ in ␣ the ␣ H / C / N / O ␣ chemical ␣ space ␣ ( drug - like ␣ and ␣ reaction relevant ␣ species , ␣ average ␣ ~15 ␣ atoms ␣ per ␣ molecule ) " ; mlips : chemicalFormula " C_xH_yN_zO_w ␣ ( organic ␣ small ␣ molecules ) " ; mlips : materialClass " Molecular ; ␣ small ␣ organic ␣ molecules ␣ over ␣ the ␣ H / C / N / O ␣ chemical ␣ space ,␣ primarily ␣ from ␣ the ␣ GDB -11 ␣ universe ␣ (~57 k ␣ distinct ␣ molecules ) " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q174211 > .

Q3 – Reference calculation method. Two reference calculations apply: a wave-function reference (CCSD(T)) for the headline fine-tuning step, and a DFT reference for the pretraining step. This is the corpus’ only WaveFunctionCalculation entry. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : ccsdt - smith2019ccx a mlips : WaveFunctionCalculation . entity : dft - smith2019ccx a mlips : DFTCalculation .

Q4 – Reference settings. The wave-function reference is DLPNO-CCSD(T)/CBS (the localised DLPNO-CCSD(T) method of Neese et al., extrapolated from cc-pVDZ / cc-pVTZ), denoted CCSD(T)*

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in the paper and computed in ORCA. The DFT pretraining reference is 𝜔B97X with the 6-31G* Gaussian basis (all-electron, Γ-only, isolated-molecule limit). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : basis -6 -31 gstar - smith2019ccx a mlips : DftBasisSet ; rdfs : comment " Pople - style ␣ split - valence ␣ double - zeta ␣ Gaussian ␣ basis ␣ with ␣ d ␣ polarisation ␣ on ␣ heavy ␣ atoms ␣ ( equivalent ␣ to ␣ 6 -31 G ( d ) ) ; ␣ molecular ␣ all - electron ␣ DFT . " ; rdfs : label " 6 -31 G * " ; mlips : candidateForVocabulary mlips : DftBasisSet . entity : ccsdt - smith2019ccx mlips : hasWaveFunctionSettings entity : wf - settings - smith2019ccx . entity : dft - settings - smith2019ccx a mlips : DFTSettings ; rdfs : comment " All - electron ␣ Gaussian ␣ basis ␣ ( no ␣ pseudopotential ) . " ; mlips : dftBasisSet entity : basis -6 -31 gstar - smith2019ccx ; mlips : kPointMesh " Gamma - only ␣ ( isolated ␣ molecules ) " ; mlips : usedDFTCode mlips : Gaussian ; mlips : xcFunctional mlips : omegaB97X . entity : dft - smith2019ccx mlips : hasDFTSettings entity : dft - settings - smith2019ccx . entity :wf - settings - smith2019ccx a mlips : WaveFunctionSettings ; rdfs : comment " CCSD ( T ) */ CBS ␣ approximation : ␣ localised ␣ DLPNO - CCSD ( T ) ␣ of ␣ Neese ␣ et ␣ al . ␣ extrapolated ␣ from ␣ cc - pVDZ / cc - pVTZ ␣ to ␣ the ␣ complete - basis - set ␣ limit . " ; mlips : basisSet " cc - pVDZ / cc - pVTZ " ; mlips : usedReferenceCode mlips : ORCA ; mlips : wfMethod mlips : DLPNO_CCSDT .

Q5 – Training dataset. The CCSD(T)*/CBS fine-tuning set has ∼500,000 data points covering ∼480,000 molecules; the pretraining ANI-1x corpus has 5 M conformations from ∼57k molecules. Energies are covered (no forces or stresses). Provenance is augmented (CCSD(T) labels are added on top of an existing DFT-labelled set). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - ani1ccx - smith2019ccx a mlips : TrainingDataset ; rdfs : label " ANI -1 ccx ␣ fine - tuning ␣ set : ␣ ~500 ,000 ␣ CCSD ( T ) */ CBS - labelled ␣ conformations ␣ grown ␣ from ␣ ~480 ,000 ␣ molecules ␣ via ␣ active ␣ learning , ␣ pre - trained ␣ model ␣ used ␣ 5 M ␣ ANI -1 x␣ DFT ␣ conformations ␣ from ␣ ~57 k ␣ molecules " ; mlips : coversMaterial entity : mat - organics - HCNO - smith2019ccx ; mlips : coversProperty mlips : Energy ; mlips : datasetProvenance mlips : Augmented ; mlips : hasDFTCalculation entity : dft - smith2019ccx ; mlips : hasReferenceCalculation entity : ccsdt - smith2019ccx ; mlips : numConfigurations 500000 ; mlips : wasRunBy entity : run - ani1ccx - smith2019ccx .

Q6 – Sampling strategies. Two strategies were combined: query-by-committee active learning (ANI’s ensemble-disagreement loop drives selection of new molecules for CCSD(T)*/CBS

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computation, growing the dataset to ∼480k molecules) and the diverse-conformer / normal-mode sampling that underlies the ANI-1x parent corpus. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : active - learning - smith2019ccx a mlips : SamplingStrategy ; rdfs : comment " ANI -1 ccx ␣ is ␣ grown ␣ via ␣ an ␣ active - learning ␣ loop : ␣ ensemble ␣ disagreement ␣ on ␣ candidate ␣ conformations ␣ selects ␣ the ␣ next ␣ round ␣ of ␣ molecules ␣ for ␣ CCSD ( T ) */ CBS ␣ recomputation . " ; rdfs : label " Active ␣ learning ␣ ( query - by - committee ␣ on ␣ ensemble ␣ disagreement ) " . entity :ds - ani1ccx - smith2019ccx mlips : samplingStrategy entity : active - learning - smith2019ccx , entity : normal - mode smith2019ccx . entity : normal - mode - smith2019ccx a mlips : SamplingStrategy ; rdfs : comment " Pretraining ␣ ANI -1 x ␣ configurations ␣ are ␣ sampled ␣ by ␣ perturbations ␣ along ␣ normal - mode ␣ coordinates ␣ and ␣ other ␣ diverse - conformation ␣ strategies ␣ (~22 M ␣ conformations ␣ from ␣ ~57 k ␣ molecules ␣ underlie ␣ the ␣ 5M - frame ␣ DFT ␣ corpus ) . " ; rdfs : label " Normal - mode ␣ + ␣ diverse - conformer ␣ sampling ␣ of ␣ the ␣ ANI -1 x ␣ parent ␣ corpus " .

Q7 – MLIP method, components, implementation. The method is the ANI Behler–Parrinello-style high-dimensional NN with ANI atom-centred symmetry functions. Per-element fully-connected feed-forward subnetworks operate on the symmetry-function inputs; total energy is the sum of per-atom contributions. Loss is energy-only MSE on per-molecule total energies (no force or stress targets). Optimisation is Adam with exponential learning-rate decay; the implementation is TorchANI. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : ANI - smith2019ccx . entity : ANI - smith2019ccx a mlips : MLIPMethod ; rdfs : label " ANI ␣ ( Behler - Parrinello - style ␣ HDNN ␣ with ␣ ANI ␣ symmetry ␣ functions ) " ; mlips : hasDescriptor mlips : ANIDescriptor ; mlips : hasFunctionalForm entity : ani - form - smith2019ccx ; mlips : hasHyperparameter mlips : cutoffRadius ; mlips : hasImplementation entity : torchani - smith2019ccx ; mlips : hasLossFunction entity : ani - loss - smith2019ccx ; mlips : hasTrainingAlgorithm entity : adam - smith2019ccx ; mlips : supportsSimulation mlips : GeometryOptimization . entity : adam - smith2019ccx a mls : Algorithm ; rdfs : label " Adam ␣ ( with ␣ exponential ␣ learning - rate ␣ decay ) " . entity : ani - form - smith2019ccx a mlips : FunctionalForm ; rdfs : label " Per - element ␣ fully - connected ␣ feed - forward ␣ subnetwork ␣ operating ␣ on ␣ ANI ␣ atom centred ␣ symmetry ␣ functions ; ␣ total ␣ energy ␣ is ␣ a ␣ sum ␣ of ␣ per - atom ␣ contributions " . entity : ani - loss - smith2019ccx a mlips : LossFunction ; rdfs : label " Energy - only ␣ MSE ␣ on ␣ per - molecule ␣ total ␣ energies ␣ ( no ␣ force ␣ or ␣ stress ␣ targets )" .

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entity : torchani - smith2019ccx a mlips : Implementation ; mlips : implementedIn mlips : TorchANI ; mlips : isImplementationOf entity : ANI - smith2019ccx .

Q8 – Hyperparameter settings. The main text does not tabulate explicit numerical values for the cutoff radius or for the radial/angular symmetry-function index counts (Section S1.2 in the Supplementary Information has the details). We therefore record no HyperparameterSetting instances in the canonical encoding; the architectural hyperparameters are referenced under hasHyperparameter only. # Q08 - hyperparameter - settings : no triples ( paper does not report this ) .

Q9 – MLIP run and trained model. The training run pretrains on the DFT (ANI-1x) corpus and then fine-tunes on the CCSD(T)*/CBS corpus, producing the ANI-1ccx 8-network ensemble. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - ani1ccx - smith2019ccx a mlips : TrainedModel ; rdfs : label " ANI -1 ccx ␣ (8 - network ␣ ensemble ) " . entity : run - ani1ccx - smith2019ccx a mlips : MLIPRun ; rdfs : label " ANI -1 ccx ␣ training : ␣ pretrain ␣ on ␣ DFT ␣ ( ANI -1 x ) ,␣ fine - tune ␣ on ␣ CCSD ( T ) */ CBS ␣ via ␣ transfer ␣ learning " ; mlips : appliesMethod entity : ANI - smith2019ccx ; mlips : produces entity : model - ani1ccx - smith2019ccx ; mlips : runsOn entity : ds - ani1ccx - smith2019ccx .

Q10 – Benchmark results. Headline accuracies (Table 1 + Fig. 2): MAE 1.46 kcal/mol vs. CCSD(T)*/CBS on the GDB-10to13 atomization-energy benchmark, and MAD 2.5 kcal/mol on the HC7/11 hydrocarbon reaction-energy benchmark. The paper additionally reports ISOL6 isomerisation energies and the Genentech torsion-profile benchmark; these are not encoded as separate BenchmarkResult instances. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - gdb10 - mae - smith2019ccx a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 1.46 ␣ [ KiloCAL - PER - MOL ] " , " MAE ␣ on ␣ the ␣ GDB -10 to13 ␣ atomization - energy ␣ benchmark ␣ vs . ␣ CCSD ( T ) */ CBS ␣ ( Table ␣ 1 , ␣ ANI -1 ccx ) " ; mlips : hasUnit unit : KiloCAL - PER - MOL ; mlips : isMetricOf entity : result - gdb10 - smith2019ccx ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 1.46 . entity : metric - hc7 - mad - smith2019ccx a mlips : AccuracyMetric ; rdfs : label " MAD ␣ on ␣ the ␣ HC7 /11 ␣ hydrocarbon ␣ reaction - energy ␣ benchmark ␣ vs . ␣ CCSD ( T ) */ CBS ␣ ( ANI -1 ccx )" , " MAE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 2.5 ␣ [ KiloCAL - PER - MOL ] " ;

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mlips : hasUnit unit : KiloCAL - PER - MOL ; mlips : isMetricOf entity : result - hc7 - smith2019ccx ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 2.5 . entity : result - gdb10 - smith2019ccx a mlips : BenchmarkResult ; rdfs : label " ANI -1 ccx ␣ (8 - network ␣ ensemble ) ␣ on ␣ Organic ␣ molecules ␣ in ␣ the ␣ H / C / N / O ␣ chemical ␣ space ␣( drug - like ␣ and ␣ reaction - relevant ␣ species , ␣ average ␣ ~15 ␣ atoms ␣ per ␣ molecule ) ␣ in ␣ Smith ␣ et ␣ al . ␣ (2019) : ␣ ANI -1 ccx ␣ via ␣ transfer ␣ learning ␣ to ␣ CCSD ( T ) " ; mlips : evaluatesModel entity : model - ani1ccx - smith2019ccx ; mlips : hasAccuracyMetric entity : metric - gdb10 - mae - smith2019ccx ; mlips : isResultOf entity : study - smith2019ccx ; mlips : targetMaterial entity : mat - organics - HCNO - smith2019ccx . entity : result - hc7 - smith2019ccx a mlips : BenchmarkResult ; rdfs : label " ANI -1 ccx ␣ (8 - network ␣ ensemble ) ␣ on ␣ Organic ␣ molecules ␣ in ␣ the ␣ H / C / N / O ␣ chemical ␣ space ␣( drug - like ␣ and ␣ reaction - relevant ␣ species , ␣ average ␣ ~15 ␣ atoms ␣ per ␣ molecule ) ␣ in ␣ Smith ␣ et ␣ al . ␣ (2019) : ␣ ANI -1 ccx ␣ via ␣ transfer ␣ learning ␣ to ␣ CCSD ( T ) " ; mlips : evaluatesModel entity : model - ani1ccx - smith2019ccx ; mlips : hasAccuracyMetric entity : metric - hc7 - mad - smith2019ccx ; mlips : isResultOf entity : study - smith2019ccx ; mlips : targetMaterial entity : mat - organics - HCNO - smith2019ccx . entity : study - smith2019ccx mlips : hasResult entity : result - gdb10 - smith2019ccx , entity : result - hc7 - smith2019ccx .

Q11 – Computational resources. The paper notes ∼30 minutes per model to train on the 500kmolecule CCSD(T)*/CBS set (the production model is an 8-network ensemble), but does not report training duration in the form the ontology expects, nor GPU hours, training hardware, peak memory, or per-atom inference time. Recorded as a Q12 gap. # Q11 - resources : no triples ( paper does not report this ) .

Q12 – Gaps. Beyond Q11, the protocol does not capture: the transfer-learning relationship between the DFT-pretrained and CCSD(T)-fine-tuned models (only their union as a single training set); the explicit DLPNO-CCSD(T) parameters (PNO thresholds, integration-grid specifications) which would refine the WaveFunctionSettings; the ANI-1x parent dataset is referenced as a published source but not modelled as a separate TrainingDataset; and the auxiliary ablation runs (ANI-1ccx-R, trained only on CCSD(T)*/CBS, no transfer learning) are not encoded as separate TrainedModel instances. K.11

Eckhoff & Behler (2021): spin-dependent HDNNP for MnO

Q1 – Bibliographic identification. Eckhoff and Behler extend the high-dimensional neural network potential framework with spin-dependent atom-centered symmetry functions (sACSFs) to capture magnetic systems. Published in npj Comput. Mater. 7, 170 (2021); arXiv:2104.14439. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0002 -1220 -1542 > a schema : Person ; schema : affiliation entity : org - UniversityofGottingen - eckhoff2021spin ; schema : familyName " Behler " ; schema : givenName " J ö rg " ; schema : identifier < https :// orcid . org /0000 -0002 -1220 -1542 > ; schema : name "Jö rg ␣ Behler " .

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< https :// orcid . org /0000 -0002 -5581 -789 X > a schema : Person ; schema : affiliation entity : org - UniversityofGottingen - eckhoff2021spin ; schema : familyName " Eckhoff " ; schema : givenName " Marco " ; schema : identifier < https :// orcid . org /0000 -0002 -5581 -789 X > ; schema : name " Marco ␣ Eckhoff " . entity : article - eckhoff2021spin a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0002 -1220 -1542 > , < https :// orcid . org /0000 -0002 -5581 -789 X > ; schema : datePublished " 2021 " ^^ xsd : gYear ; schema : name " High - Dimensional ␣ Neural ␣ Network ␣ Potentials ␣ for ␣ Magnetic ␣ Systems ␣ Using ␣ Spin - Dependent ␣ Atom - Centered ␣ Symmetry ␣ Functions " ; schema : sameAs < https :// doi . org /10.1038/ s41524 -021 -00636 - z > . entity : org - UniversityofGottingen - eckhoff2021spin a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " University ␣ of ␣ G ö ttingen " ; schema : identifier < https :// ror . org /01 y9bpm73 > ; schema : name " University ␣ of ␣ G ö ttingen " . entity : study - eckhoff2021spin a mlips : BenchmarkStudy ; rdfs : label " Eckhoff ␣ & ␣ Behler ␣ (2021) : ␣ spin - dependent ␣ HDNNP ␣ for ␣ MnO " ; mlips : reportedIn entity : article - eckhoff2021spin .

Q2 – Material system. The headline material is rock-salt MnO (and a vacancy-rich Mn0.969 O variant). The AFM-II rhombohedrally distorted ground state with Néel temperature ∼116 K is the focus. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat - MnO - eckhoff2021 a mlips : MaterialSystem ; rdfs : label " Manganese ␣ oxide ␣ ( MnO ␣ and ␣ Mn_ {0.969} O ) ,␣ rocksalt ␣ structure ␣ with ␣ AFM - II ␣ / ␣ FM ␣/␣ AFM -I␣ magnetic ␣ orders " ; mlips : chemicalFormula " MnO " ; mlips : materialClass " Antiferromagnetic ␣ transition - metal ␣ oxide ; ␣ rhombohedrally ␣ distorted ␣ rock - salt ␣ ( AFM - II ) ␣ magnetic ␣ ground ␣ state ␣ with ␣ Neel ␣ temperature ␣ ~116 ␣ K ␣ ( experiment ) " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q412356 > .

Q3 – Reference calculation method. Reference data come from spin-polarised DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - eckhoff2021spin a mlips : DFTCalculation .

Q4 – Reference settings. Calculations use FHI-aims (version 200112.2) with the HSE06 screenedhybrid functional (𝜔 = 0.11 𝑎 0−1 ), all-electron numerical atom-centred orbitals (intermediate basis,

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excluding auxiliary 5g hydrogenic functions), and a Γ-centred 2×2×2 k-mesh on 2×2×2 MnO supercells. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - eckhoff2021spin mlips : hasDFTSettings entity : dft - settings - eckhoff2021spin . entity : dft - settings - eckhoff2021spin a mlips : DFTSettings ; rdfs : comment " HSE06 ␣ screened - hybrid ␣ functional ␣ with ␣ screening ␣ parameter ␣ omega ␣ = ␣ 0.11 ␣ a0 ^ -1; ␣ collinear ␣ spin - polarised . ␣ All - electron ␣ numerical - atom - centred - orbital ␣ ( NAO ) ␣ basis ␣( FHI - aims ␣ intermediate ␣ basis , ␣ excluding ␣ auxiliary ␣ 5 g ␣ hydrogenic ␣ functions ) ; ␣ no ␣ pseudopotential . " ; mlips : dftBasisSet mlips : NAOIntermediate ; mlips : kPointMesh " Gamma - centred ␣ 2 x2x2 ␣ ( for ␣ 2 x2x2 ␣ MnO ␣ supercells , ␣ 64 ␣ atoms ␣ without ␣ vacancies ) " ; mlips : usedDFTCode mlips : FHIaims ; mlips : xcFunctional mlips : HSE06 .

Q5 – Training dataset. The reference set contains 3,101 supercells across magnetic states: 1,387 MnO + 1,421 Mn0.969 O for training, 156 MnO + 137 Mn0.969 O for testing. Energies and forces are covered. Provenance is in-house (assembled for this work). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - MnO - eckhoff2021 a mlips : TrainingDataset ; rdfs : label " mHDNNP ␣ MnO / Mn_ {0.969} O ␣ reference ␣ set : ␣ 3101 ␣ 2 x2x2 ␣ bulk ␣ supercells ␣ across ␣ magnetic ␣ states ␣ (1387 ␣ MnO ␣ + ␣ 1421 ␣ Mn_ {0.969} O ␣ training ; ␣ 156 ␣ MnO ␣ + ␣ 137 ␣ Mn_ {0.969} O ␣ test )" ; mlips : coversMaterial entity : mat - MnO - eckhoff2021 ; mlips : coversProperty mlips : Energy , mlips : Forces ; mlips : datasetProvenance mlips : InHouse ; mlips : hasDFTCalculation entity : dft - eckhoff2021spin ; mlips : numConfigurations 3101 ; mlips : wasRunBy entity : run - mhdnnp - MnO .

Q6 – Sampling strategies. Four strategies were combined: magnetic-state enumeration (FM, AFM-I, AFM-II, plus excited spin orderings); atomic-displacement perturbations from ideal lattice positions; lattice-parameter perturbations to capture the rhombohedral distortion; and Mn-vacancy sampling for off-stoichiometric configurations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : displacement - sampling - eckhoff2021 a mlips : SamplingStrategy ;

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rdfs : comment " Different ␣ atomic ␣ displacements ␣ from ␣ the ␣ ideal ␣ rock - salt ␣ lattice ␣ positions ␣ are ␣ generated ␣ to ␣ span ␣ the ␣ local ␣ PES ␣ around ␣ each ␣ magnetic ␣ order . " ; rdfs : label " Atomic - displacement ␣ perturbations " . entity :ds - MnO - eckhoff2021 mlips : samplingStrategy entity : displacement - sampling - eckhoff2021 , entity : lattice distortion - sampling - eckhoff2021 , entity : magnetic - state - sampling - eckhoff2021 , entity : vacancy - sampling - eckhoff2021 . entity : lattice - distortion - sampling - eckhoff2021 a mlips : SamplingStrategy ; rdfs : comment " Distortions ␣ of ␣ the ␣ lattice ␣ parameters ␣ ( volume ␣ / ␣ shape ) ␣ are ␣ sampled ␣ to ␣ describe ␣ the ␣ rhombohedral ␣ distortion ␣ of ␣ the ␣ AFM - II ␣ order . " ; rdfs : label " Lattice - parameter ␣ perturbations " . entity : magnetic - state - sampling - eckhoff2021 a mlips : SamplingStrategy ; rdfs : comment " Various ␣ collinear ␣ spin ␣ orderings ␣ of ␣ the ␣ rocksalt ␣ MnO ␣ supercell ␣ are ␣ computed ␣( FM , ␣ AFM -I , ␣ AFM - II , ␣ and ␣ excited ␣ orders ) ␣ so ␣ the ␣ mHDNNP ␣ can ␣ resolve ␣ their ␣ energy ␣ differences . " ; rdfs : label " Magnetic - state ␣ enumeration " . entity : vacancy - sampling - eckhoff2021 a mlips : SamplingStrategy ; rdfs : comment " Mn - vacancy ␣ supercells ␣ ( Mn_ {0.969} O ) ␣ are ␣ included ␣ to ␣ extend ␣ the ␣ mHDNNP ␣ to ␣ off - stoichiometric ␣ configurations . " ; rdfs : label " Vacancy - defect ␣ sampling " .

Q7 – MLIP method, components, implementation. The method (mHDNNP) is a Behler–Parrinello HDNNP with three hidden layers (20/15/10 neurons per element) consuming spin-augmented ACSFs: radial 𝑀 0 /𝑀 + /𝑀 − and angular 𝑀 00 /𝑀 ++ /𝑀 −− /𝑀 +− functions. Implementation is RuNNer v1.00 (modified to support sACSFs); n2p2 is used for LAMMPS MD. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : mHDNNP . entity :hp - Mthresh a mlips : Hyperparameter ; rdfs : label " HDNNP ␣ ACSF ␣ amplitude ␣ threshold " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : double ; mlips : hyperparameterName " M_thresh " ; mlips : isHyperparameterOf entity : mHDNNP . entity :hp - hidden - eckhoff2021 a mlips : Hyperparameter ; rdfs : label " HDNNP ␣ per - element ␣ hidden ␣ layer ␣ architecture " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : string ; mlips : hyperparameterName " hidden_layers " ; mlips : isHyperparameterOf entity : mHDNNP . entity : mHDNNP a mlips : MLIPMethod ; rdfs : label " Magnetic ␣ high - dimensional ␣ neural ␣ network ␣ potential ␣ ( mHDNNP ) ␣ with ␣ spin dependent ␣ atom - centered ␣ symmetry ␣ functions " ; mlips : hasDescriptor mlips : SymmetryFunctionDescriptor ; mlips : hasFunctionalForm entity : mhdnnp - functional - form ; mlips : hasHyperparameter mlips : cutoffRadius , entity : hp - Mthresh , entity : hp - hidden eckhoff2021 ; mlips : hasImplementation entity : runner - impl - eckhoff2021 ; mlips : hasLossFunction entity : mhdnnp - loss - eckhoff2021 ; mlips : hasTrainingAlgorithm entity : mhdnnp - training - eckhoff2021 ; mlips : supportsSimulation mlips : GeometryOptimization , mlips : MolecularDynamics , mlips : MonteCarlo . entity : mhdnnp - functional - form a mlips : FunctionalForm ;

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rdfs : label " Behler - Parrinello ␣ HDNNP ␣ with ␣ per - element ␣ feed - forward ␣ atomic ␣ networks ␣ (3 ␣ hidden ␣ layers ␣ of ␣ 20/15/10 ␣ neurons ) ,␣ inputs ␣ are ␣ spin - augmented ␣ ACSFs ␣ ( sACSF ) ␣ using ␣ radial ␣M ^0/ M ^+/ M ^ - ␣ and ␣ angular ␣ M ^00/ M ^++/ M ^ - -/ M ^+ - ␣ spin - augmentation ␣ functions " . entity : mhdnnp - loss - eckhoff2021 a mlips : LossFunction ; rdfs : label " Energy ␣ + ␣ atomic - force ␣ RMSE ␣ loss ␣ on ␣ cohesive ␣ energies ␣ and ␣ force ␣ components ␣ (90% ␣ train ␣ / ␣ 10% ␣ test ␣ split ) " . entity : mhdnnp - training - eckhoff2021 a mls : Algorithm ; rdfs : label " Standard ␣ HDNNP ␣ training ␣ ( gradient - based ␣ weight ␣ optimisation ␣ in ␣ RuNNer ) " . entity : runner - impl - eckhoff2021 a mlips : Implementation ; mlips : implementedIn mlips : RuNNer ; mlips : isImplementationOf entity : mHDNNP ; mlips : version " 1.00 ␣ ( modified ␣ to ␣ support ␣ sACSFs ) " .

Q8 – Hyperparameter settings. Reported settings: cutoff radius 𝑟𝑐 = 10.5 𝑎 0 (Bohr); ACSF amplitude threshold 𝑀thresh = 0.25; per-element architecture three layers × (20, 15, 10) neurons. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - Mthresh -025 a mlips : HyperparameterSetting ; rdfs : label " HDNNP ␣ ACSF ␣ amplitude ␣ threshold ␣ = ␣ 0.25 ␣ for ␣ mHDNNP ␣ training ␣ run ␣ on ␣ MnO / Mn_ {0.969} O␣ dataset " ; mlips : forHyperparameter entity : hp - Mthresh ; mlips : isSettingOf entity : run - mhdnnp - MnO ; mlips : settingValue 0.25 . entity : setting - hidden -20 -15 -10 a mlips : HyperparameterSetting ; rdfs : label " HDNNP ␣ per - element ␣ hidden ␣ layer ␣ architecture ␣ = ␣ 3 ␣ hidden ␣ layers ␣ x ␣ (20 , ␣ 15 , ␣ 10) ␣ neurons ␣ per ␣ element ␣ for ␣ mHDNNP ␣ training ␣ run ␣ on ␣ MnO / Mn_ {0.969} O ␣ dataset " ; mlips : forHyperparameter entity : hp - hidden - eckhoff2021 ; mlips : isSettingOf entity : run - mhdnnp - MnO ; mlips : settingValue " 3 ␣ hidden ␣ layers ␣ x ␣ (20 , ␣ 15 , ␣ 10) ␣ neurons ␣ per ␣ element " . entity : setting - rcut -105 - eckhoff2021 a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 10.5 ␣ a0 ␣ ( Bohr ␣ radii ) ␣ for ␣ mHDNNP ␣ training ␣ run ␣ on ␣ MnO / Mn_ {0.969} O␣ dataset " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - mhdnnp - MnO ; mlips : settingValue " 10.5 ␣ a0 ␣ ( Bohr ␣ radii ) " .

Q9 – MLIP run and trained model. A single training run produces the production mHDNNP for MnO. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - mhdnnp - MnO a mlips : TrainedModel ; rdfs : label " Magnetic ␣ HDNNP ␣ for ␣ MnO ␣ ( sACSF ␣ + ␣ 3 - layer ␣ feed - forward ␣ NN ) " . entity : run - mhdnnp - MnO a mlips : MLIPRun ; rdfs : label " mHDNNP ␣ training ␣ run ␣ on ␣ MnO / Mn_ {0.969} O ␣ dataset " ;

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Q10 – Benchmark results. Test-set RMSEs: 1.11 meV/atom on cohesive energies and 0.066 eV/Å on atomic-force components. The paper also reports phonon and Néel-temperature predictions but in derived form rather than as separate BenchmarkResult instances. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - rmse - energy - mhdnnp a mlips : AccuracyMetric ; rdfs : label " RMSE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 1.11 ␣ [ millielectronvolt ␣ per ␣ atom ] " , " Test - set ␣ RMSE ␣ on ␣ cohesive ␣ energies ␣ ( sACSF ␣ mHDNNP ) " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - mhdnnp - energy ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 1.11 . entity : metric - rmse - forces - mhdnnp a mlips : AccuracyMetric ; rdfs : label " RMSE ␣ of ␣ Force ␣ = ␣ 0.066 ␣ [ EV - PER - ANGSTROM ] " , " Test - set ␣ RMSE ␣ on ␣ atomic ␣ force ␣ components ␣ ( sACSF ␣ mHDNNP ) " ; mlips : hasUnit unit : EV - PER - ANGSTROM ; mlips : isMetricOf entity : result - mhdnnp - forces ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 0.066 . entity : result - mhdnnp - energy a mlips : BenchmarkResult ; rdfs : label " Magnetic ␣ HDNNP ␣ for ␣ MnO ␣ ( sACSF ␣ + ␣ 3 - layer ␣ feed - forward ␣ NN ) ␣ on ␣ Manganese ␣ oxide ␣( MnO ␣ and ␣ Mn_ {0.969} O ) ,␣ rocksalt ␣ structure ␣ with ␣ AFM - II ␣ / ␣ FM ␣ / ␣ AFM - I ␣ magnetic ␣ orders ␣ in ␣ Eckhoff ␣ & ␣ Behler ␣ (2021) : ␣ spin - dependent ␣ HDNNP ␣ for ␣ MnO " ; mlips : evaluatesModel entity : model - mhdnnp - MnO ; mlips : hasAccuracyMetric entity : metric - rmse - energy - mhdnnp ; mlips : isResultOf entity : study - eckhoff2021spin ; mlips : targetMaterial entity : mat - MnO - eckhoff2021 . entity : result - mhdnnp - forces a mlips : BenchmarkResult ; rdfs : label " Magnetic ␣ HDNNP ␣ for ␣ MnO ␣ ( sACSF ␣ + ␣ 3 - layer ␣ feed - forward ␣ NN ) ␣ on ␣ Manganese ␣ oxide ␣( MnO ␣ and ␣ Mn_ {0.969} O ) ,␣ rocksalt ␣ structure ␣ with ␣ AFM - II ␣ / ␣ FM ␣ / ␣ AFM - I ␣ magnetic ␣ orders ␣ in ␣ Eckhoff ␣ & ␣ Behler ␣ (2021) : ␣ spin - dependent ␣ HDNNP ␣ for ␣ MnO " ; mlips : evaluatesModel entity : model - mhdnnp - MnO ; mlips : hasAccuracyMetric entity : metric - rmse - forces - mhdnnp ; mlips : isResultOf entity : study - eckhoff2021spin ; mlips : targetMaterial entity : mat - MnO - eckhoff2021 . entity : study - eckhoff2021spin mlips : hasResult entity : result - mhdnnp - energy , entity : result - mhdnnp - forces .

Q11 – Computational resources. Not reported. # Q11 - resources : no triples ( paper does not report this ) .

Q12 – Gaps. Beyond Q11, the most consequential gap is the lack of first-class ontology coverage for spin-dependent descriptors and magnetic configurations. The mHDNNP’s spinaugmentation is currently captured only through prose in the FunctionalForm label and the magnetic-state-sampling strategy; the ontology has no concept for collinear/non-collinear spin

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states, magnetic-moment-per-atom properties, or spin descriptors. Other unreported items: the FHI-aims plane-wave-equivalent energy cutoff (replaced by basis-set choice in NAO); explicit frozenCore; and any HSE06 numerical parameters beyond the screening parameter 𝜔. K.12

Batatia et al. (2022): MACE for fast and accurate force fields

Q1 – Bibliographic identification. Batatia, Kovács, Simm, Ortner, and Csányi introduce MACE, a higher-order equivariant message-passing neural network interatomic potential. Published at NeurIPS 2022; arXiv:2206.07697. The headline benchmarks are rMD17 small organic molecules, 3BPA temperature transferability, and acetylacetone (AcAc) flexibility/reactivity. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -6815 -352 X > a schema : Person ; schema : familyName " Simm " ; schema : givenName " Gregor ␣ N . ␣ C . " ; schema : identifier < https :// orcid . org /0000 -0001 -6815 -352 X > ; schema : name " Gregor ␣ N . ␣ C . ␣ Simm " . < https :// orcid . org /0000 -0001 -6915 -9851 > a schema : Person ; schema : familyName " Batatia " ; schema : givenName " Ilyes " ; schema : identifier < https :// orcid . org /0000 -0001 -6915 -9851 > ; schema : name " Ilyes ␣ Batatia " . < https :// orcid . org /0000 -0002 -0854 -2635 > a schema : Person ; schema : familyName " Kov á cs " ; schema : givenName " D á vid ␣ P é ter " ; schema : identifier < https :// orcid . org /0000 -0002 -0854 -2635 > ; schema : name "Dá vid ␣ P é ter ␣ Kov á cs " . < https :// orcid . org /0000 -0003 -1498 -8120 > a schema : Person ; schema : familyName " Ortner " ; schema : givenName " Christoph " ; schema : identifier < https :// orcid . org /0000 -0003 -1498 -8120 > ; schema : name " Christoph ␣ Ortner " . entity : article - batatia2022 a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0001 -6815 -352 X > , < https :// orcid . org /0000 -0001 -6915 -9851 > , < https :// orcid . org /0000 -0002 -0854 -2635 > , < https :// orcid . org /0000 -0003 -1498 -8120 > , entity : person - Csanyi - batatia2022 ; schema : datePublished " 2022 " ^^ xsd : gYear ; schema : name " MACE : ␣ Higher ␣ Order ␣ Equivariant ␣ Message ␣ Passing ␣ Neural ␣ Networks ␣ for ␣ Fast ␣ and ␣ Accurate ␣ Force ␣ Fields " ; schema : sameAs < https :// doi . org /10.48550/ arXiv .2206.07697 > . entity : person - Csanyi - batatia2022 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " ; schema : familyName " Cs á nyi " ; schema : givenName " G á bor " ; schema : name "Gá bor ␣ Cs á nyi " . entity : study - batatia2022 a mlips : BenchmarkStudy ; rdfs : label " Batatia ␣ et ␣ al . ␣ (2022) : ␣ MACE ␣ equivariant ␣ message - passing ␣ MLIP " ; mlips : reportedIn entity : article - batatia2022 .

Q2 – Material system. The canonical encoding pass takes the headline rMD17 dataset, a set of ten small organic molecules (aspirin, azobenzene, benzene, ethanol, malonaldehyde, naphthalene,

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paracetamol, salicylic acid, toluene, uracil) sampled from gas-phase ab initio MD trajectories. We model the dataset at the species-set level (C/H/N/O small organics) rather than per molecule. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat - rMD17 a mlips : MaterialSystem ; rdfs : comment " Wikidata ␣ Q174211 ␣ ( ' organic ␣ compound ') ␣ is ␣ the ␣ most ␣ generic ␣ appropriate ␣ entry ;␣ rMD17 ␣ itself ␣ has ␣ no ␣ Wikidata ␣ entry ␣ as ␣ of ␣ 2026 -04 -28. " ; rdfs : label " rMD17 ␣ small ␣ organic ␣ molecules ␣ (10 ␣ molecules : ␣ aspirin , ␣ azobenzene , ␣ benzene , ␣ ethanol ,␣ malonaldehyde , ␣ naphthalene , ␣ paracetamol , ␣ salicylic ␣ acid , ␣ toluene , ␣ uracil )" ; mlips : chemicalFormula "C ,H ,N , O " ; mlips : materialClass " Small ␣ organic ␣ molecules ␣ sampled ␣ from ␣ gas - phase ␣ ab ␣ initio ␣ MD ␣ trajectories " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q174211 > .

Q3 – Reference calculation method. Reference data are produced from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - batatia2022 a mlips : DFTCalculation .

Q4 – Reference settings. For rMD17 the original MD17 trajectories are recomputed at the PBE/def2-SVP level of theory with very tight SCF convergence and a very dense DFT integration grid. The DFT engine itself is not stated in the MACE paper (the rMD17 dataset is consumed as published). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - batatia2022 mlips : hasDFTSettings entity : dft - settings - batatia2022 . entity : dft - settings - batatia2022 a mlips : DFTSettings ; rdfs : comment " rMD17 ␣ reference ␣ recomputation ␣ at ␣ the ␣ PBE / def2 - SVP ␣ level ␣ of ␣ theory ␣ with ␣ very ␣ tight ␣ SCF ␣ convergence ␣ and ␣ a ␣ very ␣ dense ␣ DFT ␣ integration ␣ grid ; ␣ engine ␣ not ␣ stated ␣ in ␣ the ␣ MACE ␣ paper ␣ ( rMD17 ␣ dataset ␣ consumed ␣ as ␣ published ) . " ; mlips : xcFunctional mlips : PBE .

Q5 – Training dataset. The rMD17 split used in the paper consists of 950 training and 50 validation configurations per molecule (1,000 total per molecule), covering energies and forces. Configurations come from the published rMD17 dataset and are reshuffled after each epoch. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > .

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@prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - rMD17 a mlips : TrainingDataset ; rdfs : label " rMD17 ␣ training ␣ split : ␣ 950 ␣ train ␣ + ␣ 50 ␣ validation ␣ per ␣ molecule ␣ (10 ␣ molecules )" ; mlips : coversMaterial entity : mat - rMD17 ; mlips : coversProperty mlips : Energy , mlips : Forces ; mlips : datasetProvenance mlips : Published ; mlips : hasDFTCalculation entity : dft - batatia2022 ; mlips : numConfigurations 1000 ; mlips : wasRunBy entity : run - mace - rMD17 .

Q6 – Sampling strategies. A single sampling strategy is in play: vibrational sampling via gas-phase ab initio MD trajectories at 500 K, recomputed at PBE/def2-SVP for rMD17. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : aimd - sampling - batatia2022 a mlips : SamplingStrategy ; rdfs : comment " Configurations ␣ sampled ␣ from ␣ long ␣ ab ␣ initio ␣ molecular ␣ dynamics ␣ trajectories ␣ at ␣ 500 ␣K , ␣ recomputed ␣ at ␣ PBE / def2 - SVP ␣ for ␣ rMD17 . " ; rdfs : label " Vibrational ␣ sampling ␣ ( gas - phase ␣ ab ␣ initio ␣ MD ␣ at ␣ 500 ␣ K ) " . entity :ds - rMD17 mlips : samplingStrategy entity : aimd - sampling - batatia2022 .

Q7 – MLIP method, components, implementation. MACE is a two-layer equivariant messagepassing GNN that uses higher body-order (4-body) tensor messages built from a complete ACE-style local basis (Bessel radial × spherical-harmonic angular) and tensor-product symmetrisation with generalised Clebsch–Gordan coefficients. The training algorithm is the AMSGrad variant of Adam (𝛽 1 = 0.9, 𝛽 2 = 0.999, 𝜖 = 10−8 ), with an on-plateau learning-rate scheduler (patience 50, decay factor 0.8). The loss is a weighted MSE with 𝜆𝐸 = 1 and 𝜆𝐹 = 1000. Implementation is the mace PyTorch code (https://github.com/ACEsuit/mace). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : bodyOrder mlips : isHyperparameterOf entity : MACE . mlips : cutoffRadius mlips : isHyperparameterOf entity : MACE . mlips : numAngularBasis mlips : isHyperparameterOf entity : MACE . mlips : numFeatures mlips : isHyperparameterOf entity : MACE . mlips : numLayers mlips : isHyperparameterOf entity : MACE . entity : MACE a mlips : MLIPMethod ; rdfs : label " MACE : ␣ higher - order ␣ equivariant ␣ message - passing ␣ neural ␣ network " ; mlips : hasFunctionalForm entity : mace - functional - form ; mlips : hasHyperparameter mlips : bodyOrder , mlips : cutoffRadius , mlips : numAngularBasis , mlips : numFeatures , mlips : numLayers ;

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mlips : hasImplementation entity : mace - impl ; mlips : hasLossFunction entity : mace - loss -1 -1000 ; mlips : hasTrainingAlgorithm entity : adam - amsgrad . entity : adam - amsgrad a mls : Algorithm ; rdfs : label " Adam ␣ ( AMSGrad ␣ variant ) ,␣ beta1 =0.9 , ␣ beta2 =0.999 , ␣ eps =1 e -8 " . entity : mace - functional - form a mlips : FunctionalForm ; rdfs : label " Two - layer ␣ equivariant ␣ message - passing ␣ network ␣ with ␣ higher - order ␣ (4 - body ) ␣ tensor ␣ messages ␣ over ␣ an ␣ O (3) - equivariant ␣ atomic ␣ cluster ␣ expansion ␣ basis " . entity : mace - impl a mlips : Implementation ; mlips : implementedIn mlips : MACE ; mlips : isImplementationOf entity : MACE . entity : mace - loss -1 -1000 a mlips : LossFunction ; rdfs : label " Weighted ␣ MSE ␣ on ␣ energies ␣ and ␣ force ␣ components ␣ ( lambda_E ␣ = ␣ 1 , ␣ lambda_F ␣ = ␣ 1000) " .

Q8 – Hyperparameter settings. The rMD17 production model uses two MACE layers, 𝑙 max = 3, 256 uncoupled feature channels, correlation order 𝜈 = 3 (4-body messages), and a 5 Å radial cutoff with 8 Bessel basis functions and a polynomial cutoff envelope (𝑝 = 5). The radial MLP is [64, 64, 64, 1024] with SiLU non-linearities, and the readout of the second layer is a single-layer MLP with 16 hidden dimensions; first-layer readout is linear. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - channels -256 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ features ␣ = ␣ 256 ␣ for ␣ MACE ␣ training ␣ run ␣ on ␣ rMD17 ␣ ( per - molecule , ␣ 1000 ␣ configs ) " ; mlips : forHyperparameter mlips : numFeatures ; mlips : isSettingOf entity : run - mace - rMD17 ; mlips : settingValue 256 . entity : setting - correlation -3 a mlips : HyperparameterSetting ; rdfs : label " body ␣ order ␣ = ␣ 3 ␣ for ␣ MACE ␣ training ␣ run ␣ on ␣ rMD17 ␣ ( per - molecule , ␣ 1000 ␣ configs ) " ; mlips : forHyperparameter mlips : bodyOrder ; mlips : isSettingOf entity : run - mace - rMD17 ; mlips : settingValue 3 . entity : setting - lmax -3 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ angular ␣ basis ␣ functions ␣ = ␣ 3 ␣ for ␣ MACE ␣ training ␣ run ␣ on ␣ rMD17 ␣ ( per molecule ,␣ 1000 ␣ configs ) " ; mlips : forHyperparameter mlips : numAngularBasis ; mlips : isSettingOf entity : run - mace - rMD17 ; mlips : settingValue 3 . entity : setting - numlayers -2 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ layers ␣ = ␣ 2 ␣ for ␣ MACE ␣ training ␣ run ␣ on ␣ rMD17 ␣ ( per - molecule , ␣ 1000 ␣ configs )" ; mlips : forHyperparameter mlips : numLayers ; mlips : isSettingOf entity : run - mace - rMD17 ; mlips : settingValue 2 . entity : setting - rcut -5 a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 5 ␣ for ␣ MACE ␣ training ␣ run ␣ on ␣ rMD17 ␣ ( per - molecule , ␣ 1000 ␣ configs )" ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - mace - rMD17 ; mlips : settingValue 5 .

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Q9 – MLIP run and trained model. A single training run per molecule produces one rMD17 MACE model (trained at float32 precision, learning rate 0.01, batch size 5, exponential weight-decay 5 × 10−7 on the 𝑊 weights of the higher-order features). Per-atom energy is shifted by the per-species training-set average and scaled by the RMS of force components. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - mace - rMD17 a mlips : TrainedModel ; rdfs : label " MACE ␣ rMD17 ␣ model ␣ ( L =3 , ␣ two - layer , ␣ 256 ␣ channels ) " . entity : run - mace - rMD17 a mlips : MLIPRun ; rdfs : label " MACE ␣ training ␣ run ␣ on ␣ rMD17 ␣ ( per - molecule , ␣ 1000 ␣ configs ) " ; mlips : appliesMethod entity : MACE ; mlips : hasHyperparameterSetting entity : setting - channels -256 , entity : setting - correlation -3 , entity : setting - lmax -3 , entity : setting - numlayers -2 , entity : setting - rcut -5 ; mlips : produces entity : model - mace - rMD17 ; mlips : runsOn entity : ds - rMD17 .

Q10 – Benchmark results. Headline accuracy figures on the rMD17 benchmark for aspirin (MACE, 1,000 train) are MAE 2.2 meV on energies and 6.6 meV/Å on force components. MACE attains state-of-the-art or near state-of-the-art accuracy across the ten rMD17 molecules. We encode the aspirin numbers as a single per-molecule benchmark result; per-molecule results for the remaining nine molecules are a Q12 gap. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - mae - rmd17 - aspirin - energy a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 2.2 ␣ [ millielectronvolt ] " , " MAE ␣ on ␣ aspirin ␣ energies , ␣ rMD17 , ␣ 1000 ␣ train " ; mlips : hasUnit mlips : MilliEV ; mlips : isMetricOf entity : result - mace - rmd17 - aspirin - energy ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 2.2 . entity : metric - mae - rmd17 - aspirin - forces a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Force ␣ = ␣ 6.6 ␣ [ millielectronvolt ␣ per ␣ angstrom ] " , " MAE ␣ on ␣ aspirin ␣ force ␣ components , ␣ rMD17 , ␣ 1000 ␣ train " ; mlips : hasUnit mlips : MilliEV - PER - ANGSTROM ; mlips : isMetricOf entity : result - mace - rmd17 - aspirin - forces ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 6.6 . entity : result - mace - rmd17 - aspirin - energy a mlips : BenchmarkResult ; rdfs : label " MACE ␣ rMD17 ␣ model ␣ ( L =3 , ␣ two - layer , ␣ 256 ␣ channels ) ␣ on ␣ rMD17 ␣ small ␣ organic ␣ molecules ␣ (10 ␣ molecules : ␣ aspirin , ␣ azobenzene , ␣ benzene , ␣ ethanol , ␣ malonaldehyde , ␣ naphthalene , ␣ paracetamol , ␣ salicylic ␣ acid , ␣ toluene , ␣ uracil ) ␣ in ␣ Batatia ␣ et ␣ al . ␣ (2022) :␣ MACE ␣ equivariant ␣ message - passing ␣ MLIP " ; mlips : evaluatesModel entity : model - mace - rMD17 ; mlips : hasAccuracyMetric entity : metric - mae - rmd17 - aspirin - energy ; mlips : isResultOf entity : study - batatia2022 ; mlips : targetMaterial entity : mat - rMD17 .

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entity : result - mace - rmd17 - aspirin - forces a mlips : BenchmarkResult ; rdfs : label " MACE ␣ rMD17 ␣ model ␣ ( L =3 , ␣ two - layer , ␣ 256 ␣ channels ) ␣ on ␣ rMD17 ␣ small ␣ organic ␣ molecules ␣ (10 ␣ molecules : ␣ aspirin , ␣ azobenzene , ␣ benzene , ␣ ethanol , ␣ malonaldehyde , ␣ naphthalene , ␣ paracetamol , ␣ salicylic ␣ acid , ␣ toluene , ␣ uracil ) ␣ in ␣ Batatia ␣ et ␣ al . ␣ (2022) :␣ MACE ␣ equivariant ␣ message - passing ␣ MLIP " ; mlips : evaluatesModel entity : model - mace - rMD17 ; mlips : hasAccuracyMetric entity : metric - mae - rmd17 - aspirin - forces ; mlips : isResultOf entity : study - batatia2022 ; mlips : targetMaterial entity : mat - rMD17 . entity : study - batatia2022 mlips : hasResult entity : result - mace - rmd17 - aspirin - energy , entity : result - mace - rmd17 aspirin - forces .

Q11 – Computational resources. Models were trained on a single NVIDIA A100 GPU; typical training time is 2–6 hours per molecule for rMD17 (specific GPU-hours, peak memory, and inference-time-per-atom are not reported for the rMD17 pass, though the paper does report a “time latency” inference figure for the 3BPA pass: 24.3 ms for a structure with ≤ 10000 atoms on an A100). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : run - mace - rMD17 mlips : trainingDuration " 2 -6 ␣ hours ␣ per ␣ molecule ␣ on ␣ a ␣ single ␣ NVIDIA ␣ A100 " ; mlips : trainingHardware " NVIDIA ␣ A100 ␣ GPU ␣ ( single ␣ GPU ) " .

Q12 – Gaps. Beyond the items already flagged, the following ontology-expressible information is not represented in this encoding pass: (i) the two additional benchmarks reported in the same paper, 3BPA (temperature-transferability of a flexible drug-like molecule, with 𝜔B97X/6-31G(d) reference) and AcAc (acetylacetone flexibility/reactivity at the same level); (ii) per-molecule benchmark results for the remaining nine rMD17 molecules; (iii) the DFT engine for the rMD17 reference recomputation (usedDFTCode on the DFT settings) and the original MD17 DFT settings beyond the XC functional/basis set; (iv) the MACE package version; (v) detailed compute-cost data (GPU-hours, peak memory, inference time per atom on rMD17). The paper also reports that one MACE training run on 3BPA reaches converged BOTNet accuracy in ∼30 min on an A100 and a fully converged 3BPA model takes >1 day; this finer-grained timing is associated with 3BPA rather than rMD17 and is not encoded here. K.13

Batzner et al. (2022): NequIP E(3)-equivariant GNN MLIP

Q1 – Bibliographic identification. Batzner, Musaelian, Sun, Geiger, Mailoa, Kornbluth, Molinari, Smidt, and Kozinsky introduce NequIP, an 𝐸 (3)-equivariant graph neural-network interatomic potential. Published in Nature Communications 13, 2453 (2022); arXiv:2101.03164. The paper benchmarks NequIP across MD17/rMD17 small molecules, Molecules@CCSD/CCSD(T), liquid water + ice phases, formate decomposition on Cu(110), Li4 P2 O7 amorphous glass, and the LiPS superionic conductor. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > .

An Ontology for Machine Learning Interatomic Potentials @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -5433 -0900 > a schema : Person ; schema : affiliation entity : org - EcolePolytechniqueFederaledeLausanne - batzner2022 , entity : org - MassachusettsInstituteofTechnology - batzner2022 ; schema : familyName " Geiger " ; schema : givenName " Mario " ; schema : identifier < https :// orcid . org /0000 -0001 -5433 -0900 > ; schema : name " Mario ␣ Geiger " . < https :// orcid . org /0000 -0001 -5581 -5344 > a schema : Person ; schema : affiliation mlips : LawrenceBerkeleyNationalLaboratory , entity : org MassachusettsInstituteofTechnology - batzner2022 , entity : org ResearchApplicationsUnitedStates - batzner2022 ; schema : familyName " Smidt " ; schema : givenName " Tess ␣ E . " ; schema : identifier < https :// orcid . org /0000 -0001 -5581 -5344 > ; schema : name " Tess ␣ E . ␣ Smidt " . < https :// orcid . org /0000 -0001 -6705 -8133 > a schema : Person ; schema : affiliation mlips : RobertBoschUnitedStates ; schema : familyName " Kornbluth " ; schema : givenName " Mordechai " ; schema : identifier < https :// orcid . org /0000 -0001 -6705 -8133 > ; schema : name " Mordechai ␣ Kornbluth " . < https :// orcid . org /0000 -0002 -0638 -539 X > a schema : Person ; schema : affiliation mlips : HarvardUniversity , mlips : RobertBoschUnitedStates , entity : org RobertBoschSlovenia - batzner2022 ; schema : familyName " Kozinsky " ; schema : givenName " Boris " ; schema : identifier < https :// orcid . org /0000 -0002 -0638 -539 X > ; schema : name " Boris ␣ Kozinsky " . < https :// orcid . org /0000 -0002 -2913 -7030 > a schema : Person ; schema : affiliation mlips : HarvardUniversity ; schema : familyName " Molinari " ; schema : givenName " Nicola " ; schema : identifier < https :// orcid . org /0000 -0002 -2913 -7030 > ; schema : name " Nicola ␣ Molinari " . < https :// orcid . org /0000 -0002 -7971 -5222 > a schema : Person ; schema : affiliation mlips : HarvardUniversity ; schema : familyName " Sun " ; schema : givenName " Lixin " ; schema : identifier < https :// orcid . org /0000 -0002 -7971 -5222 > ; schema : name " Lixin ␣ Sun " . < https :// orcid . org /0000 -0002 -8826 -2712 > a schema : Person ; schema : affiliation mlips : HarvardUniversity ; schema : familyName " Batzner " ; schema : givenName " Simon " ; schema : identifier < https :// orcid . org /0000 -0002 -8826 -2712 > ; schema : name " Simon ␣ Batzner " . < https :// orcid . org /0000 -0003 -0475 -9236 > a schema : Person ; schema : affiliation mlips : HarvardUniversity ; schema : familyName " Musaelian " ; schema : givenName " Albert " ; schema : identifier < https :// orcid . org /0000 -0003 -0475 -9236 > ; schema : name " Albert ␣ Musaelian " . < https :// orcid . org /0000 -0003 -2239 -6192 > a schema : Person ; schema : affiliation mlips : RobertBoschUnitedStates ; schema : familyName " Mailoa " ; schema : givenName " Jonathan ␣ P . " ; schema : identifier < https :// orcid . org /0000 -0003 -2239 -6192 > ; schema : name " Jonathan ␣ P . ␣ Mailoa " . entity : article - batzner2022 a schema : ScholarlyArticle ;

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schema : author < https :// orcid . org /0000 -0001 -5433 -0900 > , < https :// orcid . org /0000 -0001 -5581 -5344 > , < https :// orcid . org /0000 -0001 -6705 -8133 > , < https :// orcid . org /0000 -0002 -0638 -539 X > , < https :// orcid . org /0000 -0002 -2913 -7030 > , < https :// orcid . org /0000 -0002 -7971 -5222 > , < https :// orcid . org /0000 -0002 -8826 -2712 > , < https :// orcid . org /0000 -0003 -0475 -9236 > , < https :// orcid . org /0000 -0003 -2239 -6192 > ; schema : datePublished " 2022 " ^^ xsd : gYear ; schema : name "E (3) - Equivariant ␣ Graph ␣ Neural ␣ Networks ␣ for ␣ Data - Efficient ␣ and ␣ Accurate ␣ Interatomic ␣ Potentials " ; schema : sameAs < https :// doi . org /10.1038/ s41467 -022 -29939 -5 > . entity : org - EcolePolytechniqueFederaledeLausanne - batzner2022 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label "É cole ␣ Polytechnique ␣ F é d é rale ␣ de ␣ Lausanne " ; schema : identifier < https :// ror . org /02 s376052 > ; schema : name "É cole ␣ Polytechnique ␣ F é d é rale ␣ de ␣ Lausanne " . entity : org - MassachusettsInstituteofTechnology - batzner2022 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Massachusetts ␣ Institute ␣ of ␣ Technology " ; schema : identifier < https :// ror . org /042 nb2s44 > ; schema : name " Massachusetts ␣ Institute ␣ of ␣ Technology " . entity : org - ResearchApplicationsUnitedStates - batzner2022 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Research ␣ Applications ␣ ( United ␣ States ) " ; schema : identifier < https :// ror . org /02 q2v3574 > ; schema : name " Research ␣ Applications ␣ ( United ␣ States ) " . entity : org - RobertBoschSlovenia - batzner2022 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Robert ␣ Bosch ␣ ( Slovenia ) " ; schema : identifier < https :// ror . org /03248 dr08 > ; schema : name " Robert ␣ Bosch ␣ ( Slovenia ) " . entity : study - batzner2022 a mlips : BenchmarkStudy ; rdfs : label " Batzner ␣ et ␣ al . ␣ (2022) : ␣ NequIP ␣ E (3) - equivariant ␣ GNN ␣ MLIP ␣ on ␣ water ␣ and ␣ ices " ; mlips : reportedIn entity : article - batzner2022 .

Q2 – Material system. The canonical encoding pass takes the bulk water and ice phases benchmark as the headline extended-system application: 64 H2 O molecules in the liquid phase, 96 H2 O molecules in three ice Ih phases (1 bar/273 K, 1 bar/330 K, 2.13 kbar/238 K). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat - water - ice a mlips : MaterialSystem ; rdfs : label " Liquid ␣ water ␣ and ␣ three ␣ ice ␣ phases ␣ ( Ih ␣ at ␣ 1 bar /273 K , ␣ 1 bar /330 K , ␣ 2.13 kbar /238 K)" ; mlips : chemicalFormula " H2O " ; mlips : materialClass " Hydrogen - bonded ␣ molecular ␣ liquid ␣ and ␣ ice ␣ polymorphs ␣ ( PBC ) ; ␣ 64 ␣ H2O ␣ for ␣ liquid , ␣ 96 ␣ H2O ␣ for ␣ ices " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q283 > .

Q3 – Reference calculation method. Reference data are produced from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > .

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@prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - batzner2022 a mlips : DFTCalculation .

Q4 – Reference settings. The water + ices reference data are computed at the PBE0-TS level of theory (hybrid PBE0 with Tkatchenko–Scheffler dispersion), generated from a mix of classical AIMD and path-integral AIMD trajectories. The DFT engine for these reference data is not stated in the paper (it inherits the published Cheng et al. dataset). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - batzner2022 mlips : hasDFTSettings entity : dft - settings - batzner2022 . entity : dft - settings - batzner2022 a mlips : DFTSettings ; rdfs : comment " Hybrid ␣ PBE0 ␣ with ␣ Tkatchenko - Scheffler ␣ dispersion ␣ correction ␣ ( PBE0 - TS ) . " ; mlips : xcFunctional mlips : PBE0 .

Q5 – Training dataset. The water + ices joint training set used in the data-efficiency experiment consists of 133 structures sampled uniformly from a 140,000-frame full set (100,000 liquid water; 20,000 ice Ih b; 10,000 ice Ih c; 10,000 ice Ih d). The training labels are energies and forces. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - water - ice a mlips : TrainingDataset ; rdfs : label " Water ␣ + ␣ 3 ␣ ices ␣ joint ␣ training ␣ set ␣ (133 ␣ structures ␣ sampled ␣ from ␣ 140000 frame ␣ full ␣ set ) " ; mlips : coversMaterial entity : mat - water - ice ; mlips : coversProperty mlips : Energy , mlips : Forces ; mlips : datasetProvenance mlips : Published ; mlips : hasDFTCalculation entity : dft - batzner2022 ; mlips : numConfigurations 133 ; mlips : wasRunBy entity : run - nequip - water .

Q6 – Sampling strategies. A single sampling strategy is in play: vibrational sampling via classical and path-integral AIMD trajectories at multiple temperatures and pressures. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : aimd - sampling - batzner2022

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a mlips : SamplingStrategy ; rdfs : comment " 133 ␣ frames ␣ sampled ␣ uniformly ␣ from ␣ a ␣ 140000 - frame ␣ full ␣ set ␣ spanning ␣ liquid ␣ water ␣ and ␣ three ␣ ice ␣ Ih ␣ phases ␣ at ␣ the ␣ PBE0 - TS ␣ level ; ␣ the ␣ full ␣ set ␣ is ␣ generated ␣ from ␣ classical ␣ AIMD ␣ and ␣ path - integral ␣ AIMD ␣ trajectories . " ; rdfs : label " Vibrational ␣ sampling ␣ ( classical ␣ and ␣ path - integral ␣ AIMD ) ␣ at ␣ multiple ␣ temperatures ␣ and ␣ pressures " . entity :ds - water - ice mlips : samplingStrategy entity : aimd - sampling - batzner2022 .

Q7 – MLIP method, components, implementation. NequIP is an 𝐸 (3)-equivariant messagepassing GNN that uses tensor-product convolutions over geometric tensors of irreducible 𝑂 (3) representations of order ℓ = 0 . . . 𝑙 max , parities 𝑝 ∈ {−1, 1}, with SiLU/tanh gate non-linearities, a ResNet-style self-interaction–convolution–concatenation update, and a final atom-wise output block. The training algorithm is the AMSGrad variant of Adam (𝛽 1 = 0.9, 𝛽 2 = 0.999, 𝜖 = 10−8 , no weight decay) with an on-plateau learning-rate scheduler (patience 50, decay factor 0.8). The loss is a weighted MSE on energies and force components (𝜆𝐹 = 100 000, 𝜆𝐸 = 1 for the model c run reported below). Implementation is the nequip PyTorch code, version 0.3.3. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : NequIP . mlips : numAngularBasis mlips : isHyperparameterOf entity : NequIP . mlips : numFeatures mlips : isHyperparameterOf entity : NequIP . mlips : numLayers mlips : isHyperparameterOf entity : NequIP . entity : NequIP a mlips : MLIPMethod ; rdfs : label " NequIP ␣ ( Neural ␣ Equivariant ␣ Interatomic ␣ Potential ) " ; mlips : hasFunctionalForm entity : nequip - functional - form ; mlips : hasHyperparameter mlips : cutoffRadius , mlips : numAngularBasis , mlips : numFeatures , mlips : numLayers ; mlips : hasImplementation entity : nequip - impl ; mlips : hasLossFunction entity : nequip - loss - energy - force ; mlips : hasTrainingAlgorithm entity : adam - amsgrad - nequip ; mlips : supportsSimulation mlips : MolecularDynamics . entity : adam - amsgrad - nequip a mls : Algorithm ; rdfs : label " Adam ␣ ( AMSGrad ␣ variant ) ,␣ beta1 =0.9 , ␣ beta2 =0.999 , ␣ eps =1 e -8 , ␣ no ␣ weight ␣ decay " . entity : nequip - functional - form a mlips : FunctionalForm ; rdfs : label "E (3) - equivariant ␣ graph ␣ neural ␣ network ␣ with ␣ tensor - product ␣ convolutions ␣ over ␣ geometric ␣ tensors ␣ of ␣ irreps ␣ l =0.. lmax ␣ ( atom ␣ embeddings , ␣ interaction ␣ blocks ␣ with ␣ self - interaction ␣ + ␣ convolution ␣ + ␣ concatenation ␣ + ␣ nonlinearity , ␣ output ␣ block ) " . entity : nequip - impl a mlips : Implementation ; mlips : implementedIn mlips : NequIP ; mlips : isImplementationOf entity : NequIP ; mlips : version " 0.3.3 " . entity : nequip - loss - energy - force a mlips : LossFunction ; rdfs : label " Weighted ␣ MSE ␣ on ␣ energies ␣ and ␣ force ␣ components , ␣ lambda_E ␣ and ␣ lambda_F ␣ set ␣ per ␣ system ␣ ( e . g . ␣ 100000:1 ␣ for ␣ water ␣ model ␣ c ) " .

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Q8 – Hyperparameter settings. The water + ices model uses 6 interaction blocks, 𝑙 max = 2, 32 features (with both even and odd parity), and a 6 Å radial cutoff. Radial features are 8 trainable Bessel basis functions processed by a 3-hidden-layer MLP of size 64 with SiLU non-linearities. Learning rate 0.005, batch size 1 (with weight 0.99 EMA on training weights for evaluation). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - features -32 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ features ␣ = ␣ 32 ␣ for ␣ NequIP ␣ training ␣ run ␣ on ␣ water + ices ␣ (133 ␣ frames , ␣ lmax =2 , ␣6 ␣ layers , ␣ 32 ␣ features ) " ; mlips : forHyperparameter mlips : numFeatures ; mlips : isSettingOf entity : run - nequip - water ; mlips : settingValue 32 . entity : setting - lmax -2 - batzner a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ angular ␣ basis ␣ functions ␣ = ␣ 2 ␣ for ␣ NequIP ␣ training ␣ run ␣ on ␣ water + ices ␣ (133 ␣ frames , ␣ lmax =2 , ␣ 6 ␣ layers , ␣ 32 ␣ features ) " ; mlips : forHyperparameter mlips : numAngularBasis ; mlips : isSettingOf entity : run - nequip - water ; mlips : settingValue 2 . entity : setting - numlayers -6 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ layers ␣ = ␣ 6 ␣ for ␣ NequIP ␣ training ␣ run ␣ on ␣ water + ices ␣ (133 ␣ frames , ␣ lmax =2 , ␣6␣ layers , ␣ 32 ␣ features ) " ; mlips : forHyperparameter mlips : numLayers ; mlips : isSettingOf entity : run - nequip - water ; mlips : settingValue 6 . entity : setting - rcut -6 - batzner a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 6 ␣ for ␣ NequIP ␣ training ␣ run ␣ on ␣ water + ices ␣ (133 ␣ frames , ␣ lmax =2 , ␣6␣ layers , ␣ 32 ␣ features ) " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - nequip - water ; mlips : settingValue 6 .

Q9 – MLIP run and trained model. A single training run on 133 structures produces one trained NequIP water+ices model. Three loss-weighting variants are reported (model a: 𝜆𝐹 = 1, 𝜆𝐸 = 0; model b: 𝜆𝐹 = 100; model c: 𝜆𝐹 = 100 000); we encode model c as the headline. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - nequip - water a mlips : TrainedModel ; rdfs : label " NequIP ␣ water + ices ␣ model ␣ ( lmax =2 , ␣ 6 ␣ interaction ␣ blocks , ␣ 32 ␣ features ) " . entity : run - nequip - water a mlips : MLIPRun ; rdfs : label " NequIP ␣ training ␣ run ␣ on ␣ water + ices ␣ (133 ␣ frames , ␣ lmax =2 , ␣ 6 ␣ layers , ␣ 32 ␣ features )" ; mlips : appliesMethod entity : NequIP ; mlips : hasHyperparameterSetting entity : setting - features -32 , entity : setting - lmax -2 batzner , entity : setting - numlayers -6 , entity : setting - rcut -6 - batzner ; mlips : produces entity : model - nequip - water ; mlips : runsOn entity : ds - water - ice .

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Q10 – Benchmark results. Headline figures for the water + ices test set (model c, 𝜆𝐹 = 100 000, 𝜆𝐸 = 1, 133 train) are RMSEs of 1.7 meV per H2 O molecule on energies and 12.2 meV/Å on liquid-water force components. NequIP is competitive with DeepMD trained on ∼1000× more data and significantly outperforms it on three of four phases. Per-phase results for the three ice configurations are an additional Q12 gap. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - rmse - water - energy a mlips : AccuracyMetric ; rdfs : label " RMSE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 1.7 ␣ [ millielectronvolt ] " , " RMSE ␣ on ␣ liquid - water ␣ energies ␣ ( model ␣c , ␣ lambda_F =100000 , ␣ lambda_E =1; ␣ per - molecule ) " ; mlips : hasUnit mlips : MilliEV ; mlips : isMetricOf entity : result - nequip - water - energy ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 1.7 . entity : metric - rmse - water - forces a mlips : AccuracyMetric ; rdfs : label " RMSE ␣ of ␣ Force ␣ = ␣ 12.2 ␣ [ millielectronvolt ␣ per ␣ angstrom ] " , " RMSE ␣ on ␣ liquid water ␣ force ␣ components ␣ ( model ␣c , ␣ lambda_F =100000 , ␣ lambda_E =1) " ; mlips : hasUnit mlips : MilliEV - PER - ANGSTROM ; mlips : isMetricOf entity : result - nequip - water - forces ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 12.2 . entity : result - nequip - water - energy a mlips : BenchmarkResult ; rdfs : label " NequIP ␣ water + ices ␣ model ␣ ( lmax =2 , ␣ 6 ␣ interaction ␣ blocks , ␣ 32 ␣ features ) ␣ on ␣ Liquid ␣ water ␣ and ␣ three ␣ ice ␣ phases ␣ ( Ih ␣ at ␣ 1 bar /273 K , ␣ 1 bar /330 K , ␣ 2.13 kbar /238 K ) ␣ in ␣ Batzner ␣ et ␣ al . ␣ (2022) : ␣ NequIP ␣ E (3) - equivariant ␣ GNN ␣ MLIP ␣ on ␣ water ␣ and ␣ ices " ; mlips : evaluatesModel entity : model - nequip - water ; mlips : hasAccuracyMetric entity : metric - rmse - water - energy ; mlips : isResultOf entity : study - batzner2022 ; mlips : targetMaterial entity : mat - water - ice . entity : result - nequip - water - forces a mlips : BenchmarkResult ; rdfs : label " NequIP ␣ water + ices ␣ model ␣ ( lmax =2 , ␣ 6 ␣ interaction ␣ blocks , ␣ 32 ␣ features ) ␣ on ␣ Liquid ␣ water ␣ and ␣ three ␣ ice ␣ phases ␣ ( Ih ␣ at ␣ 1 bar /273 K , ␣ 1 bar /330 K , ␣ 2.13 kbar /238 K ) ␣ in ␣ Batzner ␣ et ␣ al . ␣ (2022) : ␣ NequIP ␣ E (3) - equivariant ␣ GNN ␣ MLIP ␣ on ␣ water ␣ and ␣ ices " ; mlips : evaluatesModel entity : model - nequip - water ; mlips : hasAccuracyMetric entity : metric - rmse - water - forces ; mlips : isResultOf entity : study - batzner2022 ; mlips : targetMaterial entity : mat - water - ice . entity : study - batzner2022 mlips : hasResult entity : result - nequip - water - energy , entity : result - nequip - water - forces .

Q11 – Computational resources. All NequIP models were trained on an NVIDIA Tesla V100 GPU in single-GPU training. The paper does not report a specific training duration or GPU-hour count for the water+ices run (only that “competitive results can typically be obtained within a matter of hours or often even minutes”), nor peak memory or inference time per atom for the headline pass. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : run - nequip - water

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mlips : trainingHardware " NVIDIA ␣ Tesla ␣ V100 ␣ GPU ␣ ( single - GPU ␣ training ) " .

Q12 – Gaps. Beyond Q11, the following ontology-expressible items are not represented in this encoding pass: (i) the six additional benchmarks reported in the same paper (MD17/rMD17 small molecules, Molecules@CCSD/CCSD(T), formate decomposition on Cu⟨110⟩, Li4 P2 O7 amorphous glass, LiPS superionic conductor); (ii) per-phase benchmark results for the three ice Ih configurations and the data-efficiency learning-curve sweep across {10, 100, 1000, 2500} training-set sizes for LiPS; (iii) the DFT engine for the water reference data (usedDFTCode); (iv) detailed PBE0-TS reference settings (k-point mesh, energy cutoff, pseudopotential type); (v) the PyTorch / PyTorch Geometric / e3nn / Python versions used for training (the paper does report all of these but our protocol does not capture secondary toolchain libraries beyond the MLIP Library hook); (vi) the AMSGrad-Adam learning-rate schedule on a per-system basis. The paper also reports a “temperature transferability” benchmark on 3BPA but only as cited in the Allegro paper (Musaelian et al. 2023); this is not encoded here. K.14

Chen & Ong (2022): M3GNet universal graph IAP

Q1 – Bibliographic identification. Chen and Ong introduce M3GNet, a materials graph network with explicit three-body interactions trained as a universal interatomic potential across the periodic table. Published in Nat. Comput. Sci. 2, 718–728 (2022); arXiv:2202.02450. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -5726 -2587 > a schema : Person ; schema : affiliation mlips : UniversityofCaliforniaSanDiego ; schema : familyName " Ong " ; schema : givenName " Shyue ␣ Ping " ; schema : identifier < https :// orcid . org /0000 -0001 -5726 -2587 > ; schema : name " Shyue ␣ Ping ␣ Ong " . < https :// orcid . org /0000 -0001 -8008 -7043 > a schema : Person ; schema : affiliation mlips : UniversityofCaliforniaSanDiego ; schema : familyName " Chen " ; schema : givenName " Chi " ; schema : identifier < https :// orcid . org /0000 -0001 -8008 -7043 > ; schema : name " Chi ␣ Chen " . entity : article - chen2022 a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0001 -5726 -2587 > , < https :// orcid . org /0000 -0001 -8008 -7043 > ; schema : datePublished " 2022 " ^^ xsd : gYear ; schema : name "A␣ Universal ␣ Graph ␣ Deep ␣ Learning ␣ Interatomic ␣ Potential ␣ for ␣ the ␣ Periodic ␣ Table " ; schema : sameAs < https :// doi . org /10.1038/ s43588 -022 -00349 -3 > . entity : study - chen2022 a mlips : BenchmarkStudy ; rdfs : label " Chen ␣ and ␣ Ong ␣ (2022) : ␣ M3GNet ␣ universal ␣ graph ␣ IAP ␣ for ␣ the ␣ periodic ␣ table " ; mlips : reportedIn entity : article - chen2022 .

Q2 – Material system. The MLIP covers Materials Project crystals across 89 elements (62,783 distinct compounds spanning binaries, ternaries, and quaternaries from the MPF.2021.2.8 subset). We model this as a single MaterialSystem at the database-coverage level rather than enumerating individual compounds.

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@base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat -MP - universal - chen2022 a mlips : MaterialSystem ; rdfs : comment " No ␣ single ␣ Wikidata ␣ entry ␣ applies : ␣ this ␣ is ␣ the ␣ universal ␣ coverage ␣ of ␣ the ␣ Materials ␣ Project ␣ relaxation ␣ database ␣ ( MPF .2021.2.8) ,␣ spanning ␣ 89 ␣ elements . " ; rdfs : label " Materials ␣ Project ␣ crystals ␣ ( universal ␣ coverage , ␣ 89 ␣ elements ) " ; mlips : chemicalFormula " any " ; mlips : materialClass " Universal ␣ crystal ␣ coverage : ␣ 89 ␣ elements ␣ of ␣ the ␣ periodic ␣ table ; ␣ 62 ,783 ␣ distinct ␣ compounds ␣ spanning ␣ binaries , ␣ ternaries , ␣ and ␣ quaternaries ␣ from ␣ the ␣ MPF .2021.2.8 ␣ subset ␣ of ␣ the ␣ Materials ␣ Project ␣ relaxation ␣ database " .

Q3 – Reference calculation method. Reference data come from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - chen2022 a mlips : DFTCalculation .

Q4 – Reference settings. DFT settings inherit the Materials Project defaults: VASP with PBE GGA (or PBE+U for transition-metal-containing compounds) and PAW pseudopotentials. The energy cutoff and k-mesh follow the per-task MP workflow rather than a single fixed value. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - chen2022 mlips : hasDFTSettings entity : dft - settings - chen2022 . entity : dft - settings - chen2022 a mlips : DFTSettings ; rdfs : comment " PBE + U ␣ applied ␣ for ␣ transition - metal - containing ␣ compounds , ␣ as ␣ set ␣ by ␣ the ␣ Materials ␣ Project ␣ workflow . " ; mlips : pseudopotentialType mlips : PAW ; mlips : usedDFTCode mlips : VASP ; mlips : xcFunctional mlips : PBE .

Q5 – Training dataset. MPF.2021.2.8 contains 187,687 ionic-step configurations from 62,783 compounds, covering energies, forces, and stresses. Provenance is published (the dataset is reused from MP). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > .

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@prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - MPF -2021 -2 -8 a mlips : TrainingDataset ; rdfs : label " MPF .2021.2.8: ␣ 187 ,687 ␣ ionic ␣ steps ␣ from ␣ 62 ,783 ␣ Materials ␣ Project ␣ compounds " ; mlips : coversMaterial entity : mat - MP - universal - chen2022 ; mlips : coversProperty mlips : Energy , mlips : Forces , mlips : Stresses ; mlips : datasetProvenance mlips : Published ; mlips : hasDFTCalculation entity : dft - chen2022 ; mlips : numConfigurations 187687 ; mlips : wasRunBy entity : run - m3gnet - chen2022 .

Q6 – Sampling strategies. Two strategies were combined: structural-relaxation trajectory sampling (first and middle ionic steps of the first relaxation plus the last step of the second relaxation, with high-energy or short-distance frames filtered out), and periodic-table chemicalspace coverage (89 elements; 90/5/5 train/val/test split by material rather than by configuration to avoid leakage). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - MPF -2021 -2 -8 mlips : samplingStrategy entity : periodic - table - coverage - sampling - chen2022 , entity : relaxation - trajectory - sampling - chen2022 . entity : periodic - table - coverage - sampling - chen2022 a mlips : SamplingStrategy ; rdfs : comment " Compounds ␣ drawn ␣ from ␣ the ␣ Materials ␣ Project ␣ so ␣ as ␣ to ␣ span ␣ 89 ␣ elements ␣ of ␣ the ␣ periodic ␣ table ␣ across ␣ binary , ␣ ternary , ␣ and ␣ quaternary ␣ chemistries ; ␣ train / val / test ␣ split ␣ 90/5/5 ␣ by ␣ material ␣ ( not ␣ by ␣ configuration ) . " ; rdfs : label " Periodic - table ␣ chemical - space ␣ coverage " . entity : relaxation - trajectory - sampling - chen2022 a mlips : SamplingStrategy ; rdfs : comment " Snapshots ␣ taken ␣ from ␣ Materials ␣ Project ␣ relaxation ␣ trajectories : ␣ first ␣ and ␣ middle ␣ ionic ␣ steps ␣ of ␣ the ␣ first ␣ relaxation ␣ plus ␣ the ␣ last ␣ step ␣ of ␣ the ␣ second ␣ relaxation , ␣ for ␣ tasks ␣ tagged ␣ ' GGA ␣ Structure ␣ Optimization ' ␣ or ␣ ' GGA + U ␣ Structure ␣ Optimization ' ␣ as ␣ of ␣ Feb ␣ 8 , ␣ 2021. ␣ Frames ␣ with ␣ final ␣ energy ␣ per ␣ atom ␣ >␣ 50 ␣ eV / atom ␣ or ␣ interatomic ␣ distance ␣ <␣ 0.5 ␣ A ␣ were ␣ filtered ␣ out . " ; rdfs : label " Structural - relaxation ␣ trajectory ␣ sampling " .

Q7 – MLIP method, components, implementation. M3GNet is a materials graph neural network with explicit three-body angular interactions; energy is a sum of atomic contributions from a gated MLP readout, with forces and stresses obtained by auto-differentiation. Loss is Huber (𝛿 = 0.01) on energy, forces, and stresses with weights 𝑤 𝐸 = 1, 𝑤 𝑓 = 1, 𝑤 𝜎 = 0.1. Optimisation is Adam with cosine learning-rate decay; the implementation is the m3gnet TensorFlow package. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : angularCutoff mlips : isHyperparameterOf entity : M3GNet . mlips : cutoffRadius

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mlips : isHyperparameterOf entity : M3GNet . mlips : numFeatures mlips : isHyperparameterOf entity : M3GNet . mlips : numLayers mlips : isHyperparameterOf entity : M3GNet . mlips : numRadialBasis mlips : isHyperparameterOf entity : M3GNet . entity : M3GNet a mlips : MLIPMethod ; rdfs : label " M3GNet : ␣ materials ␣ graph ␣ network ␣ with ␣ three - body ␣ interactions " ; mlips : hasFunctionalForm entity : m3gnet - functional - form ; mlips : hasHyperparameter mlips : angularCutoff , mlips : cutoffRadius , mlips : numFeatures , mlips : numLayers , mlips : numRadialBasis ; mlips : hasImplementation entity : m3gnet - impl - chen2022 ; mlips : hasLossFunction entity : m3gnet - huber - loss ; mlips : hasTrainingAlgorithm entity : adam ; mlips : supportsSimulation mlips : GeometryOptimization , mlips : MolecularDynamics , mlips : PhononCalculation . entity : adam a mls : Algorithm ; rdfs : label " Adam ␣ optimiser ␣ ( initial ␣ lr =0.001 , ␣ cosine ␣ decay ␣ to ␣ 1% ␣ over ␣ 100 ␣ epochs , ␣ early ␣ stopping ␣ on ␣ validation ␣ metric ␣ after ␣ 200 ␣ epochs ) " . entity : m3gnet - functional - form a mlips : FunctionalForm ; rdfs : label " Materials ␣ graph ␣ neural ␣ network ␣ with ␣ explicit ␣ three - body ␣ angular ␣ interactions ; ␣ energy ␣ is ␣ a ␣ sum ␣ of ␣ atomic ␣ contributions ␣ from ␣ a ␣ gated ␣ MLP ␣ readout , ␣ with ␣ forces ␣ and ␣ stresses ␣ obtained ␣ by ␣ auto - differentiation . " . entity : m3gnet - huber - loss a mlips : LossFunction ; rdfs : label " Huber ␣ loss ␣ ( delta =0.01) ␣ on ␣ energy , ␣ forces , ␣ and ␣ stresses ␣ with ␣ weights ␣ w_E =1 , ␣ w_f =1 , ␣ w_sigma =0.1 " . entity : m3gnet - impl - chen2022 a mlips : Implementation ; mlips : implementedIn mlips : M3GNet ; mlips : isImplementationOf entity : M3GNet .

Q8 – Hyperparameter settings. Reported settings: 2-body cutoff 𝑟𝑐 = 5.0 Å, 3-body cutoff 4.0 Å, embedding dimension 64, 3 graph-network blocks, 3 radial basis functions. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting -3 body - cutoff -4 - chen2022 a mlips : HyperparameterSetting ; rdfs : label " angular ␣ cutoff ␣ = ␣ 4 ␣ for ␣ M3GNet - EFS ␣ training ␣ run ␣ on ␣ MPF .2021.2.8 " ; mlips : forHyperparameter mlips : angularCutoff ; mlips : isSettingOf entity : run - m3gnet - chen2022 ; mlips : settingValue 4 . entity : setting - embedding - dim -64 - chen2022 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ features ␣ = ␣ 64 ␣ for ␣ M3GNet - EFS ␣ training ␣ run ␣ on ␣ MPF .2021.2.8 " ; mlips : forHyperparameter mlips : numFeatures ; mlips : isSettingOf entity : run - m3gnet - chen2022 ; mlips : settingValue 64 . entity : setting - num - blocks -3 - chen2022 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ layers ␣ = ␣ 3 ␣ for ␣ M3GNet - EFS ␣ training ␣ run ␣ on ␣ MPF .2021.2.8 " ; mlips : forHyperparameter mlips : numLayers ; mlips : isSettingOf entity : run - m3gnet - chen2022 ; mlips : settingValue 3 . entity : setting - num - radial - basis -3 - chen2022 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ radial ␣ basis ␣ functions ␣ = ␣ 3 ␣ for ␣ M3GNet - EFS ␣ training ␣ run ␣ on ␣ MPF .2021.2.8 " ;

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mlips : forHyperparameter mlips : numRadialBasis ; mlips : isSettingOf entity : run - m3gnet - chen2022 ; mlips : settingValue 3 . entity : setting - rcut -5 - chen2022 a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 5 ␣ for ␣ M3GNet - EFS ␣ training ␣ run ␣ on ␣ MPF .2021.2.8 " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - m3gnet - chen2022 ; mlips : settingValue 5 .

Q9 – MLIP run and trained model. A single training run on MPF.2021.2.8 produces the universal M3GNet-EFS model. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - m3gnet - chen2022 a mlips : TrainedModel ; rdfs : label " M3GNet ␣ universal ␣ IAP ␣ ( M3GNet - EFS ) ␣ trained ␣ on ␣ MPF .2021.2.8 " . entity : run - m3gnet - chen2022 a mlips : MLIPRun ; rdfs : label " M3GNet - EFS ␣ training ␣ run ␣ on ␣ MPF .2021.2.8 " ; mlips : appliesMethod entity : M3GNet ; mlips : hasHyperparameterSetting entity : setting -3 body - cutoff -4 - chen2022 , entity : setting embedding - dim -64 - chen2022 , entity : setting - num - blocks -3 - chen2022 , entity : setting num - radial - basis -3 - chen2022 , entity : setting - rcut -5 - chen2022 ; mlips : produces entity : model - m3gnet - chen2022 ; mlips : runsOn entity : ds - MPF -2021 -2 -8 .

Q10 – Benchmark results. Test-set MAEs on the held-out MPF.2021.2.8 split: 35 meV/atom on energy, 72 meV/Å on force components, 0.41 GPa on stress components. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - mae - energy - chen2022 a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 35 ␣ [ millielectronvolt ␣ per ␣ atom ] " , " Test ␣ MAE ␣ on ␣ energy ␣ per ␣ atom ␣ ( MPF .2021.2.8 ␣ held - out ) " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - mae - energy - chen2022 ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 35 . entity : metric - mae - force - chen2022 a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Force ␣ = ␣ 72 ␣ [ millielectronvolt ␣ per ␣ angstrom ] " , " Test ␣ MAE ␣ on ␣ force ␣ components ␣ ( MPF .2021.2.8 ␣ held - out ) " ; mlips : hasUnit mlips : MilliEV - PER - ANGSTROM ; mlips : isMetricOf entity : result - mae - force - chen2022 ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 72 . entity : metric - mae - stress - chen2022 a mlips : AccuracyMetric ; rdfs : label " Test ␣ MAE ␣ on ␣ stress ␣ components ␣ ( MPF .2021.2.8 ␣ held - out ) " ;

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mlips : hasUnit unit : GigaPA ; mlips : isMetricOf entity : result - mae - stress - chen2022 ; mlips : metricType mlips : MAE ; mlips : metricValue 0.41 . entity : result - mae - energy - chen2022 a mlips : BenchmarkResult ; rdfs : label " M3GNet ␣ universal ␣ IAP ␣ ( M3GNet - EFS ) ␣ trained ␣ on ␣ MPF .2021.2.8 ␣ on ␣ Materials ␣ Project ␣ crystals ␣ ( universal ␣ coverage , ␣ 89 ␣ elements ) ␣ in ␣ Chen ␣ and ␣ Ong ␣ (2022) : ␣ M3GNet ␣ universal ␣ graph ␣ IAP ␣ for ␣ the ␣ periodic ␣ table " ; mlips : evaluatesModel entity : model - m3gnet - chen2022 ; mlips : hasAccuracyMetric entity : metric - mae - energy - chen2022 ; mlips : isResultOf entity : study - chen2022 ; mlips : targetMaterial entity : mat - MP - universal - chen2022 . entity : result - mae - force - chen2022 a mlips : BenchmarkResult ; rdfs : label " M3GNet ␣ universal ␣ IAP ␣ ( M3GNet - EFS ) ␣ trained ␣ on ␣ MPF .2021.2.8 ␣ on ␣ Materials ␣ Project ␣ crystals ␣ ( universal ␣ coverage , ␣ 89 ␣ elements ) ␣ in ␣ Chen ␣ and ␣ Ong ␣ (2022) : ␣ M3GNet ␣ universal ␣ graph ␣ IAP ␣ for ␣ the ␣ periodic ␣ table " ; mlips : evaluatesModel entity : model - m3gnet - chen2022 ; mlips : hasAccuracyMetric entity : metric - mae - force - chen2022 ; mlips : isResultOf entity : study - chen2022 ; mlips : targetMaterial entity : mat - MP - universal - chen2022 . entity : result - mae - stress - chen2022 a mlips : BenchmarkResult ; rdfs : label " M3GNet ␣ universal ␣ IAP ␣ ( M3GNet - EFS ) ␣ trained ␣ on ␣ MPF .2021.2.8 ␣ on ␣ Materials ␣ Project ␣ crystals ␣ ( universal ␣ coverage , ␣ 89 ␣ elements ) ␣ in ␣ Chen ␣ and ␣ Ong ␣ (2022) : ␣ M3GNet ␣ universal ␣ graph ␣ IAP ␣ for ␣ the ␣ periodic ␣ table " ; mlips : evaluatesModel entity : model - m3gnet - chen2022 ; mlips : hasAccuracyMetric entity : metric - mae - stress - chen2022 ; mlips : isResultOf entity : study - chen2022 ; mlips : targetMaterial entity : mat - MP - universal - chen2022 . entity : study - chen2022 mlips : hasResult entity : result - mae - energy - chen2022 , entity : result - mae - force - chen2022 , entity : result - mae - stress - chen2022 .

Q11 – Computational resources. Not reported as ontology-encodable data. The paper notes a single inference example (100-step relaxation of K57 Se34 on one Intel Xeon E5-2620 v4 core takes ∼22 s); recording this as inferenceTimePerAtom would require imputing per-atom and per-step rates, which we leave to Q12. # Q11 - resources : no triples ( paper does not report this ) .

Q12 – Gaps. Beyond Q11, the protocol’s "one paper ≡ one method × one material system" framing is stretched: the universal coverage is recorded as a single MaterialSystem but cannot enumerate the elements, space groups, or chemistries the model covers without extending the ontology. DFT settings that vary by MP task (energy cutoff, k-mesh) are not surfaced. The paper also reports zero-shot relaxations against a held-out 14,055-compound test set and crystal-structure prediction across selected systems; these downstream evaluations are not encoded as separate BenchmarkResult instances. K.15

Deng et al. (2023): CHGNet charge-informed universal MLIP

Q1 – Bibliographic identification. Deng, Zhong, Jun, Riebesell, Han, Bartel, and Ceder introduce CHGNet, a charge-informed universal interatomic potential trained on the Materials Project Trajectory Dataset (MPtrj). Published in Nat. Mach. Intell. 5, 1031–1041 (2023); arXiv:2302.14231. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > .

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@prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -5233 -3462 > schema : affiliation mlips : LawrenceBerkeleyNationalLaboratory , mlips : UniversityofCambridge . < https :// orcid . org /0000 -0001 -9275 -3605 > a schema : Person ; schema : affiliation mlips : LawrenceBerkeleyNationalLaboratory , mlips : UniversityofCaliforniaBerkeley ; schema : familyName " Ceder " ; schema : givenName " Gerbrand " ; schema : identifier < https :// orcid . org /0000 -0001 -9275 -3605 > ; schema : name " Gerbrand ␣ Ceder " . < https :// orcid . org /0000 -0002 -2995 -8381 > a schema : Person ; schema : affiliation mlips : LawrenceBerkeleyNationalLaboratory ; schema : familyName " Han " ; schema : givenName " Kevin " ; schema : identifier < https :// orcid . org /0000 -0002 -2995 -8381 > ; schema : name " Kevin ␣ Han " . < https :// orcid . org /0000 -0002 -5198 -5036 > a schema : Person ; schema : affiliation mlips : UniversityofCaliforniaBerkeley , entity : org UniversityofMinnesota - deng2023 ; schema : familyName " Bartel " ; schema : givenName " Christopher ␣ J . " ; schema : identifier < https :// orcid . org /0000 -0002 -5198 -5036 > ; schema : name " Christopher ␣ J . ␣ Bartel " . < https :// orcid . org /0000 -0003 -1921 -1628 > a schema : Person ; schema : affiliation mlips : LawrenceBerkeleyNationalLaboratory , mlips : UniversityofCaliforniaBerkeley ; schema : familyName " Zhong " ; schema : givenName " Peichen " ; schema : identifier < https :// orcid . org /0000 -0003 -1921 -1628 > ; schema : name " Peichen ␣ Zhong " . < https :// orcid . org /0000 -0003 -1974 -028 X > a schema : Person ; schema : affiliation mlips : LawrenceBerkeleyNationalLaboratory , mlips : UniversityofCaliforniaBerkeley ; schema : familyName " Jun " ; schema : givenName " KyuJung " ; schema : identifier < https :// orcid . org /0000 -0003 -1974 -028 X > ; schema : name " KyuJung ␣ Jun " . < https :// orcid . org /0000 -0003 -4085 -381 X > a schema : Person ; schema : affiliation mlips : LawrenceBerkeleyNationalLaboratory , mlips : UniversityofCaliforniaBerkeley ; schema : familyName " Deng " ; schema : givenName " Bowen " ; schema : identifier < https :// orcid . org /0000 -0003 -4085 -381 X > ; schema : name " Bowen ␣ Deng " . entity : article - deng2023 a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0001 -5233 -3462 > , < https :// orcid . org /0000 -0001 -9275 -3605 > , < https :// orcid . org /0000 -0002 -2995 -8381 > , < https :// orcid . org /0000 -0002 -5198 -5036 > , < https :// orcid . org /0000 -0003 -1921 -1628 > , < https :// orcid . org /0000 -0003 -1974 -028 X > , < https :// orcid . org /0000 -0003 -4085 -381 X > ; schema : datePublished " 2023 " ^^ xsd : gYear ; schema : name " CHGNet : ␣ Pretrained ␣ Universal ␣ Neural ␣ Network ␣ Potential ␣ for ␣ Charge - Informed ␣ Atomistic ␣ Modeling " ; schema : sameAs < https :// doi . org /10.1038/ s42256 -023 -00716 -3 > . entity : org - UniversityofMinnesota - deng2023 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " University ␣ of ␣ Minnesota " ; schema : identifier < https :// ror . org /017 zqws13 > ; schema : name " University ␣ of ␣ Minnesota " . entity : study - deng2023 a mlips : BenchmarkStudy ;

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Hernández et al. rdfs : label " Deng ␣ et ␣ al . ␣ (2023) : ␣ CHGNet ␣ charge - informed ␣ universal ␣ MLIP " ; mlips : reportedIn entity : article - deng2023 .

Q2 – Material system. The MLIP covers the September 2022 Materials Project release: 145,923 inorganic compounds spanning 94 elements. Modelled as a single MaterialSystem at the database-coverage level. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat -MP - universal - deng2023 a mlips : MaterialSystem ; rdfs : comment " No ␣ single ␣ Wikidata ␣ entry ␣ applies : ␣ this ␣ is ␣ the ␣ universal ␣ coverage ␣ of ␣ the ␣ Materials ␣ Project ␣ September ␣ 2022 ␣ release , ␣ spanning ␣ 94 ␣ elements . " ; rdfs : label " Materials ␣ Project ␣ Trajectory ␣ Dataset ␣ coverage ␣ ( universal , ␣ 94 ␣ elements ) " ; mlips : chemicalFormula " any " ; mlips : materialClass " Universal ␣ inorganic ␣ crystal ␣ coverage : ␣ 94 ␣ elements ␣ of ␣ the ␣ periodic ␣ table ;␣ 145 ,923 ␣ distinct ␣ compounds ␣ spanning ␣ the ␣ Materials ␣ Project ␣ September ␣ 2022 ␣ release " .

Q3 – Reference calculation method. Reference data come from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - deng2023 a mlips : DFTCalculation .

Q4 – Reference settings. DFT calculations use VASP with PAW pseudopotentials, PBE GGA (with GGA+U on transition-metal atoms, e.g. 𝑈 = 3.9 eV for Mn), a 520 eV plane-wave cutoff, and a reciprocal-space discretisation of 25 k-points/Å−1 . The MP GGA/GGA+U mixing compatibility correction is applied. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - deng2023 mlips : hasDFTSettings entity : dft - settings - deng2023 . entity : dft - settings - deng2023 a mlips : DFTSettings ; rdfs : comment " Rotationally - averaged ␣ Hubbard ␣ U ␣ correction ␣ ( GGA + U ) ␣ on ␣ transition - metal ␣ atoms ␣(e.g . ␣ U =3.9 ␣ eV ␣ for ␣ Mn ) ; ␣ GGA / GGA + U ␣ mixing ␣ compatibility ␣ correction ␣ applied ␣ across ␣ MPtrj . " ; mlips : energyCutoff 520 ; mlips : kPointMesh " Reciprocal - space ␣ discretisation ␣ of ␣ 25 ␣k - points ␣ per ␣ A ^ -1 " ; mlips : pseudopotentialType mlips : PAW ; mlips : usedDFTCode mlips : VASP ; mlips : xcFunctional mlips : PBE .

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Q5 – Training dataset. MPtrj contains 1,580,395 atomic configurations from 145,923 MP compounds, with energies, forces, and stresses (plus 7,944,833 site magnetic moments used as auxiliary supervision). Provenance is published. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - MPtrj a mlips : TrainingDataset ; rdfs : label " MPtrj : ␣ 1 ,580 ,395 ␣ atomic ␣ configurations ␣ from ␣ 145 ,923 ␣ Materials ␣ Project ␣ compounds , ␣ with ␣ energies , ␣ forces , ␣ stresses , ␣ and ␣ 7 ,944 ,833 ␣ site ␣ magnetic ␣ moments " ; mlips : coversMaterial entity : mat - MP - universal - deng2023 ; mlips : coversProperty mlips : Energy , mlips : Forces , mlips : Stresses ; mlips : datasetProvenance mlips : Published ; mlips : hasDFTCalculation entity : dft - deng2023 ; mlips : numConfigurations 1580395 ; mlips : wasRunBy entity : run - chgnet - deng2023 .

Q6 – Sampling strategies. Three strategies were combined: MP relaxation-trajectory sampling (with extensive filtering for SCF convergence, energy bounds, and StructureMatcher deduplication, then 8:1:1 train/val/test split by mp-id); periodic-table chemical-space coverage (94 elements; 60+ elements with >100k site occurrences; 76 elements with magnetic-moment annotations); and site-magnetic-moment decoration (magmom auxiliary supervision acting as a charge-state regulariser on the latent space). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - MPtrj mlips : samplingStrategy entity : magmom - decoration - sampling - deng2023 , entity : periodic table - coverage - sampling - deng2023 , entity : relaxation - trajectory - sampling - deng2023 . entity : magmom - decoration - sampling - deng2023 a mlips : SamplingStrategy ; rdfs : comment " Each ␣ MPtrj ␣ atomic ␣ configuration ␣ is ␣ decorated ␣ with ␣ site ␣ magnetic ␣ moments ␣ from ␣ the ␣ underlying ␣ spin - polarised ␣ DFT ␣ (7 ,944 ,833 ␣ magmom ␣ labels ␣ in ␣ total ) ,␣ used ␣ as ␣ auxiliary ␣ supervision ␣ targets ␣ that ␣ act ␣ as ␣ a ␣ charge - state ␣ regulariser ␣ on ␣ the ␣ latent ␣ space . " ; rdfs : label " Site - magnetic - moment ␣ decoration " . entity : periodic - table - coverage - sampling - deng2023 a mlips : SamplingStrategy ; rdfs : comment " Compounds ␣ drawn ␣ from ␣ the ␣ Materials ␣ Project ␣ so ␣ as ␣ to ␣ span ␣ 94 ␣ elements ␣ of ␣ the ␣ periodic ␣ table ; ␣ 60+ ␣ elements ␣ have ␣ over ␣ 100 ,000 ␣ site ␣ occurrences ␣ and ␣ 76 ␣ elements ␣ carry ␣ magnetic - moment ␣ annotations . " ; rdfs : label " Periodic - table ␣ chemical - space ␣ coverage " . entity : relaxation - trajectory - sampling - deng2023 a mlips : SamplingStrategy ; rdfs : comment " All ␣ GGA ␣ and ␣ GGA + U ␣ task ␣ trajectories ␣ under ␣ each ␣ material - id ␣ from ␣ the ␣ September ␣ 2022 ␣ Materials ␣ Project ␣ dump . ␣ Tasks ␣ were ␣ filtered ␣ to ␣ share ␣ calculation ␣ settings ␣ with ␣ the ␣ primary ␣ task ␣ ( same ␣ + U ␣ setting ; ␣ final - frame ␣ energy ␣ within ␣ 20 ␣ meV / atom ␣ of ␣ the ␣ primary ␣ task ) ,␣ to ␣ drop ␣ frames ␣ lacking ␣ energy / force ␣ or ␣ with ␣ bad ␣ SCF ␣ convergence , ␣ to ␣ drop ␣ frames ␣ with ␣ energy ␣ >1 ␣ eV / atom ␣ or ␣ < -10 ␣ meV / atom ␣ relative ␣ to ␣ the ␣ relaxed ␣ structure , ␣ and ␣ to ␣ deduplicate ␣ via ␣ pymatgen ␣ StructureMatcher . ␣ The ␣ cleaned ␣ set ␣ was ␣ split ␣ 8:1:1 ␣ train / val / test ␣ by ␣ compound ␣ ( mp - id ) . " ; rdfs : label " Materials ␣ Project ␣ relaxation - trajectory ␣ sampling " .

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Q7 – MLIP method, components, implementation. CHGNet is a two-graph (atom + bond) messagepassing network with explicit angle features, atom/bond/angle convolution blocks, and magmom regularisation of the latent atom features. Outputs are energy, forces, stresses (auto-differentiated), and magnetic moments. Loss is Huber (𝛿 = 0.1) on all four with weights 𝑤 𝐸 = 1, 𝑤 𝑓 = 1, 𝑤 𝜎 = 0.1, 𝑤𝑚 = 0.1. Optimisation is Adam with CosineAnnealingLR. Implementation: CHGNet (PyTorch 1.12.0). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : angularCutoff mlips : isHyperparameterOf entity : CHGNet . mlips : batchSize mlips : isHyperparameterOf entity : CHGNet . mlips : cutoffRadius mlips : isHyperparameterOf entity : CHGNet . mlips : learningRate mlips : isHyperparameterOf entity : CHGNet . mlips : numFeatures mlips : isHyperparameterOf entity : CHGNet . mlips : numLayers mlips : isHyperparameterOf entity : CHGNet . entity : CHGNet a mlips : MLIPMethod ; rdfs : label " CHGNet : ␣ Crystal ␣ Hamiltonian ␣ Graph ␣ neural ␣ Network ␣ with ␣ charge - informed ␣ ( magmom )␣ outputs " ; mlips : hasFunctionalForm entity : chgnet - functional - form ; mlips : hasHyperparameter mlips : angularCutoff , mlips : batchSize , mlips : cutoffRadius , mlips : learningRate , mlips : numFeatures , mlips : numLayers ; mlips : hasImplementation entity : chgnet - impl - deng2023 ; mlips : hasLossFunction entity : chgnet - huber - loss ; mlips : hasTrainingAlgorithm entity : adam - deng2023 ; mlips : supportsSimulation mlips : GeometryOptimization , mlips : MolecularDynamics , mlips : MonteCarlo . entity : adam - deng2023 a mls : Algorithm ; rdfs : label " Adam ␣ optimiser ␣ with ␣ CosineAnnealingLR ␣ scheduler ␣ ( initial ␣ lr =1 e -3 , ␣ decays ␣ to ␣1e -5 ␣ by ␣ epoch ␣ 20 , ␣ learning ␣ rate ␣ adjusted ␣ ten ␣ times ␣ per ␣ epoch ) " . entity : chgnet - functional - form a mlips : FunctionalForm ; rdfs : label " Two - graph ␣ ( atom ␣ + ␣ bond ) ␣ message - passing ␣ neural ␣ network ␣ with ␣ explicit ␣ angle ␣ features , ␣ atom / bond / angle ␣ convolution ␣ blocks , ␣ magmom ␣ regularisation ␣ of ␣ the ␣ latent ␣ atom ␣ features , ␣ and ␣ energy / force / stress / magmom ␣ outputs ␣ ( forces ␣ and ␣ stresses ␣ by ␣ auto - differentiation ␣ of ␣ total ␣ energy ) . " . entity : chgnet - huber - loss a mlips : LossFunction ; rdfs : label " Huber ␣ loss ␣ ( delta =0.1) ␣ on ␣ energy , ␣ forces , ␣ stresses , ␣ and ␣ magnetic ␣ moments ␣ with ␣ weights ␣ w_E =1 , ␣ w_f =1 , ␣ w_sigma =0.1 , ␣ w_m =0.1 " . entity : chgnet - impl - deng2023 a mlips : Implementation ; mlips : implementedIn mlips : CHGNet ; mlips : isImplementationOf entity : CHGNet ; mlips : version " PyTorch ␣ 1.12.0 " .

Q8 – Hyperparameter settings. Reported settings: atom-graph cutoff 𝑟𝑐 = 5.0 Å, bond-graph cutoff 3.0 Å, feature dimension 64, 4 convolution layers, batch size 40, initial learning rate 10−3 . @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > .

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@prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - batch - size -40 - deng2023 a mlips : HyperparameterSetting ; rdfs : label " batch ␣ size ␣ = ␣ 40 ␣ for ␣ CHGNet ␣ ( with - magmom ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : batchSize ; mlips : isSettingOf entity : run - chgnet - deng2023 ; mlips : settingValue 40 . entity : setting - bond - cutoff -3 - deng2023 a mlips : HyperparameterSetting ; rdfs : label " angular ␣ cutoff ␣ = ␣ 3 ␣ for ␣ CHGNet ␣ ( with - magmom ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : angularCutoff ; mlips : isSettingOf entity : run - chgnet - deng2023 ; mlips : settingValue 3 . entity : setting - feature - dim -64 - deng2023 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ features ␣ = ␣ 64 ␣ for ␣ CHGNet ␣ ( with - magmom ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : numFeatures ; mlips : isSettingOf entity : run - chgnet - deng2023 ; mlips : settingValue 64 . entity : setting - initial - lr -1 e -3 - deng2023 a mlips : HyperparameterSetting ; rdfs : label " learning ␣ rate ␣ = ␣ 0.001 ␣ for ␣ CHGNet ␣ ( with - magmom ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : learningRate ; mlips : isSettingOf entity : run - chgnet - deng2023 ; mlips : settingValue 0.001 . entity : setting - num - conv - layers -4 - deng2023 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ layers ␣ = ␣ 4 ␣ for ␣ CHGNet ␣ ( with - magmom ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : numLayers ; mlips : isSettingOf entity : run - chgnet - deng2023 ; mlips : settingValue 4 . entity : setting - rcut -5 - deng2023 a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 5 ␣ for ␣ CHGNet ␣ ( with - magmom ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - chgnet - deng2023 ; mlips : settingValue 5 .

Q9 – MLIP run and trained model. A single training run on MPtrj produces the pretrained universal CHGNet (with-magmom variant, 400,438 trainable parameters). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - chgnet - deng2023 a mlips : TrainedModel ; rdfs : label " CHGNet ␣ pretrained ␣ universal ␣ MLIP ␣ ( with ␣ magmoms , ␣ 400 ,438 ␣ trainable ␣ parameters ) " . entity : run - chgnet - deng2023 a mlips : MLIPRun ; rdfs : label " CHGNet ␣ ( with - magmom ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : appliesMethod entity : CHGNet ; mlips : hasHyperparameterSetting entity : setting - batch - size -40 - deng2023 , entity : setting bond - cutoff -3 - deng2023 , entity : setting - feature - dim -64 - deng2023 , entity : setting initial -lr -1 e -3 - deng2023 , entity : setting - num - conv - layers -4 - deng2023 , entity : setting - rcut -5 - deng2023 ; mlips : produces entity : model - chgnet - deng2023 ; mlips : runsOn entity : ds - MPtrj .

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Q10 – Benchmark results. Test-set MAEs on the held-out MPtrj split (157,955 structures from 14,572 materials): 30 meV/atom on energy, 77 meV/Å on force components, 0.348 GPa on stress components. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - mae - energy - deng2023 a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 30 ␣ [ millielectronvolt ␣ per ␣ atom ] " , " Test ␣ MAE ␣ on ␣ energy ␣ per ␣ atom ␣ ( MPtrj ␣ test ␣ split , ␣ 157 ,955 ␣ structures ␣ from ␣ 14 ,572 ␣ materials ,␣ with - magmom ␣ CHGNet ) " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - mae - energy - deng2023 ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 30 . entity : metric - mae - force - deng2023 a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Force ␣ = ␣ 77 ␣ [ millielectronvolt ␣ per ␣ angstrom ] " , " Test ␣ MAE ␣ on ␣ force ␣ components ␣ ( MPtrj ␣ test ␣ split , ␣ with - magmom ␣ CHGNet ) " ; mlips : hasUnit mlips : MilliEV - PER - ANGSTROM ; mlips : isMetricOf entity : result - mae - force - deng2023 ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 77 . entity : metric - mae - stress - deng2023 a mlips : AccuracyMetric ; rdfs : label " Test ␣ MAE ␣ on ␣ stress ␣ components ␣ ( MPtrj ␣ test ␣ split , ␣ with - magmom ␣ CHGNet ) " ; mlips : hasUnit unit : GigaPA ; mlips : isMetricOf entity : result - mae - stress - deng2023 ; mlips : metricType mlips : MAE ; mlips : metricValue 0.348 . entity : result - mae - energy - deng2023 a mlips : BenchmarkResult ; rdfs : label " CHGNet ␣ pretrained ␣ universal ␣ MLIP ␣ ( with ␣ magmoms , ␣ 400 ,438 ␣ trainable ␣ parameters ) ␣ on ␣ Materials ␣ Project ␣ Trajectory ␣ Dataset ␣ coverage ␣ ( universal , ␣ 94 ␣ elements )␣ in ␣ Deng ␣ et ␣ al . ␣ (2023) : ␣ CHGNet ␣ charge - informed ␣ universal ␣ MLIP " ; mlips : evaluatesModel entity : model - chgnet - deng2023 ; mlips : hasAccuracyMetric entity : metric - mae - energy - deng2023 ; mlips : isResultOf entity : study - deng2023 ; mlips : targetMaterial entity : mat - MP - universal - deng2023 . entity : result - mae - force - deng2023 a mlips : BenchmarkResult ; rdfs : label " CHGNet ␣ pretrained ␣ universal ␣ MLIP ␣ ( with ␣ magmoms , ␣ 400 ,438 ␣ trainable ␣ parameters ) ␣ on ␣ Materials ␣ Project ␣ Trajectory ␣ Dataset ␣ coverage ␣ ( universal , ␣ 94 ␣ elements )␣ in ␣ Deng ␣ et ␣ al . ␣ (2023) : ␣ CHGNet ␣ charge - informed ␣ universal ␣ MLIP " ; mlips : evaluatesModel entity : model - chgnet - deng2023 ; mlips : hasAccuracyMetric entity : metric - mae - force - deng2023 ; mlips : isResultOf entity : study - deng2023 ; mlips : targetMaterial entity : mat - MP - universal - deng2023 . entity : result - mae - stress - deng2023 a mlips : BenchmarkResult ; rdfs : label " CHGNet ␣ pretrained ␣ universal ␣ MLIP ␣ ( with ␣ magmoms , ␣ 400 ,438 ␣ trainable ␣ parameters ) ␣ on ␣ Materials ␣ Project ␣ Trajectory ␣ Dataset ␣ coverage ␣ ( universal , ␣ 94 ␣ elements )␣ in ␣ Deng ␣ et ␣ al . ␣ (2023) : ␣ CHGNet ␣ charge - informed ␣ universal ␣ MLIP " ; mlips : evaluatesModel entity : model - chgnet - deng2023 ; mlips : hasAccuracyMetric entity : metric - mae - stress - deng2023 ; mlips : isResultOf entity : study - deng2023 ; mlips : targetMaterial entity : mat - MP - universal - deng2023 . entity : study - deng2023 mlips : hasResult entity : result - mae - energy - deng2023 , entity : result - mae - force - deng2023 , entity : result - mae - stress - deng2023 .

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Q11 – Computational resources. Not reported. # Q11 - resources : no triples ( paper does not report this ) .

Q12 – Gaps. Beyond Q11, the most prominent gap is the charge-informed aspect of CHGNet: site magnetic moments are auxiliary outputs that the ontology cannot represent as a first-class CoveredProperty (the model encodes them at a hyperparameter- loss-weight level but not as a queryable target property). The universal-coverage simplification of Q2/Q5 carries the same limitation as for chen2022: 94 elements and many MP-task variants collapse to a single MaterialSystem. Downstream applications (LiMnO2 MD, NaMnO2 phase prediction, Li-ion conductor relaxations) are also not encoded as separate BenchmarkResult instances. K.16

Gubaev et al. (2023): MTP for the TaVCrW high-entropy alloy

Q1 – Bibliographic identification. Gubaev, Zaverkin, Srinivasan, Duff, Kästner, and Grabowski compare two complementary machine-learned potentials—a Moment Tensor Potential (MTP) and a Gaussian-Moment Neural Network (GM-NN)—on the TaVCrW BCC refractory high-entropy alloy. Published in npj Computational Materials 9, 129 (2023); doi:10.1038/s41524-023-01073-w. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -6178 -7669 > a schema : Person ; schema : affiliation mlips : UniversityofStuttgart ; schema : familyName " K ä stner " ; schema : givenName " Johannes " ; schema : identifier < https :// orcid . org /0000 -0001 -6178 -7669 > ; schema : name " Johannes ␣ K ä stner " . < https :// orcid . org /0000 -0001 -9940 -8548 > a schema : Person ; schema : affiliation mlips : UniversityofStuttgart ; schema : familyName " Zaverkin " ; schema : givenName " Viktor " ; schema : identifier < https :// orcid . org /0000 -0001 -9940 -8548 > ; schema : name " Viktor ␣ Zaverkin " . < https :// orcid . org /0000 -0002 -5073 -4112 > a schema : Person ; schema : affiliation entity : org - DaresburyLaboratory - gubaev2023 ; schema : familyName " Duff " ; schema : givenName " Andrew ␣ Ian " ; schema : identifier < https :// orcid . org /0000 -0002 -5073 -4112 > ; schema : name " Andrew ␣ Ian ␣ Duff " . < https :// orcid . org /0000 -0002 -9199 -4340 > a schema : Person ; schema : affiliation mlips : UniversityofStuttgart ; schema : familyName " Srinivasan " ; schema : givenName " Prashanth " ; schema : identifier < https :// orcid . org /0000 -0002 -9199 -4340 > ; schema : name " Prashanth ␣ Srinivasan " . < https :// orcid . org /0000 -0003 -2612 -8515 > a schema : Person ; schema : affiliation mlips : UniversityofStuttgart ; schema : familyName " Gubaev " ; schema : givenName " Konstantin " ; schema : identifier < https :// orcid . org /0000 -0003 -2612 -8515 > ; schema : name " Konstantin ␣ Gubaev " . < https :// orcid . org /0000 -0003 -4281 -5665 > a schema : Person ;

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schema : affiliation mlips : UniversityofStuttgart ; schema : familyName " Grabowski " ; schema : givenName " Blazej " ; schema : identifier < https :// orcid . org /0000 -0003 -4281 -5665 > ; schema : name " Blazej ␣ Grabowski " . entity : article - gubaev2023 a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0001 -6178 -7669 > , < https :// orcid . org /0000 -0001 -9940 -8548 > , < https :// orcid . org /0000 -0002 -5073 -4112 > , < https :// orcid . org /0000 -0002 -9199 -4340 > , < https :// orcid . org /0000 -0003 -2612 -8515 > , < https :// orcid . org /0000 -0003 -4281 -5665 > ; schema : datePublished " 2023 " ^^ xsd : gYear ; schema : name " Performance ␣ of ␣ two ␣ complementary ␣ machine - learned ␣ potentials ␣ in ␣ modelling ␣ chemically ␣ complex ␣ systems " ; schema : sameAs < https :// doi . org /10.1038/ s41524 -023 -01073 - w > . entity : org - DaresburyLaboratory - gubaev2023 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Daresbury ␣ Laboratory " ; schema : identifier < https :// ror . org /0089 bg420 > ; schema : name " Daresbury ␣ Laboratory " . entity : study - gubaev2023 a mlips : BenchmarkStudy ; rdfs : label " Gubaev ␣ et ␣ al . ␣ (2023) : ␣ MTP ␣ for ␣ TaVCrW ␣ BCC ␣ refractory ␣ high - entropy ␣ alloy " ; mlips : reportedIn entity : article - gubaev2023 .

Q2 – Material system. The studied system is the equiatomic TaVCrW BCC refractory highentropy alloy (space group 𝐼𝑚 3̄𝑚). Training and validation sets span its 2-, 3-, and 4-component subsystems, plus a deformed B2/B2 phase-segregated quaternary used as out-of-distribution test. We model the chemistry at the four-component level and record the subsystem coverage in materialClass. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat - TaVCrW a mlips : MaterialSystem ; rdfs : comment " Wikidata ␣ Q18405127 ␣ ( ' high ␣ entropy ␣ alloy ') ␣ is ␣ the ␣ most ␣ generic ␣ appropriate ␣ entry ; ␣ TaVCrW ␣ itself ␣ has ␣ no ␣ Wikidata ␣ entry ␣ as ␣ of ␣ 2026 -04 -28. " ; rdfs : label " TaVCrW ␣ equiatomic ␣ BCC ␣ refractory ␣ high - entropy ␣ alloy ␣ ( with ␣ binary , ␣ ternary , ␣ and ␣ quaternary ␣ subsystems ) " ; mlips : chemicalFormula " TaVCrW " ; mlips : materialClass " Refractory ␣ high - entropy ␣ alloy , ␣ BCC ␣ ( Im -3 m ) ,␣ four ␣ equiatomic ␣ constituents ␣ ( Ta , ␣V , ␣ Cr , ␣ W ) ; ␣ training ␣ set ␣ spans ␣ 2 - , ␣ 3 - , ␣ and ␣ 4 - component ␣ BCC ␣ subsystems ␣ plus ␣ a ␣ deformed ␣ B2 / B2 ␣ phase - segregated ␣ quaternary ␣ used ␣ as ␣ out - of distribution ␣ test " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q18405127 > .

Q3 – Reference calculation method. Reference data are produced from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - TaVCrW

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a mlips : DFTCalculation .

Q4 – Reference settings. DFT calculations are performed with VASP at the PBE/GGA level using PAW pseudopotentials (11 valence electrons for Ta and V; 12 for Cr and W; spin-unpolarised), with Methfessel–Paxton smearing of order 1 (𝜎 = 0.1), a 350 eV plane-wave cutoff, and an automatic k-mesh generated by VASP at KSPACING = 0.12. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - TaVCrW mlips : hasDFTSettings entity : dft - settings - TaVCrW . entity : dft - settings - TaVCrW a mlips : DFTSettings ; rdfs : comment " 11 ␣ valence ␣ electrons ␣ for ␣ Ta ␣ and ␣ V ; ␣ 12 ␣ for ␣ Cr ␣ and ␣ W ; ␣ spin - unpolarised . " ; mlips : energyCutoff 350 ; mlips : kPointMesh " Automatic ␣k - mesh ␣ with ␣ KSPACING =0.12 , ␣ Methfessel - Paxton ␣ smearing ␣ of ␣ order ␣1␣ with ␣ sigma =0.1 " ; mlips : pseudopotentialType mlips : PAW ; mlips : usedDFTCode mlips : VASP ; mlips : xcFunctional mlips : PBE .

Q5 – Training dataset. The training+validation set has 6,711 DFT configurations: 5,680 at 0 K (4,491 binary, 595 ternary, 594 quaternary) plus 1,031 MD-sampled at 2,500 K (close to the melting point). Energies, forces, and stresses are covered. Provenance is in-house. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - TaVCrW a mlips : TrainingDataset ; rdfs : label " TaVCrW ␣ MTP + GM - NN ␣ training + validation ␣ set : ␣ 6711 ␣ DFT ␣ configurations ␣ (5680 ␣ at ␣0␣K␣=␣ 4491 ␣ binary ␣ + ␣ 595 ␣ ternary ␣ + ␣ 594 ␣ quaternary ; ␣ plus ␣ 1031 ␣ MD - sampled ␣ at ␣ 2500 ␣ K ) " ; mlips : coversMaterial entity : mat - TaVCrW ; mlips : coversProperty mlips : Energy , mlips : Forces , mlips : Stresses ; mlips : datasetProvenance mlips : InHouse ; mlips : hasDFTCalculation entity : dft - TaVCrW ; mlips : numConfigurations 6711 ; mlips : wasRunBy entity : run - mtp - TaVCrW .

Q6 – Sampling strategies. Four strategies are combined: 0 K small-supercell enumeration with enumlib (2–8 atom non-repetitive symmetry-unique supercells; 2,500 binary structures plus ternaries, equiatomic and off-equiatomic quaternaries); vibrational sampling via DFT MD at 2,500 K; active learning using the MaxVol extrapolation grade (selecting MD frames with grade above threshold for DFT recomputation); and phase-segregation sampling via 432-atom B2/B2 deformed-binary structures. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > .

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@prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : active - learning - sampling - gubaev2023 a mlips : SamplingStrategy ; rdfs : comment " Iterative ␣ dataset ␣ growth : ␣ an ␣ MD ␣ trajectory ␣ using ␣ the ␣ current ␣ MTP ␣ is ␣ mined ␣ for ␣ configurations ␣ whose ␣ extrapolation ␣ grade ␣ exceeds ␣ a ␣ threshold ; ␣ selected ␣ configurations ␣ are ␣ re - computed ␣ with ␣ DFT ␣ and ␣ added ␣ to ␣ the ␣ training ␣ data , ␣ then ␣ the ␣ MTP ␣ is ␣ retrained . ␣ The ␣ same ␣ configurations ␣ are ␣ reused ␣ for ␣ the ␣ GM - NN ␣ comparison . " ; rdfs : label " Active ␣ learning ␣ ( MaxVol ␣ extrapolation ␣ grade ) " . entity : deformed - binary - sampling - gubaev2023 a mlips : SamplingStrategy ; rdfs : comment " 432 - atom ␣ B2 / B2 ␣ deformed ␣ quaternary ␣ structures ␣ constructed ␣ by ␣ joining ␣ strained ␣ binary ␣ halves ␣ ( TaV ␣ +3.7% , ␣ CrW ␣ -1.28% , ␣ TaCr ␣ +0.27% , ␣ VW ␣ -0.14% , ␣ TaW ␣ +4.06% , ␣ VCr ␣ -4.71%) ␣ along ␣ [100] , ␣ used ␣ as ␣ a ␣ test ␣ set ␣ for ␣ the ␣ phase - segregated ␣ quaternary . " ; rdfs : label " Deformed - binary ␣ phase - segregation ␣ sampling " . entity :ds - TaVCrW mlips : samplingStrategy entity : active - learning - sampling - gubaev2023 , entity : deformed binary - sampling - gubaev2023 , entity : enumlib - sampling - gubaev2023 , entity : vib sampling - gubaev2023 . entity : enumlib - sampling - gubaev2023 a mlips : SamplingStrategy ; rdfs : comment " 0 ␣ K ␣ configurations ␣ in ␣ 2 -8 ␣ atom ␣ supercells ␣ generated ␣ with ␣ the ␣ enumlib ␣ library ;␣ non - repetitive ␣ symmetries ␣ are ␣ enumerated ␣ and ␣ 2500 ␣ binary ␣ structures ␣ are ␣ sampled ␣( plus ␣ ternaries , ␣ plus ␣ equiatomic ␣ and ␣ off - equiatomic ␣ quaternaries ) . " ; rdfs : label "0␣K ␣ small - supercell ␣ enumeration ␣ ( enumlib ) " . entity : vib - sampling - gubaev2023 a mlips : SamplingStrategy ; rdfs : comment " 1031 ␣ unrelaxed ␣ snapshots ␣ from ␣ DFT ␣ MD ␣ at ␣ 2500 ␣ K ␣ ( close ␣ to ␣ the ␣ melting ␣ point ) ,␣ spanning ␣ the ␣ disordered ␣ TaVCrW ␣ phase ␣ and ␣ its ␣ compositional ␣ subsystems . " ; rdfs : label " Vibrational ␣ sampling ␣ ( DFT ␣ MD ␣ at ␣ 2500 ␣ K ) " .

Q7 – MLIP method, components, implementation. We encode the MTP arm. The method is a Moment Tensor Potential with a level-restricted basis (lev max controls the radial+angular truncation), implemented in the MLIP package (https://gitlab.com/ashapeev/mlip-2). Loss is weighted MSE on energies/forces/stresses with weights 𝑤 𝐸 = 1/𝑁 at , 𝑤 𝑓 = 0.1, 𝑤 𝜎 = 0.001. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : MTP . mlips : momentLevel mlips : isHyperparameterOf entity : MTP . entity : MTP a mlips : MLIPMethod ; rdfs : label " Moment ␣ Tensor ␣ Potential " ; mlips : hasDescriptor mlips : MomentTensorDescriptor ; mlips : hasFunctionalForm entity : mtp - functional - form ; mlips : hasHyperparameter mlips : cutoffRadius , mlips : momentLevel ; mlips : hasImplementation entity : mlip - package - gubaev2023 ; mlips : hasLossFunction entity : mtp - loss - gubaev2023 ; mlips : supportsSimulation mlips : MolecularDynamics , mlips : ThermodynamicIntegration . entity : mlip - package - gubaev2023 a mlips : Implementation ; mlips : implementedIn mlips : MLIP ; mlips : isImplementationOf entity : MTP . entity : mtp - functional - form a mlips : FunctionalForm ;

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rdfs : label " MTP ␣ moment - tensor ␣ polynomial ␣ with ␣ level - restricted ␣ basis ␣ ( lev_max ␣ controls ␣ the ␣ radial + angular ␣ truncation ) " . entity : mtp - loss - gubaev2023 a mlips : LossFunction ; rdfs : label " Weighted ␣ MSE ␣ on ␣ energies , ␣ forces , ␣ and ␣ stresses ␣ with ␣ weights ␣ w_E =1/ N_at , ␣ w_f =0.1 , ␣ w_sigma =0.001 " .

Q8 – Hyperparameter settings. Reported setting: cutoff radius 𝑟𝑐 = 5.0 Å. The lev max value is referenced under hasHyperparameter but the paper compares several values (0, 2, . . . ) without designating one as canonical, so we omit a HyperparameterSetting instance for it. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - rcut -50 - gubaev2023 a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 5 ␣ for ␣ MTP ␣ training ␣ run ␣ on ␣ the ␣ TaVCrW ␣ HEA ␣ dataset ␣ (6711 ␣ configurations ) " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - mtp - TaVCrW ; mlips : settingValue 5 .

Q9 – MLIP run and trained model. A single MTP training run on the 6,711-configuration training set produces one trained TaVCrW MTP. No active-learning ensemble structure is recorded at the level of separate MLIPRun instances. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - mtp - TaVCrW a mlips : TrainedModel ; rdfs : label " TaVCrW ␣ MTP " . entity : run - mtp - TaVCrW a mlips : MLIPRun ; rdfs : label " MTP ␣ training ␣ run ␣ on ␣ the ␣ TaVCrW ␣ HEA ␣ dataset ␣ (6711 ␣ configurations ) " ; mlips : appliesMethod entity : MTP ; mlips : hasHyperparameterSetting entity : setting - rcut -50 - gubaev2023 ; mlips : produces entity : model - mtp - TaVCrW ; mlips : runsOn entity : ds - TaVCrW .

Q10 – Benchmark results. Overall RMSEs across the in-distribution Ta–V–Cr–W subsystems (Table 1, MTP): 2.43 meV/atom on energy, 0.054 eV/Å on forces. The 2,500 K disordered TaVCrW point alone has RMSEs of 2.40 meV/atom and 0.156 eV/Å; the cross-method comparison with GM-NN and EAM is in the same table. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > .

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@prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - rmse - energy - gubaev2023 a mlips : AccuracyMetric ; rdfs : label " Overall ␣ RMSE ␣ in ␣ predicted ␣ energy ␣ across ␣ in - distribution ␣ Ta -V - Cr - W ␣ subsystems ␣ ( Table ␣ 1 , ␣ MTP ) " , " RMSE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 2.43 ␣ [ millielectronvolt ␣ per ␣ atom ] " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - mtp - energy - gubaev2023 ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 2.43 . entity : metric - rmse - forces - gubaev2023 a mlips : AccuracyMetric ; rdfs : label " Overall ␣ RMSE ␣ in ␣ predicted ␣ atomic ␣ forces ␣ across ␣ in - distribution ␣ Ta -V - Cr - W ␣ subsystems ␣ ( Table ␣ 1 , ␣ MTP ) " , " RMSE ␣ of ␣ Force ␣ = ␣ 0.054 ␣ [ EV - PER - ANGSTROM ] " ; mlips : hasUnit unit : EV - PER - ANGSTROM ; mlips : isMetricOf entity : result - mtp - forces - gubaev2023 ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 0.054 . entity : result - mtp - energy - gubaev2023 a mlips : BenchmarkResult ; rdfs : label " TaVCrW ␣ MTP ␣ on ␣ TaVCrW ␣ equiatomic ␣ BCC ␣ refractory ␣ high - entropy ␣ alloy ␣ ( with ␣ binary ,␣ ternary , ␣ and ␣ quaternary ␣ subsystems ) ␣ in ␣ Gubaev ␣ et ␣ al . ␣ (2023) : ␣ MTP ␣ for ␣ TaVCrW ␣ BCC ␣ refractory ␣ high - entropy ␣ alloy " ; mlips : evaluatesModel entity : model - mtp - TaVCrW ; mlips : hasAccuracyMetric entity : metric - rmse - energy - gubaev2023 ; mlips : isResultOf entity : study - gubaev2023 ; mlips : targetMaterial entity : mat - TaVCrW . entity : result - mtp - forces - gubaev2023 a mlips : BenchmarkResult ; rdfs : label " TaVCrW ␣ MTP ␣ on ␣ TaVCrW ␣ equiatomic ␣ BCC ␣ refractory ␣ high - entropy ␣ alloy ␣ ( with ␣ binary ,␣ ternary , ␣ and ␣ quaternary ␣ subsystems ) ␣ in ␣ Gubaev ␣ et ␣ al . ␣ (2023) : ␣ MTP ␣ for ␣ TaVCrW ␣ BCC ␣ refractory ␣ high - entropy ␣ alloy " ; mlips : evaluatesModel entity : model - mtp - TaVCrW ; mlips : hasAccuracyMetric entity : metric - rmse - forces - gubaev2023 ; mlips : isResultOf entity : study - gubaev2023 ; mlips : targetMaterial entity : mat - TaVCrW . entity : study - gubaev2023 mlips : hasResult entity : result - mtp - energy - gubaev2023 , entity : result - mtp - forces gubaev2023 .

Q11 – Computational resources. Not reported in absolute form. The paper compares MTP and GM-NN convergence with training-set size and execution speed qualitatively but gives no training duration, GPU/CPU hours, training hardware, peak memory, or per-atom inference time. # Q11 - resources : no triples ( paper does not report this ) .

Q12 – Gaps. The most consequential omission is the GM-NN arm: the paper trains both an MTP and a GM-NN on the same data and frames the comparison as the main contribution. The ontology can express each as an MLIPMethod instance with its own MLIPRun and TrainedModel, and a sibling gubaev2023-gmnn.ttl would mirror this file with ex:GM-NN and the gm-nn package as Library. Other unreported items: lev max as a HyperparameterSetting (the paper sweeps several values); the GM-NN architectural hyperparameters (number of layers, channel widths, learning rate); active-learning iteration counts; downstream phonon and elastic-constant benchmarks; and compute-cost metadata. K.17

Musaelian et al. (2023): Allegro strictly local equivariant MLIP

Q1 – Bibliographic identification. Musaelian, Batzner, Johansson, Sun, Owen, Kornbluth, and Kozinsky introduce Allegro, a strictly local equivariant deep-learning interatomic potential that combines the accuracy of equivariant message passing with the parallel scalability of local descriptor methods. Published in Nature Communications 14, 579 (2023); arXiv:2204.05249. The

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paper reports benchmarks on revised MD17, QM9, the 3BPA temperature-transferability set, the Li3 PO4 amorphous phosphate solid electrolyte, and an Ag bulk-crystal scaling experiment up to 100 million atoms. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -6705 -8133 > a schema : Person ; schema : affiliation mlips : RobertBoschUnitedStates ; schema : familyName " Kornbluth " ; schema : givenName " Mordechai " ; schema : identifier < https :// orcid . org /0000 -0001 -6705 -8133 > ; schema : name " Mordechai ␣ Kornbluth " . < https :// orcid . org /0000 -0002 -0544 -7202 > a schema : Person ; schema : affiliation mlips : HarvardUniversity ; schema : familyName " Johansson " ; schema : givenName " Anders " ; schema : identifier < https :// orcid . org /0000 -0002 -0544 -7202 > ; schema : name " Anders ␣ Johansson " . < https :// orcid . org /0000 -0002 -0638 -539 X > a schema : Person ; schema : affiliation mlips : HarvardUniversity , mlips : RobertBoschUnitedStates , entity : org RobertBoschSlovenia - musaelian2023allegro ; schema : familyName " Kozinsky " ; schema : givenName " Boris " ; schema : identifier < https :// orcid . org /0000 -0002 -0638 -539 X > ; schema : name " Boris ␣ Kozinsky " . < https :// orcid . org /0000 -0002 -2543 -7415 > a schema : Person ; schema : affiliation mlips : HarvardUniversity ; schema : familyName " Owen " ; schema : givenName " Cameron ␣ J . " ; schema : identifier < https :// orcid . org /0000 -0002 -2543 -7415 > ; schema : name " Cameron ␣ J . ␣ Owen " . < https :// orcid . org /0000 -0002 -7971 -5222 > schema : affiliation mlips : HarvardUniversity . < https :// orcid . org /0000 -0002 -8826 -2712 > a schema : Person ; schema : affiliation mlips : HarvardUniversity ; schema : familyName " Batzner " ; schema : givenName " Simon " ; schema : identifier < https :// orcid . org /0000 -0002 -8826 -2712 > ; schema : name " Simon ␣ Batzner " . < https :// orcid . org /0000 -0003 -0475 -9236 > schema : affiliation mlips : HarvardUniversity . entity : article - musaelian2023allegro a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0001 -6705 -8133 > , < https :// orcid . org /0000 -0002 -0544 -7202 > , < https :// orcid . org /0000 -0002 -0638 -539 X > , < https :// orcid . org /0000 -0002 -2543 -7415 > , < https :// orcid . org /0000 -0002 -7971 -5222 > , < https :// orcid . org /0000 -0002 -8826 -2712 > , < https :// orcid . org /0000 -0003 -0475 -9236 > ; schema : datePublished " 2023 " ^^ xsd : gYear ; schema : name " Learning ␣ Local ␣ Equivariant ␣ Representations ␣ for ␣ Large - Scale ␣ Atomistic ␣ Dynamics " ; schema : sameAs < https :// doi . org /10.1038/ s41467 -023 -36329 - y > . entity : org - RobertBoschSlovenia - musaelian2023allegro a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " Robert ␣ Bosch ␣ ( Slovenia ) " ; schema : identifier < https :// ror . org /03248 dr08 > ; schema : name " Robert ␣ Bosch ␣ ( Slovenia ) " . entity : study - musaelian2023allegro

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Hernández et al. a mlips : BenchmarkStudy ; rdfs : label " Musaelian ␣ et ␣ al . ␣ (2023) : ␣ Allegro ␣ strictly ␣ local ␣ equivariant ␣ MLIP ␣ on ␣ Li3PO4 " ; mlips : reportedIn entity : article - musaelian2023allegro .

Q2 – Material system. The canonical encoding pass takes the Li3 PO4 amorphous phosphate solid electrolyte (192-atom cell) as the headline materials/MD application: a class of solid-state electrolytes characterised by an intricate dependence of conductivity and mechanical properties on the degree of crystallinity. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat - Li3PO4 a mlips : MaterialSystem ; rdfs : label " Li3PO4 ␣ amorphous ␣ phosphate ␣ solid ␣ electrolyte ␣ (192 - atom ␣ cell ) " ; mlips : chemicalFormula " Li3PO4 " ; mlips : materialClass " Amorphous ␣ Li - ion ␣ solid ␣ electrolyte ␣ ( melt - quench , ␣ 50 ␣ ps ␣ melt ␣ at ␣ 3000 ␣K␣ then ␣ quench ␣ to ␣ 600 ␣ K ) " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q426354 > .

Q3 – Reference calculation method. Reference data are produced from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - musaelian2023allegro a mlips : DFTCalculation .

Q4 – Reference settings. The Li3 PO4 reference is generated with VASP using the PBE functional, PAW pseudopotentials, a 400 eV plane-wave cutoff, and a Γ-point reciprocal-space mesh, in NVT (Nosé–Hoover) at 2 fs time step. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - musaelian2023allegro mlips : hasDFTSettings entity : dft - settings - musaelian2023allegro . entity : dft - settings - musaelian2023allegro a mlips : DFTSettings ; mlips : energyCutoff 400 ; mlips : kPointMesh " Gamma - point ␣ only " ; mlips : pseudopotentialType mlips : PAW ; mlips : usedDFTCode mlips : VASP ; mlips : xcFunctional mlips : PBE .

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Q5 – Training dataset. The Li3 PO4 training set consists of 10,000 structures sampled randomly from the combined 50,000-frame melt + quench AIMD dataset, with 1,000 validation structures held out. The set covers energies and forces. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - Li3PO4 a mlips : TrainingDataset ; rdfs : label " Li3PO4 ␣ melt ␣ + ␣ quench ␣ AIMD ␣ training ␣ set ␣ (10000 ␣ train ␣ + ␣ 1000 ␣ validation , ␣ sampled ␣ from ␣ a ␣ 50000 - frame ␣ combined ␣ melt + quench ␣ AIMD ␣ trajectory ) " ; mlips : coversMaterial entity : mat - Li3PO4 ; mlips : coversProperty mlips : Energy , mlips : Forces ; mlips : datasetProvenance mlips : InHouse ; mlips : hasDFTCalculation entity : dft - musaelian2023allegro ; mlips : numConfigurations 10000 ; mlips : wasRunBy entity : run - allegro - Li3PO4 .

Q6 – Sampling strategies. A single sampling strategy is in play: AIMD melt-quench sampling. The data set comes from a 50 ps AIMD trajectory in the melted state at 𝑇 = 3000 K, an instant quench to 600 K, then a 50 ps AIMD trajectory in the quenched state at 𝑇 = 600 K (Vienna ab-initio Simulation Package, NVT, Nosé–Hoover, 2 fs). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - Li3PO4 mlips : samplingStrategy entity : meltquench - sampling - musaelian2023allegro . entity : meltquench - sampling - musaelian2023allegro a mlips : SamplingStrategy ; rdfs : comment " 50 ␣ ps ␣ AIMD ␣ at ␣ T =3000 ␣ K ␣ in ␣ the ␣ melted ␣ state , ␣ instantly ␣ quenched ␣ to ␣ T =600 ␣ K ,␣ then ␣ 50 ␣ ps ␣ at ␣ T =600 ␣ K . ␣ Train + validation ␣ sampled ␣ randomly ␣ from ␣ the ␣ combined ␣ 50000 - frame ␣ trajectory . " ; rdfs : label " AIMD ␣ melt - quench ␣ sampling ␣ ( NVT , ␣ 2 ␣ fs ␣ time ␣ step , ␣ Nose - Hoover ␣ thermostat ) " .

Q7 – MLIP method, components, implementation. Allegro is a strictly local equivariant network: each pair (𝑖, 𝑗) within the cutoff carries a scalar latent space x𝑖 𝑗,𝐿 and an equivariant latent space 𝑖 𝑗,𝐿 V𝑛,ℓ,𝑝 , updated layer by layer through tensor products with the spherical-harmonic projections of neighbour bonds, weighted by the central atom’s environment embedding. Pair energies 𝐸𝑖 𝑗 are summed to give per-atom energies; forces are autodiff-derived. The training algorithm is Adam (𝛽 1 = 0.9, 𝛽 2 = 0.999, 𝜖 = 10−8 , no weight decay) with an on-plateau scheduler (patience 100, decay factor 0.8). The loss is a weighted MSE on per-atom energies and force components (𝜆𝐸 = 𝜆𝐹 = 1 after per-atom normalisation; 𝜆𝐸 = 1, 𝜆𝐹 = 1000 for revMD17). Implementation is the allegro PyTorch code (https://github.com/mir-group/allegro), with LAMMPS production runs via the pair_allegro extension. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > .

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@prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : Allegro . mlips : numAngularBasis mlips : isHyperparameterOf entity : Allegro . mlips : numFeatures mlips : isHyperparameterOf entity : Allegro . mlips : numLayers mlips : isHyperparameterOf entity : Allegro . entity : Allegro a mlips : MLIPMethod ; rdfs : label " Allegro ␣ ( strictly ␣ local ␣ equivariant ␣ interatomic ␣ potential ) " ; mlips : hasFunctionalForm entity : allegro - functional - form ; mlips : hasHyperparameter mlips : cutoffRadius , mlips : numAngularBasis , mlips : numFeatures , mlips : numLayers , entity : hp - numbasis ; mlips : hasImplementation entity : allegro - impl ; mlips : hasLossFunction entity : allegro - loss ; mlips : hasTrainingAlgorithm entity : adam - allegro ; mlips : supportsSimulation mlips : MolecularDynamics . entity : adam - allegro a mls : Algorithm ; rdfs : label " Adam , ␣ beta1 =0.9 , ␣ beta2 =0.999 , ␣ eps =1 e -8 , ␣ no ␣ weight ␣ decay " . entity : allegro - functional - form a mlips : FunctionalForm ; rdfs : label " Strictly ␣ local ␣ equivariant ␣ tensor - product ␣ network ␣ on ␣ per - pair ␣ latent ␣ spaces ␣( scalar ␣ + ␣ equivariant ) ,␣ no ␣ inter - atom ␣ message ␣ passing ; ␣ pairwise ␣ energies ␣ E_ij ␣ summed ␣ over ␣ neighbours ␣ to ␣ give ␣ per - atom ␣ energies " . entity : allegro - impl a mlips : Implementation ; mlips : implementedIn mlips : Allegro ; mlips : isImplementationOf entity : Allegro . entity : allegro - loss a mlips : LossFunction ; rdfs : label " Weighted ␣ MSE ␣ on ␣ energies ␣ ( per - atom ) ␣ and ␣ force ␣ components ␣ ( lambda_E ␣ = ␣ 1 , ␣ lambda_F ␣= ␣ 1 ␣ after ␣ per - atom ␣ normalisation ; ␣ lambda_E ␣ = ␣ 1 , ␣ lambda_F ␣ = ␣ 1000 ␣ raw ␣ for ␣ revMD17 )" . entity :hp - numbasis a mlips : Hyperparameter ; rdfs : label " Allegro ␣ tensor - product ␣ basis ␣ count " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : integer ; mlips : hyperparameterName " num_basis_functions " ; mlips : isHyperparameterOf entity : Allegro .

Q8 – Hyperparameter settings. The Li3 PO4 production model uses 3 layers, 128 features for even and odd irreps, ℓmax = 3, and a 6 Å radial cutoff with 8 non-trainable Bessel basis functions and a polynomial envelope (𝑝 = 6). The two-body latent MLP is [128, 256, 512, 1024] with SiLU non-linearities; the later latent MLPs are [1024, 1024, 1024] with SiLU; the embedding weight projection is a single linear layer; the output edge-energy MLP is a single hidden layer of dimension 128. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - features - allegro a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ features ␣ = ␣ 128 ␣ for ␣ Allegro ␣ training ␣ run ␣ on ␣ Li3PO4 ␣ melt + quench ␣ (3 ␣ layers ,␣ lmax =3 , ␣ 128 ␣ features ) " ; mlips : forHyperparameter mlips : numFeatures ; mlips : isSettingOf entity : run - allegro - Li3PO4 ; mlips : settingValue 128 . entity : setting - lmax - allegro

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a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ angular ␣ basis ␣ functions ␣ = ␣ 3 ␣ for ␣ Allegro ␣ training ␣ run ␣ on ␣ Li3PO4 ␣ melt + quench ␣ (3 ␣ layers , ␣ lmax =3 , ␣ 128 ␣ features ) " ; mlips : forHyperparameter mlips : numAngularBasis ; mlips : isSettingOf entity : run - allegro - Li3PO4 ; mlips : settingValue 3 . entity : setting - numbasis - allegro a mlips : HyperparameterSetting ; rdfs : label " Allegro ␣ tensor - product ␣ basis ␣ count ␣ = ␣ 8 ␣ for ␣ Allegro ␣ training ␣ run ␣ on ␣ Li3PO4 ␣ melt + quench ␣ (3 ␣ layers , ␣ lmax =3 , ␣ 128 ␣ features ) " ; mlips : forHyperparameter entity : hp - numbasis ; mlips : isSettingOf entity : run - allegro - Li3PO4 ; mlips : settingValue 8 . entity : setting - numlayers - allegro a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ layers ␣ = ␣ 3 ␣ for ␣ Allegro ␣ training ␣ run ␣ on ␣ Li3PO4 ␣ melt + quench ␣ (3 ␣ layers ,␣ lmax =3 , ␣ 128 ␣ features ) " ; mlips : forHyperparameter mlips : numLayers ; mlips : isSettingOf entity : run - allegro - Li3PO4 ; mlips : settingValue 3 . entity : setting - rcut - allegro a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 6 ␣ for ␣ Allegro ␣ training ␣ run ␣ on ␣ Li3PO4 ␣ melt + quench ␣ (3 ␣ layers ,␣ lmax =3 , ␣ 128 ␣ features ) " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - allegro - Li3PO4 ; mlips : settingValue 6 .

Q9 – MLIP run and trained model. A single training run on 10,000 frames produces one Li3 PO4 Allegro model. Training is at float32 precision with learning rate 0.002 and batch size 5; an EMA with weight 0.99 tracks the validation model. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - allegro - Li3PO4 a mlips : TrainedModel ; rdfs : label " Allegro ␣ Li3PO4 ␣ model ␣ (3 ␣ layers , ␣ lmax =3 , ␣ 128 ␣ features ) " . entity : run - allegro - Li3PO4 a mlips : MLIPRun ; rdfs : label " Allegro ␣ training ␣ run ␣ on ␣ Li3PO4 ␣ melt + quench ␣ (3 ␣ layers , ␣ lmax =3 , ␣ 128 ␣ features )" ; mlips : appliesMethod entity : Allegro ; mlips : hasHyperparameterSetting entity : setting - features - allegro , entity : setting - lmax allegro , entity : setting - numbasis - allegro , entity : setting - numlayers - allegro , entity : setting - rcut - allegro ; mlips : produces entity : model - allegro - Li3PO4 ; mlips : runsOn entity : ds - Li3PO4 .

Q10 – Benchmark results. Headline figures on the Li3 PO4 quenched-state test set are MAE 1.7 meV/atom on energies and 75.7 meV/Å on force components. Allegro accurately recovers the AIMD radial distribution function and the tetrahedral P–O–O angular distribution, and the AIMD-vs.-Allegro Li MSD agree well in the quenched state at 600 K. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > .

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entity : metric - mae - Li3PO4 - energy a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 1.7 ␣ [ millielectronvolt ␣ per ␣ atom ] " , " MAE ␣ on ␣ Li3PO4 ␣ quenched - state ␣ energies " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - allegro - Li3PO4 - energy ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 1.7 . entity : metric - mae - Li3PO4 - forces a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Force ␣ = ␣ 75.7 ␣ [ millielectronvolt ␣ per ␣ angstrom ] " , " MAE ␣ on ␣ Li3PO4 ␣ quenched - state ␣ force ␣ components " ; mlips : hasUnit mlips : MilliEV - PER - ANGSTROM ; mlips : isMetricOf entity : result - allegro - Li3PO4 - forces ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 75.7 . entity : result - allegro - Li3PO4 - energy a mlips : BenchmarkResult ; rdfs : label " Allegro ␣ Li3PO4 ␣ model ␣ (3 ␣ layers , ␣ lmax =3 , ␣ 128 ␣ features ) ␣ on ␣ Li3PO4 ␣ amorphous ␣ phosphate ␣ solid ␣ electrolyte ␣ (192 - atom ␣ cell ) ␣ in ␣ Musaelian ␣ et ␣ al . ␣ (2023) : ␣ Allegro ␣ strictly ␣ local ␣ equivariant ␣ MLIP ␣ on ␣ Li3PO4 " ; mlips : evaluatesModel entity : model - allegro - Li3PO4 ; mlips : hasAccuracyMetric entity : metric - mae - Li3PO4 - energy ; mlips : isResultOf entity : study - musaelian2023allegro ; mlips : targetMaterial entity : mat - Li3PO4 . entity : result - allegro - Li3PO4 - forces a mlips : BenchmarkResult ; rdfs : label " Allegro ␣ Li3PO4 ␣ model ␣ (3 ␣ layers , ␣ lmax =3 , ␣ 128 ␣ features ) ␣ on ␣ Li3PO4 ␣ amorphous ␣ phosphate ␣ solid ␣ electrolyte ␣ (192 - atom ␣ cell ) ␣ in ␣ Musaelian ␣ et ␣ al . ␣ (2023) : ␣ Allegro ␣ strictly ␣ local ␣ equivariant ␣ MLIP ␣ on ␣ Li3PO4 " ; mlips : evaluatesModel entity : model - allegro - Li3PO4 ; mlips : hasAccuracyMetric entity : metric - mae - Li3PO4 - forces ; mlips : isResultOf entity : study - musaelian2023allegro ; mlips : targetMaterial entity : mat - Li3PO4 . entity : study - musaelian2023allegro mlips : hasResult entity : result - allegro - Li3PO4 - energy , entity : result - allegro - Li3PO4 forces .

Q11 – Computational resources. Allegro models were trained on a single NVIDIA V100 GPU; specific training duration and GPU-hours for the Li3 PO4 pass are not reported (the paper notes “a matter of hours or even minutes”). For inference, the paper reports detailed strong-scaling times on the Theta-GPU NVIDIA DGX A100 cluster: a 50.3M-atom Li3 PO4 run on 128 A100 GPUs achieves 0.013 𝜇s per atom per MD step, and a 100M-atom Ag run on 128 A100 GPUs is reported in Table IV; we encode the Li3 PO4 atomic-throughput figure as inferenceTimePerAtom on the trained model. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - allegro - Li3PO4 mlips : inferenceHardware " NVIDIA ␣ DGX ␣ A100 ␣ cluster ␣ ( Theta - GPU , ␣ ALCF ) ,␣ 128 ␣ A100 ␣ GPUs ␣ across ␣ 16 ␣ nodes " ; mlips : inferenceTimePerAtom " 0.013 ␣ microseconds ␣ per ␣ atom ␣ per ␣ MD ␣ step ␣ on ␣ 128 ␣ NVIDIA ␣ A100 ␣ GPUs ␣ (50.3 M - atom ␣ Li3PO4 ␣ system , ␣ LAMMPS ␣ pair_allegro ␣ at ␣ float32 ) " . entity : run - allegro - Li3PO4 mlips : trainingHardware " NVIDIA ␣ V100 ␣ GPU ␣ ( single - GPU ␣ training ) " .

Q12 – Gaps. Beyond Q11, the following ontology-expressible items are not represented in this encoding pass: (i) the four additional benchmarks reported in the same paper (revised MD17 with PBE/def2-SVP reference, QM9 with DFT/B3LYP/6-31G(2df,p) reference, the 3BPA 𝜔B97X/6-31G(d)

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temperature-transferability set, and the Ag scaling test); (ii) detailed strong-scaling figures for the 100M-atom Ag dataset; (iii) the 16 kbar / 90% melting-point / 2×2×3 Γ-centred grid / Methfessel–Paxton smearing details specific to the Ag DFT settings; (iv) the allegro, nequip, e3nn, PyTorch, and LAMMPS commit hashes used in the experiments; (v) the per-pair-species scaling factors 𝜎𝑍𝑖 ,𝑍 𝑗 that are technically hyperparameters but are not given specific reported values in the paper; (vi) the Li-ion diffusivity recovery (Allegro vs. AIMD MSD) which is a downstream observable rather than an AccuracyMetric per the ontology’s current vocabulary. K.18

Qi et al. (2023): MTP for L10 -TiAl and D019 -Ti3 Al

Q1 – Bibliographic identification. Qi, Aitken, Pei, Tan, Zuo, Jhon, Quek, Wen, Wu, and Ong train a single Moment Tensor Potential covering the binary Ti–Al system, with focus on the dual-phase 𝛾-TiAl (L10 ) and 𝛼 2 -Ti3 Al (D019 ) intermetallics. Published in Phys. Rev. Materials 7, 103602 (2023); arXiv:2305.11825. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -5726 -2587 > a schema : Person ; schema : affiliation mlips : UniversityofCaliforniaSanDiego ; schema : familyName " Ong " ; schema : givenName " Shyue ␣ Ping " ; schema : identifier < https :// orcid . org /0000 -0001 -5726 -2587 > ; schema : name " Shyue ␣ Ping ␣ Ong " . < https :// orcid . org /0000 -0001 -5808 -9931 > a schema : Person ; schema : affiliation mlips : UniversityofCaliforniaSanDiego ; schema : familyName " Qi " ; schema : givenName " Ji " ; schema : identifier < https :// orcid . org /0000 -0001 -5808 -9931 > ; schema : name " Ji ␣ Qi " . < https :// orcid . org /0000 -0001 -8711 -2854 > a schema : Person ; schema : affiliation mlips : AgencyforScienceTechnologyandResearch , mlips : InstituteofHighPerformanceComputing ; schema : familyName " Pei " ; schema : givenName " Qingxiang " ; schema : identifier < https :// orcid . org /0000 -0001 -8711 -2854 > ; schema : name " Qingxiang ␣ Pei " . < https :// orcid . org /0000 -0002 -2734 -7720 > a schema : Person ; schema : affiliation mlips : UniversityofCaliforniaSanDiego ; schema : familyName " Zuo " ; schema : givenName " Yunxing " ; schema : identifier < https :// orcid . org /0000 -0002 -2734 -7720 > ; schema : name " Yunxing ␣ Zuo " . < https :// orcid . org /0000 -0002 -4739 -1139 > a schema : Person ; schema : affiliation entity : org - CityUniversityofHongKong - qi2023 ; schema : familyName " Wu " ; schema : givenName " Zhaoxuan " ; schema : identifier < https :// orcid . org /0000 -0002 -4739 -1139 > ; schema : name " Zhaoxuan ␣ Wu " . < https :// orcid . org /0000 -0002 -5074 -4660 > a schema : Person ; schema : affiliation mlips : AgencyforScienceTechnologyandResearch , mlips : InstituteofHighPerformanceComputing ; schema : familyName " Tan " ; schema : givenName " Anne ␣ Marie ␣ Z . " ; schema : identifier < https :// orcid . org /0000 -0002 -5074 -4660 > ;

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schema : name " Anne ␣ Marie ␣ Z . ␣ Tan " . < https :// orcid . org /0000 -0002 -8181 -9485 > a schema : Person ; schema : affiliation mlips : AgencyforScienceTechnologyandResearch , mlips : InstituteofHighPerformanceComputing ; schema : familyName " Quek " ; schema : givenName " S . ␣ S . " ; schema : identifier < https :// orcid . org /0000 -0002 -8181 -9485 > ; schema : name "S. ␣ S . ␣ Quek " . < https :// orcid . org /0000 -0002 -9407 -8452 > a schema : Person ; schema : affiliation mlips : AgencyforScienceTechnologyandResearch , mlips : InstituteofHighPerformanceComputing ; schema : familyName " Jhon " ; schema : givenName " M . ␣ H . " ; schema : identifier < https :// orcid . org /0000 -0002 -9407 -8452 > ; schema : name "M. ␣ H . ␣ Jhon " . < https :// orcid . org /0000 -0003 -1692 -2512 > a schema : Person ; schema : affiliation entity : org - UniversityofHongKong - qi2023 ; schema : familyName " Wen " ; schema : givenName " T . " ; schema : identifier < https :// orcid . org /0000 -0003 -1692 -2512 > ; schema : name "T. ␣ Wen " . entity : article - qi2023 a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0001 -5726 -2587 > , < https :// orcid . org /0000 -0001 -5808 -9931 > , < https :// orcid . org /0000 -0001 -8711 -2854 > , < https :// orcid . org /0000 -0002 -2734 -7720 > , < https :// orcid . org /0000 -0002 -4739 -1139 > , < https :// orcid . org /0000 -0002 -5074 -4660 > , < https :// orcid . org /0000 -0002 -8181 -9485 > , < https :// orcid . org /0000 -0002 -9407 -8452 > , < https :// orcid . org /0000 -0003 -1692 -2512 > , entity : person Aitken - qi2023 ; schema : datePublished " 2023 " ^^ xsd : gYear ; schema : name " Machine ␣ Learning ␣ Moment ␣ Tensor ␣ Potential ␣ for ␣ Modelling ␣ Dislocation ␣ and ␣ Fracture ␣ in ␣ L1_0 - TiAl ␣ and ␣ D0_19 - Ti3Al ␣ Alloys " ; schema : sameAs < https :// doi . org /10.1103/ PhysRevMaterials .7.103602 > . entity : org - CityUniversityofHongKong - qi2023 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " City ␣ University ␣ of ␣ Hong ␣ Kong " ; schema : identifier < https :// ror . org /03 q8dnn23 > ; schema : name " City ␣ University ␣ of ␣ Hong ␣ Kong " . entity : org - UniversityofHongKong - qi2023 a schema : Organization ; rdfs : comment " Paper - local ␣ Organization ␣ IRI ; ␣ not ␣ promoted ␣ to ␣ mlips - vocab . ttl ␣ ( occurs ␣ in ␣ fewer ␣ than ␣ 3 ␣ papers ) . " ; rdfs : label " University ␣ of ␣ Hong ␣ Kong " ; schema : identifier < https :// ror . org /02 zhqgq86 > ; schema : name " University ␣ of ␣ Hong ␣ Kong " . entity : person - Aitken - qi2023 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " ; schema : affiliation mlips : AgencyforScienceTechnologyandResearch , mlips : InstituteofHighPerformanceComputing ; schema : familyName " Aitken " ; schema : givenName " Z . ␣ H . " ; schema : name "Z. ␣ H . ␣ Aitken " . entity : study - qi2023 a mlips : BenchmarkStudy ; rdfs : label " Qi ␣ et ␣ al . ␣ (2023) : ␣ MTP ␣ for ␣ L1_0 - TiAl ␣ and ␣ D0_19 - Ti3Al " ; mlips : reportedIn entity : article - qi2023 .

Q2 – Material system. The MTP is trained over the Ti–Al binary phase diagram and benchmarked on the two technologically relevant intermetallics, 𝛾-TiAl (L10 , P4/mmm) and 𝛼 2 -Ti3 Al (D019 , P63 /mmc), as well as on FCC-Al, HCP-Ti, TiAl2 , and TiAl3 . We model this as one MaterialSystem at the binary level, with the phase information recorded in materialClass. @base < http :// example . org / > .

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@prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat - TiAl a mlips : MaterialSystem ; rdfs : comment " Wikidata ␣ Q408746 ␣ ( ' titanium ␣ aluminide ' , ␣ intermetallic ␣ chemical ␣ compound ) ␣ is ␣ the ␣ closest ␣ entry ␣ covering ␣ the ␣ gamma - TiAl ␣ and ␣ alpha2 - Ti3Al ␣ phases ; ␣ the ␣ Ti - Al ␣ binary ␣ system ␣ itself ␣ has ␣ no ␣ Wikidata ␣ entry ␣ as ␣ of ␣ 2026 -07 -25. " ; rdfs : label "Ti - Al ␣ binary ␣ ( focus ␣ on ␣ L1_0 ␣ gamma - TiAl ␣ and ␣ D0_19 ␣ alpha2 - Ti3Al ) " ; mlips : chemicalFormula " Ti - Al " ; mlips : materialClass " Binary ␣ intermetallic ; ␣ benchmarked ␣ on ␣ L1_0 ␣ ( P4 / mmm ) ␣ gamma - TiAl ␣ and ␣ D0_19 ␣( P6_3 / mmc ) ␣ alpha2 - Ti3Al ␣ phases " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q408746 > .

Q3 – Reference calculation method. Reference data are produced from spin-polarised DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - qi2023 a mlips : DFTCalculation .

Q4 – Reference settings. DFT calculations use VASP with the PBE/GGA exchange–correlation functional and PAW pseudopotentials (3p6 3d3 4s1 valence for Ti, 3s2 3p1 for Al), a 520 eV plane-wave 3 cutoff, and Monkhorst–Pack k-point meshes with density ≥ 100/Å (a single Γ-point is used during AIMD). Frozen-core treatment beyond the PAW partition is not explicitly reported. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - qi2023 mlips : hasDFTSettings entity : dft - settings - qi2023 . entity : dft - settings - qi2023 a mlips : DFTSettings ; mlips : energyCutoff 520 ; mlips : kPointMesh " Monkhorst - Pack ␣ with ␣k - point ␣ density ␣ >= ␣ 100/ Ang ^3 ␣ for ␣ static ; ␣ single ␣ Gamma ␣ point ␣ for ␣ AIMD " ; mlips : pseudopotentialType mlips : PAW ; mlips : usedDFTCode mlips : VASP ; mlips : xcFunctional mlips : PBE .

Q5 – Training dataset. The training set comprises 3,798 configurations produced from five sampling categories (see Q6): 33 ground-state polymorphs, 2,160 AIMD snapshots, 185 surface structures, 580 solid-solution configurations, and 840 strained supercells. Configurations cover energies and forces; stresses appear in the loss function with weight zero, so they are not effectively learned and not recorded as a covered property. A 90:10 train:test split is applied. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > .

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@prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - TiAl a mlips : TrainingDataset ; rdfs : label "Ti - Al ␣ MTP ␣ training ␣ set ␣ (33 ␣ polymorphs ␣ + ␣ 2160 ␣ AIMD ␣ + ␣ 185 ␣ surfaces ␣ + ␣ 580 ␣ solid - solutions ␣ + ␣ 840 ␣ strained ␣ = ␣ 3798 ␣ configs ) " ; mlips : coversMaterial entity : mat - TiAl ; mlips : coversProperty mlips : Energy , mlips : Forces ; mlips : datasetProvenance mlips : Published ; mlips : hasDFTCalculation entity : dft - qi2023 ; mlips : numConfigurations 3798 ; mlips : wasRunBy entity : run - mtp - TiAl .

Q6 – Sampling strategies. Five strategies were combined: ground-state polymorph enumeration from the Materials Project, vibrational sampling via NVT AIMD at 300, 1000, and 3000 K and at 90/100/110% of the ground-state volume, surface enumeration with Miller indices up to three, solid-solution chemical sampling at 12.5% steps, and homogeneous strain sampling (±10% in 1% intervals across six modes). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : aimd - sampling a mlips : SamplingStrategy ; rdfs : comment " 2160 ␣ snapshots ␣ from ␣ NVT ␣ AIMD ␣ trajectories ␣ of ␣ 6 ␣ stable ␣ phases ␣ at ␣ 300 , ␣ 1000 ␣ and ␣ 3000 ␣K , ␣ 90/100/110% ␣ of ␣ ground - state ␣ volume ; ␣ 40 ␣ configs ␣ per ␣ 10 ␣ ps ␣ run . " ; rdfs : label " Vibrational ␣ sampling ␣ ( NVT ␣ AIMD ) " . entity :ds - TiAl mlips : samplingStrategy entity : aimd - sampling , entity : polymorph - sampling , entity : solid solution - sampling , entity : strain - sampling , entity : surface - sampling . entity : polymorph - sampling a mlips : SamplingStrategy ; rdfs : comment " 33 ␣ ground - state ␣ polymorphs ␣ of ␣ the ␣ Ti - Al ␣ system ␣ retrieved ␣ from ␣ the ␣ Materials ␣ Project . " ; rdfs : label " Ground - state ␣ polymorph ␣ enumeration " . entity : solid - solution - sampling a mlips : SamplingStrategy ; rdfs : comment " 580 ␣ Al_xTi_ {1 - x } ␣ solid - solution ␣ structures ␣ ( x ␣ from ␣ 12.5 ␣ to ␣ 87.5 ␣ at .% ␣ in ␣ 12.5% ␣ steps ) ,␣ up ␣ to ␣ 30 ␣ enumerations ␣ per ␣ scenario . " ; rdfs : label " Solid - solution ␣ chemical ␣ sampling " . entity : strain - sampling a mlips : SamplingStrategy ; rdfs : comment " 840 ␣ strained ␣ supercells : ␣ +/ -10% ␣ strain ␣ at ␣ 1% ␣ intervals ␣ across ␣ 6 ␣ strain ␣ modes ␣ for ␣ the ␣ 6 ␣ stable ␣ phases . " ; rdfs : label " Homogeneous ␣ strain ␣ sampling " . entity : surface - sampling a mlips : SamplingStrategy ; rdfs : comment " 185 ␣ surface ␣ structures ␣ with ␣ Miller ␣ indices ␣ up ␣ to ␣ three ␣ for ␣ the ␣ 6 ␣ stable ␣ Ti - Al ␣ phases . " ; rdfs : label " Surface ␣ enumeration " .

Q7 – MLIP method, components, implementation. The method is a Moment Tensor Potential (MTP) implemented in the MLIP package [42, 49] for training, with downstream simulations in LAMMPS via the maml workflow library. The loss function is a weighted MSE with energy:force:stress weights of 100:1:0. The training algorithm is not explicitly named in the paper. @base < http :// example . org / > .

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@prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : cutoffRadius mlips : isHyperparameterOf entity : MTP . mlips : momentLevel mlips : isHyperparameterOf entity : MTP . entity : MTP a mlips : MLIPMethod ; rdfs : label " Moment ␣ Tensor ␣ Potential " ; mlips : hasDescriptor mlips : MomentTensorDescriptor ; mlips : hasFunctionalForm entity : mtp - functional - form ; mlips : hasHyperparameter mlips : cutoffRadius , mlips : momentLevel ; mlips : hasImplementation entity : mlip - package ; mlips : hasLossFunction entity : mtp - loss -100 -1 -0 ; mlips : supportsSimulation mlips : GeometryOptimization . entity : mlip - package a mlips : Implementation ; mlips : implementedIn mlips : MLIP ; mlips : isImplementationOf entity : MTP . entity : mtp - functional - form a mlips : FunctionalForm ; rdfs : label " MTP ␣ moment - tensor ␣ polynomial " . entity : mtp - loss -100 -1 -0 a mlips : LossFunction ; rdfs : label " Weighted ␣ MSE ␣ ( energy ␣ 100 , ␣ force ␣ 1 , ␣ stress ␣ 0) " .

Q8 – Hyperparameter settings. A grid search over cutoff radius 𝑟𝑐 ∈ [4.4, 7.0] Å (steps of 0.2 Å) and maximum level lev max ∈ [18, 24] (even integers), with five random initialisations per cell, was performed (280 candidate MTPs in total). The selected production MTP uses 𝑟𝑐 = 4.8 Å and lev max = 22. Other implementation hyperparameters (radial-basis count, regularisation, optimiser schedule) are not reported. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - levmax -22 a mlips : HyperparameterSetting ; rdfs : label " MTP ␣ moment ␣ level ␣ = ␣ 22 ␣ for ␣ MTP ␣ training ␣ run , ␣ Ti - Al ␣ binary " ; mlips : forHyperparameter mlips : momentLevel ; mlips : isSettingOf entity : run - mtp - TiAl ; mlips : settingValue 22 . entity : setting - rcut -4 _8 a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 4.8 ␣ for ␣ MTP ␣ training ␣ run , ␣ Ti - Al ␣ binary " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - mtp - TiAl ; mlips : settingValue 4.8 .

Q9 – MLIP run and trained model. A single training run produces one trained MTP that is used across all benchmarked phases. No active-learning or fold-ensemble structure is reported. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > .

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@prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - mtp - TiAl a mlips : TrainedModel ; rdfs : label "Ti - Al ␣ MTP ␣ ( rcut =4.8 ␣ Ang , ␣ levmax =22) " . entity : run - mtp - TiAl a mlips : MLIPRun ; rdfs : label " MTP ␣ training ␣ run , ␣ Ti - Al ␣ binary " ; mlips : appliesMethod entity : MTP ; mlips : hasHyperparameterSetting entity : setting - levmax -22 , entity : setting - rcut -4 _8 ; mlips : produces entity : model - mtp - TiAl ; mlips : runsOn entity : ds - TiAl .

Q10 – Benchmark results. Headline accuracy figures are MAEs of formation energies of (i) surface structures (8 meV/atom for the MTP, vs. 51 meV/atom for the MLP3 of Seko) and (ii) ground-state polymorphs (18 meV/atom for the MTP, vs. 13 meV/atom for MLP3). The MTP further attains Δ𝐸 EOS < 2 meV/atom in the L10 -TiAl, D019 -Ti3 Al, HCP-Ti, and FCC-Al phases. Per-property numerical errors on elastic constants, surface energies, and GSFEs are discussed at length in the paper but reported as derived figures rather than as a single accuracy metric per property. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - mae - polymorph a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 18 ␣ [ millielectronvolt ␣ per ␣ atom ] " , " MAE ␣ on ␣ formation ␣ energies ␣ of ␣ polymorph ␣ structures ␣ ( vs . ␣ DFT ) " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - mtp - polymorph ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 18 . entity : metric - mae - surface a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 8 ␣ [ millielectronvolt ␣ per ␣ atom ] " , " MAE ␣ on ␣ formation ␣ energies ␣ of ␣ surface ␣ structures ␣ ( vs . ␣ DFT ) " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - mtp - surface ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 8 . entity : result - mtp - polymorph a mlips : BenchmarkResult ; rdfs : label "Ti - Al ␣ MTP ␣ ( rcut =4.8 ␣ Ang , ␣ levmax =22) ␣ on ␣ Ti - Al ␣ binary ␣ ( focus ␣ on ␣ L1_0 ␣ gamma TiAl ␣ and ␣ D0_19 ␣ alpha2 - Ti3Al ) ␣ in ␣ Qi ␣ et ␣ al . ␣ (2023) : ␣ MTP ␣ for ␣ L1_0 - TiAl ␣ and ␣ D0_19 Ti3Al " ; mlips : evaluatesModel entity : model - mtp - TiAl ; mlips : hasAccuracyMetric entity : metric - mae - polymorph ; mlips : isResultOf entity : study - qi2023 ; mlips : targetMaterial entity : mat - TiAl . entity : result - mtp - surface a mlips : BenchmarkResult ; rdfs : label "Ti - Al ␣ MTP ␣ ( rcut =4.8 ␣ Ang , ␣ levmax =22) ␣ on ␣ Ti - Al ␣ binary ␣ ( focus ␣ on ␣ L1_0 ␣ gamma TiAl ␣ and ␣ D0_19 ␣ alpha2 - Ti3Al ) ␣ in ␣ Qi ␣ et ␣ al . ␣ (2023) : ␣ MTP ␣ for ␣ L1_0 - TiAl ␣ and ␣ D0_19 Ti3Al " ; mlips : evaluatesModel entity : model - mtp - TiAl ; mlips : hasAccuracyMetric entity : metric - mae - surface ; mlips : isResultOf entity : study - qi2023 ; mlips : targetMaterial entity : mat - TiAl . entity : study - qi2023 mlips : hasResult entity : result - mtp - polymorph , entity : result - mtp - surface .

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Q11 – Computational resources. Not reported. The paper gives no training duration, GPU hours, training hardware, peak memory, inference time per atom, or inference hardware. # Q11 - resources : no triples ( paper does not report this ) .

Q12 – Gaps. Beyond Q11 (compute resources entirely absent), the following ontology-expressible items are not reported: the training algorithm or optimiser used by the MLIP package; the MLIP package version; detailed MTP architectural hyperparameters beyond 𝑟𝑐 and lev max (radial/angular basis counts, regularisation, loss-function temperature scheduling); explicit frozenCore treatment beyond the PAW partition; and a controlled-vocabulary individual for AIMD as a sampling strategy (currently encoded as an ad-hoc instance with rdfs:label and rdfs:comment). K.19

Batatia et al. (2024): MACE-MP-0 foundation model

Q1 – Bibliographic identification. Batatia, Benner, Chiang, et al. (Csányi group) release MACE-MP0, an equivariant message-passing foundation model trained on the MPtrj dataset and demonstrated zero-shot across solids, liquids, gases, surfaces, MOFs, and a small protein. arXiv:2401.00096. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0001 -5116 -3027 > a schema : Person ; schema : familyName " Moore " ; schema : givenName " J . ␣ Harry " ; schema : identifier < https :// orcid . org /0000 -0001 -5116 -3027 > ; schema : name "J. ␣ Harry ␣ Moore " . < https :// orcid . org /0000 -0001 -5233 -3462 > a schema : Person ; schema : familyName " Riebesell " ; schema : givenName " Janosh " ; schema : identifier < https :// orcid . org /0000 -0001 -5233 -3462 > ; schema : name " Janosh ␣ Riebesell " . < https :// orcid . org /0000 -0001 -5572 -192 X > a schema : Person ; schema : familyName " Grey " ; schema : givenName " Clare ␣ P . " ; schema : identifier < https :// orcid . org /0000 -0001 -5572 -192 X > ; schema : name " Clare ␣ P . ␣ Grey " . < https :// orcid . org /0000 -0001 -5626 -2438 > a schema : Person ; schema : familyName " Genreith - Schriever " ; schema : givenName " Annalena " ; schema : identifier < https :// orcid . org /0000 -0001 -5626 -2438 > ; schema : name " Annalena ␣ Genreith - Schriever " . < https :// orcid . org /0000 -0001 -6375 -1459 > a schema : Person ; schema : familyName " Hofmann " ; schema : givenName " Stephan " ; schema : identifier < https :// orcid . org /0000 -0001 -6375 -1459 > ; schema : name " Stephan ␣ Hofmann " . < https :// orcid . org /0000 -0001 -6397 -0002 > a schema : Person ; schema : familyName " Elijo š ius " ; schema : givenName " Rokas " ; schema : identifier < https :// orcid . org /0000 -0001 -6397 -0002 > ; schema : name " Rokas ␣ Elijo š ius " . < https :// orcid . org /0000 -0001 -6873 -0278 > a schema : Person ; schema : familyName " Deringer " ; schema : givenName " Volker ␣ L . " ;

166 schema : identifier < https :// orcid . org /0000 -0001 -6873 -0278 > ; schema : name " Volker ␣ L . ␣ Deringer " . < https :// orcid . org /0000 -0001 -8434 -3497 > a schema : Person ; schema : familyName " De " ; schema : givenName " Sandip " ; schema : identifier < https :// orcid . org /0000 -0001 -8434 -3497 > ; schema : name " Sandip ␣ De " . < https :// orcid . org /0000 -0001 -8473 -8659 > a schema : Person ; schema : familyName " Reuter " ; schema : givenName " Karsten " ; schema : identifier < https :// orcid . org /0000 -0001 -8473 -8659 > ; schema : name " Karsten ␣ Reuter " . < https :// orcid . org /0000 -0001 -8907 -0336 > a schema : Person ; schema : familyName " George " ; schema : givenName " Janine " ; schema : identifier < https :// orcid . org /0000 -0001 -8907 -0336 > ; schema : name " Janine ␣ George " . < https :// orcid . org /0000 -0002 -0043 -5907 > a schema : Person ; schema : familyName " Fako " ; schema : givenName " Edvin " ; schema : identifier < https :// orcid . org /0000 -0002 -0043 -5907 > ; schema : name " Edvin ␣ Fako " . < https :// orcid . org /0000 -0002 -0141 -7006 > a schema : Person ; schema : familyName " Rosen " ; schema : givenName " Andrew ␣ S . " ; schema : identifier < https :// orcid . org /0000 -0002 -0141 -7006 > ; schema : name " Andrew ␣ S . ␣ Rosen " . < https :// orcid . org /0000 -0002 -0750 -6229 > a schema : Person ; schema : familyName " Han " ; schema : givenName " Shuang " ; schema : identifier < https :// orcid . org /0000 -0002 -0750 -6229 > ; schema : name " Shuang ␣ Han " . < https :// orcid . org /0000 -0002 -0862 -5289 > a schema : Person ; schema : familyName " Margraf " ; schema : givenName " Johannes ␣ T . " ; schema : identifier < https :// orcid . org /0000 -0002 -0862 -5289 > ; schema : name " Johannes ␣ T . ␣ Margraf " . < https :// orcid . org /0000 -0002 -0912 -8137 > a schema : Person ; schema : familyName " Benner " ; schema : givenName " Philipp " ; schema : identifier < https :// orcid . org /0000 -0002 -0912 -8137 > ; schema : name " Philipp ␣ Benner " . < https :// orcid . org /0000 -0002 -1484 -0284 > a schema : Person ; schema : familyName " Vegge " ; schema : givenName " Tejs " ; schema : identifier < https :// orcid . org /0000 -0002 -1484 -0284 > ; schema : name " Tejs ␣ Vegge " . < https :// orcid . org /0000 -0002 -1578 -1888 > a schema : Person ; schema : familyName " Witt " ; schema : givenName " William ␣ C . " ; schema : identifier < https :// orcid . org /0000 -0002 -1578 -1888 > ; schema : name " William ␣ C . ␣ Witt " . < https :// orcid . org /0000 -0002 -1935 -236 X > a schema : Person ; schema : familyName " Schaaf " ; schema : givenName " Lars ␣ L . " ; schema : identifier < https :// orcid . org /0000 -0002 -1935 -236 X > ; schema : name " Lars ␣ L . ␣ Schaaf " . < https :// orcid . org /0000 -0002 -3365 -599 X > a schema : Person ; schema : familyName " Darby " ;

Hernández et al.

An Ontology for Machine Learning Interatomic Potentials schema : givenName " James ␣ P . " ; schema : identifier < https :// orcid . org /0000 -0002 -3365 -599 X > ; schema : name " James ␣ P . ␣ Darby " . < https :// orcid . org /0000 -0002 -3963 -5076 > a schema : Person ; schema : familyName " Magd ă u " ; schema : givenName " Ioan - Bogdan " ; schema : identifier < https :// orcid . org /0000 -0002 -3963 -5076 > ; schema : name " Ioan - Bogdan ␣ Magd ă u " . < https :// orcid . org /0000 -0002 -4017 -7084 > a schema : Person ; schema : familyName " Chiang " ; schema : givenName " Yuan " ; schema : identifier < https :// orcid . org /0000 -0002 -4017 -7084 > ; schema : name " Yuan ␣ Chiang " . < https :// orcid . org /0000 -0002 -4326 -7229 > a schema : Person ; schema : familyName " Liepuoniute " ; schema : givenName " Guoda " ; schema : identifier < https :// orcid . org /0000 -0002 -4326 -7229 > ; schema : name " Guoda ␣ Liepuoniute " . < https :// orcid . org /0000 -0002 -5866 -0445 > a schema : Person ; schema : familyName " Handley " ; schema : givenName " Will " ; schema : identifier < https :// orcid . org /0000 -0002 -5866 -0445 > ; schema : name " Will ␣ Handley " . < https :// orcid . org /0000 -0002 -5914 -5218 > a schema : Person ; schema : familyName " Karimitari " ; schema : givenName " Nima " ; schema : identifier < https :// orcid . org /0000 -0002 -5914 -5218 > ; schema : name " Nima ␣ Karimitari " . < https :// orcid . org /0000 -0002 -6071 -6786 > a schema : Person ; schema : familyName " Naik " ; schema : givenName " Aakash ␣ A . " ; schema : identifier < https :// orcid . org /0000 -0002 -6071 -6786 > ; schema : name " Aakash ␣ A . ␣ Naik " . < https :// orcid . org /0000 -0002 -6408 -1255 > a schema : Person ; schema : familyName " Sivonxay " ; schema : givenName " Eric " ; schema : identifier < https :// orcid . org /0000 -0002 -6408 -1255 > ; schema : name " Eric ␣ Sivonxay " . < https :// orcid . org /0000 -0002 -6589 -1700 > a schema : Person ; schema : familyName " Goodall " ; schema : givenName " Rhys ␣ E . ␣ A . " ; schema : identifier < https :// orcid . org /0000 -0002 -6589 -1700 > ; schema : name " Rhys ␣ E . ␣ A . ␣ Goodall " . < https :// orcid . org /0000 -0002 -6936 -4692 > a schema : Person ; schema : familyName " Zills " ; schema : givenName " Fabian " ; schema : identifier < https :// orcid . org /0000 -0002 -6936 -4692 > ; schema : name " Fabian ␣ Zills " . < https :// orcid . org /0000 -0002 -8218 -8558 > a schema : Person ; schema : familyName " Kuner " ; schema : givenName " Matthew ␣ C . " ; schema : identifier < https :// orcid . org /0000 -0002 -8218 -8558 > ; schema : name " Matthew ␣ C . ␣ Kuner " . < https :// orcid . org /0000 -0002 -8968 -321 X > a schema : Person ; schema : familyName " Asta " ; schema : givenName " Mark " ; schema : identifier < https :// orcid . org /0000 -0002 -8968 -321 X > ; schema : name " Mark ␣ Asta " . < https :// orcid . org /0000 -0002 -9169 -169 X > a schema : Person ;

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168 schema : familyName " Michaelides " ; schema : givenName " Angelos " ; schema : identifier < https :// orcid . org /0000 -0002 -9169 -169 X > ; schema : name " Angelos ␣ Michaelides " . < https :// orcid . org /0000 -0002 -9702 -9795 > a schema : Person ; schema : familyName " Pia " ; schema : givenName " Flaviano ␣ Della " ; schema : identifier < https :// orcid . org /0000 -0002 -9702 -9795 > ; schema : name " Flaviano ␣ Della ␣ Pia " . < https :// orcid . org /0000 -0003 -0324 -2198 > a schema : Person ; schema : familyName " Kapil " ; schema : givenName " Venkat " ; schema : identifier < https :// orcid . org /0000 -0003 -0324 -2198 > ; schema : name " Venkat ␣ Kapil " . < https :// orcid . org /0000 -0003 -0337 -0464 > a schema : Person ; schema : familyName " Niblett " ; schema : givenName " Samuel ␣ P . " ; schema : identifier < https :// orcid . org /0000 -0003 -0337 -0464 > ; schema : name " Samuel ␣ P . ␣ Niblett " . < https :// orcid . org /0000 -0003 -0696 -8445 > a schema : Person ; schema : familyName " Heenen " ; schema : givenName " Hendrik ␣ H . " ; schema : identifier < https :// orcid . org /0000 -0003 -0696 -8445 > ; schema : name " Hendrik ␣ H . ␣ Heenen " . < https :// orcid . org /0000 -0003 -0907 -9993 > a schema : Person ; schema : familyName " Ferrari " ; schema : givenName " Andrea ␣ C . " ; schema : identifier < https :// orcid . org /0000 -0003 -0907 -9993 > ; schema : name " Andrea ␣ C . ␣ Ferrari " . < https :// orcid . org /0000 -0003 -1242 -775 X > a schema : Person ; schema : familyName " Jung " ; schema : givenName " Hyunwook " ; schema : identifier < https :// orcid . org /0000 -0003 -1242 -775 X > ; schema : name " Hyunwook ␣ Jung " . < https :// orcid . org /0000 -0003 -1808 -0814 > a schema : Person ; schema : familyName "O ' Neill " ; schema : givenName " Niamh " ; schema : identifier < https :// orcid . org /0000 -0003 -1808 -0814 > ; schema : name " Niamh ␣O ' Neill " . < https :// orcid . org /0000 -0003 -2352 -0458 > a schema : Person ; schema : familyName " Hermansson " ; schema : givenName " Kersti " ; schema : identifier < https :// orcid . org /0000 -0003 -2352 -0458 > ; schema : name " Kersti ␣ Hermansson " . < https :// orcid . org /0000 -0003 -2495 -5509 > a schema : Person ; schema : familyName " Persson " ; schema : givenName " Kristin ␣ A . " ; schema : identifier < https :// orcid . org /0000 -0003 -2495 -5509 > ; schema : name " Kristin ␣ A . ␣ Persson " . < https :// orcid . org /0000 -0003 -2739 -310 X > a schema : Person ; schema : familyName " Holm " ; schema : givenName " Christian " ; schema : identifier < https :// orcid . org /0000 -0003 -2739 -310 X > ; schema : name " Christian ␣ Holm " . < https :// orcid . org /0000 -0003 -2871 -8965 > a schema : Person ; schema : familyName " Varga - Umbrich " ; schema : givenName " Eszter " ; schema : identifier < https :// orcid . org /0000 -0003 -2871 -8965 > ; schema : name " Eszter ␣ Varga - Umbrich " . < https :// orcid . org /0000 -0003 -2922 -8706 >

Hernández et al.

An Ontology for Machine Learning Interatomic Potentials a schema : Person ; schema : familyName " Stenczel " ; schema : givenName " Tam á s ␣ K . " ; schema : identifier < https :// orcid . org /0000 -0003 -2922 -8706 > ; schema : name " Tam á s ␣ K . ␣ Stenczel " . < https :// orcid . org /0000 -0003 -3132 -3032 > a schema : Person ; schema : familyName " Blau " ; schema : givenName " Samuel ␣ M . " ; schema : identifier < https :// orcid . org /0000 -0003 -3132 -3032 > ; schema : name " Samuel ␣ M . ␣ Blau " . < https :// orcid . org /0000 -0003 -3198 -5116 > a schema : Person ; schema : familyName " Bhowmik " ; schema : givenName " Arghya " ; schema : identifier < https :// orcid . org /0000 -0003 -3198 -5116 > ; schema : name " Arghya ␣ Bhowmik " . < https :// orcid . org /0000 -0003 -3212 -1168 > a schema : Person ; schema : familyName " Sutton " ; schema : givenName " Christopher " ; schema : identifier < https :// orcid . org /0000 -0003 -3212 -1168 > ; schema : name " Christopher ␣ Sutton " . < https :// orcid . org /0000 -0003 -3290 -4787 > a schema : Person ; schema : familyName " El - Machachi " ; schema : givenName " Zakariya " ; schema : identifier < https :// orcid . org /0000 -0003 -3290 -4787 > ; schema : name " Zakariya ␣ El - Machachi " . < https :// orcid . org /0000 -0003 -3439 -4856 > a schema : Person ; schema : familyName " Kaplan " ; schema : givenName " Aaron ␣ D . " ; schema : identifier < https :// orcid . org /0000 -0003 -3439 -4856 > ; schema : name " Aaron ␣ D . ␣ Kaplan " . < https :// orcid . org /0000 -0003 -3570 -0050 > a schema : Person ; schema : familyName " Kullgren " ; schema : givenName " Jolla " ; schema : identifier < https :// orcid . org /0000 -0003 -3570 -0050 > ; schema : name " Jolla ␣ Kullgren " . < https :// orcid . org /0000 -0003 -4595 -5073 > a schema : Person ; schema : familyName " Schran " ; schema : givenName " Christoph " ; schema : identifier < https :// orcid . org /0000 -0003 -4595 -5073 > ; schema : name " Christoph ␣ Schran " . < https :// orcid . org /0009 -0000 -1808 -8352 > a schema : Person ; schema : familyName " Svahn " ; schema : givenName " Viktor " ; schema : identifier < https :// orcid . org /0009 -0000 -1808 -8352 > ; schema : name " Viktor ␣ Svahn " . < https :// orcid . org /0009 -0001 -2369 -3693 > a schema : Person ; schema : familyName " Kuryla " ; schema : givenName " Domantas " ; schema : identifier < https :// orcid . org /0009 -0001 -2369 -3693 > ; schema : name " Domantas ␣ Kuryla " . < https :// orcid . org /0009 -0001 -5343 -0456 > a schema : Person ; schema : familyName " Advincula " ; schema : givenName " Xavier ␣ R . " ; schema : identifier < https :// orcid . org /0009 -0001 -5343 -0456 > ; schema : name " Xavier ␣ R . ␣ Advincula " . < https :// orcid . org /0009 -0002 -7236 -501 X > a schema : Person ; schema : familyName " Vondr á k " ; schema : givenName " Martin " ; schema : identifier < https :// orcid . org /0009 -0002 -7236 -501 X > ; schema : name " Martin ␣ Vondr á k " .

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< https :// orcid . org /0009 -0002 -8173 -5596 > a schema : Person ; schema : familyName " Jakob " ; schema : givenName " Konstantin ␣ S . " ; schema : identifier < https :// orcid . org /0009 -0002 -8173 -5596 > ; schema : name " Konstantin ␣ S . ␣ Jakob " . < https :// orcid . org /0009 -0003 -1249 -0318 > a schema : Person ; schema : familyName " Kroupa " ; schema : givenName " Namu " ; schema : identifier < https :// orcid . org /0009 -0003 -1249 -0318 > ; schema : name " Namu ␣ Kroupa " . < https :// orcid . org /0009 -0004 -1300 -012 X > a schema : Person ; schema : familyName " Jaafar " ; schema : givenName " Jad " ; schema : identifier < https :// orcid . org /0009 -0004 -1300 -012 X > ; schema : name " Jad ␣ Jaafar " . < https :// orcid . org /0009 -0005 -9863 -6422 > a schema : Person ; schema : familyName " Baldwin " ; schema : givenName " William ␣ J . 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An Ontology for Machine Learning Interatomic Potentials schema : datePublished " 2024 " ^^ xsd : gYear ; schema : name "A␣ Foundation ␣ Model ␣ for ␣ Atomistic ␣ Materials ␣ Chemistry " ; schema : sameAs < https :// doi . org /10.48550/ arXiv .2401.00096 > . entity : person - Avaylon - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Avaylon " ; schema : givenName " Matthew " ; schema : name " Matthew ␣ Avaylon " . entity : person - Batatia - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Batatia " ; schema : givenName " Ilyes " ; schema : name " Ilyes ␣ Batatia " . entity : person - Berger - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Berger " ; schema : givenName " Fabian " ; schema : name " Fabian ␣ Berger " . entity : person - Bigi - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Bigi " ; schema : givenName " Filippo " ; schema : name " Filippo ␣ Bigi " . entity : person - Carare - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " C ă rare " ; schema : givenName " Vlad " ; schema : name " Vlad ␣ C ă rare " . entity : person - Ceriotti - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Ceriotti " ; schema : givenName " Michele " ; schema : name " Michele ␣ Ceriotti " . entity : person - Chong - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Chong " ; schema : givenName " Sanggyu " ; schema : name " Sanggyu ␣ Chong " . entity : person - Csanyi - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Cs á nyi " ; schema : givenName " G á bor " ; schema : name "Gá bor ␣ Cs á nyi " . entity : person - Elena - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Elena " ; schema : givenName " Alin ␣ M . " ; schema : name " Alin ␣ M . ␣ Elena " . entity : person - Falcioni - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Falcioni " ; schema : givenName " Fabio " ; schema : name " Fabio ␣ Falcioni " . entity : person - Gardner - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Gardner " ; schema : givenName " John ␣ L . ␣ A . " ; schema : name " John ␣ L . ␣ A . ␣ Gardner " . entity : person - Gawkowski - batatia2024mp0 a schema : Person ;

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172 rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Gawkowski " ; schema : givenName " Mikolaj ␣ J . " ; schema : name " Mikolaj ␣ J . ␣ Gawkowski " . entity : person - Grandel - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Grandel " ; schema : givenName " Jonas " ; schema : name " Jonas ␣ Grandel " . entity : person - Grigorev - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Grigorev " ; schema : givenName " Petr " ; schema : name " Petr ␣ Grigorev " . entity : person -Ho - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Ho " ; schema : givenName " Cheuk ␣ Hin " ; schema : name " Cheuk ␣ Hin ␣ Ho " . entity : person - Kermode - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Kermode " ; schema : givenName " James ␣ R . " ; schema : name " James ␣ R . ␣ Kermode " . entity : person - Kourtis - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Kourtis " ; schema : givenName " Panagiotis " ; schema : name " Panagiotis ␣ Kourtis " . entity : person - Lin - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Lin " ; schema : givenName " Chen " ; schema : name " Chen ␣ Lin " . entity : person - Norwood - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Norwood " ; schema : givenName " Sam ␣ Walton " ; schema : name " Sam ␣ Walton ␣ Norwood " . entity : person - Oord - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Oord " ; schema : givenName " Cas ␣ van ␣ der " ; schema : name " Cas ␣ van ␣ der ␣ Oord " . entity : person - Rosset - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Rosset " ; schema : givenName " Louise ␣ A . ␣ M . " ; schema : name " Louise ␣ A . ␣ M . ␣ Rosset " . entity : person - Shi - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Shi " ; schema : givenName " Benjamin ␣ X . " ; schema : name " Benjamin ␣ X . ␣ Shi " . entity : person - Swinburne - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Swinburne " ; schema : givenName " Thomas ␣ D . " ; schema : name " Thomas ␣ D . ␣ Swinburne " . entity : person - Tilly - batatia2024mp0

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An Ontology for Machine Learning Interatomic Potentials a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Tilly " ; schema : givenName " Jules " ; schema : name " Jules ␣ Tilly " . entity : person - Vargas - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Vargas " ; schema : givenName " Santiago " ; schema : name " Santiago ␣ Vargas " . entity : person - Wang - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Wang " ; schema : givenName " Yangshuai " ; schema : name " Yangshuai ␣ Wang " . entity : person - Wolf - batatia2024mp0 a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " schema : familyName " Wolf " ; schema : givenName " Thomas " ; schema : name " Thomas ␣ Wolf " . entity : study - batatia2024mp0 a mlips : BenchmarkStudy ; rdfs : label " Batatia ␣ et ␣ al . ␣ (2024) : ␣ MACE - MP -0 ␣ foundation ␣ model " ; mlips : reportedIn entity : article - batatia2024mp0 .

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Q2 – Material system. The MLIP covers MPtrj’s ∼150,000 Materials Project structures across 89 elements, with 90% of unit cells under 70 atoms. We model this as a single MaterialSystem; the paper’s out-of-distribution demonstrations (water, organics, MOFs, protein) are documented in Q12. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat -MP - universal - batatia2024mp0 a mlips : MaterialSystem ; rdfs : comment " No ␣ single ␣ Wikidata ␣ entry ␣ applies : ␣ this ␣ is ␣ the ␣ universal ␣ foundation - model ␣ coverage ␣ of ␣ the ␣ Materials ␣ Project ␣ database , ␣ spanning ␣ 89 ␣ elements . " ; rdfs : label " Materials ␣ Project ␣ Trajectory ␣ coverage ␣ ( foundation - model ␣ scope , ␣ 89 ␣ elements )" ; mlips : chemicalFormula " any " ; mlips : materialClass " Universal ␣ inorganic ␣ crystal ␣ coverage ␣ from ␣ MPtrj ␣ (~150 ,000 ␣ unique ␣ Materials ␣ Project ␣ structures , ␣ mainly ␣ small ␣ periodic ␣ unit ␣ cells ␣ with ␣ under ␣ 70 ␣ atoms ␣ in ␣ 90% ␣ of ␣ cases ) . ␣ MACE - MP -0 ␣ is ␣ demonstrated ␣ out - of - the - box ␣ on ␣ solids , ␣ liquids , ␣ gases ,␣ surfaces , ␣ MOFs , ␣ and ␣ a ␣ small ␣ protein , ␣ well ␣ beyond ␣ the ␣ training ␣ distribution " .

Q3 – Reference calculation method. Reference data come from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - batatia2024mp0 a mlips : DFTCalculation .

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Q4 – Reference settings. DFT uses VASP with PAW pseudopotentials and PBE GGA, with Hubbard 𝑈 applied on transition-metal oxides containing Co/Cr/Fe/Mn/Mo/Ni/V/W combined with O or F (Materials Project default 𝑈 -values). No dispersion correction is used in training. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - batatia2024mp0 mlips : hasDFTSettings entity : dft - settings - batatia2024mp0 . entity : dft - settings - batatia2024mp0 a mlips : DFTSettings ; rdfs : comment " Hubbard ␣ U ␣ applied ␣ on ␣ transition - metal ␣ oxides ␣ containing ␣ Co , ␣ Cr , ␣ Fe , ␣ Mn , ␣ Mo ,␣Ni ,␣V , ␣ W ␣ combined ␣ with ␣ O ␣ or ␣ F ␣ ( Materials ␣ Project ␣ default ␣U - values ) ; ␣ no ␣ dispersion ␣ correction ␣ in ␣ training . " ; mlips : pseudopotentialType mlips : PAW ; mlips : usedDFTCode mlips : VASP ; mlips : xcFunctional mlips : PBE .

Q5 – Training dataset. ∼1.5 M static and structural-relaxation configurations across ∼150,000 MP compounds, covering energies, forces, and stresses. Provenance is published (re-using the CHGNet-curated MPtrj split). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - MPtrj - batatia2024mp0 a mlips : TrainingDataset ; rdfs : label " MPtrj ␣ subset ␣ used ␣ for ␣ MACE - MP -0: ␣ ~1.5 M ␣ static ␣ and ␣ structural - relaxation ␣ configurations ␣ across ␣ ~150 ,000 ␣ Materials ␣ Project ␣ compounds ; ␣ 90% ␣ of ␣ unit ␣ cells ␣ have ␣ under ␣ 70 ␣ atoms " ; mlips : coversMaterial entity : mat - MP - universal - batatia2024mp0 ; mlips : coversProperty mlips : Energy , mlips : Forces , mlips : Stresses ; mlips : datasetProvenance mlips : Published ; mlips : hasDFTCalculation entity : dft - batatia2024mp0 ; mlips : numConfigurations 1500000 ; mlips : wasRunBy entity : run - mace - mp -0 - batatia2024mp0 .

Q6 – Sampling strategies. Two strategies were combined: MP relaxation-trajectory sampling (reusing the CHGNet/Deng et al. 2023 curated set) and periodic-table chemical-space coverage (89 elements; binary, ternary, and higher-order chemistries). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - MPtrj - batatia2024mp0 mlips : samplingStrategy entity : periodic - table - coverage - sampling - batatia2024mp0 , entity : relaxation - trajectory - sampling - batatia2024mp0 . entity : periodic - table - coverage - sampling - batatia2024mp0 a mlips : SamplingStrategy ; rdfs : comment " MPtrj ␣ configurations ␣ span ␣ 89 ␣ elements ␣ across ␣ binary , ␣ ternary , ␣ and ␣ higher - order ␣ inorganic ␣ compositions ; ␣ 90% ␣ of ␣ structures ␣ contain ␣ under ␣ 70 ␣ atoms ␣ per ␣ unit ␣ cell ." ;

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rdfs : label " Periodic - table ␣ chemical - space ␣ coverage " . entity : relaxation - trajectory - sampling - batatia2024mp0 a mlips : SamplingStrategy ; rdfs : comment " Static ␣ and ␣ relaxation - trajectory ␣ frames ␣ from ␣ the ␣ Materials ␣ Project , ␣ originally ␣ compiled ␣ for ␣ CHGNet ␣ ( Deng ␣ et ␣ al . ␣ 2023) . ␣ MACE - MP -0 ␣ inherits ␣ the ␣ MPtrj ␣ curation :␣ deduplicated , ␣ energy / force - quality - filtered ␣ configurations ␣ from ␣ ~150 k ␣ Materials ␣ Project ␣ structures . " ; rdfs : label " Materials ␣ Project ␣ relaxation - trajectory ␣ sampling ␣ ( re - using ␣ the ␣ CHGNet curated ␣ MPtrj ␣ training ␣ set ) " .

Q7 – MLIP method, components, implementation. MACE-MP-0 is an equivariant message-passing graph network (e3nn) with two layers of higher-order equivariant messages built from sums of two-body permutation-invariant polynomials in a spherical basis; correlation order 3 (4-body messages per layer); a tensor-decomposition parameterisation; and a ZBL repulsive pair potential at close range with Agnesi distance transform. The MACE-MP-0b3 release is the L=1 medium-sized variant in 128×0𝑒 + 128×1𝑜 irreps. Loss is a weighted Huber on energy/forces/stresses with weights (1, 10, 10) and a force Huber-𝛿 that decays with force magnitude. Optimisation is AMSGrad with EMA learning-rate schedule. Implementation: mace-mp (PyTorch + e3nn). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : bodyOrder mlips : isHyperparameterOf entity : MACE - MP -0 . mlips : cutoffRadius mlips : isHyperparameterOf entity : MACE - MP -0 . mlips : learningRate mlips : isHyperparameterOf entity : MACE - MP -0 . mlips : numAngularBasis mlips : isHyperparameterOf entity : MACE - MP -0 . mlips : numEpochs mlips : isHyperparameterOf entity : MACE - MP -0 . mlips : numFeatures mlips : isHyperparameterOf entity : MACE - MP -0 . mlips : numLayers mlips : isHyperparameterOf entity : MACE - MP -0 . mlips : numRadialBasis mlips : isHyperparameterOf entity : MACE - MP -0 . entity : MACE -MP -0 a mlips : MLIPMethod ; rdfs : label " MACE : ␣ equivariant ␣ higher - order ␣ message - passing ␣ graph ␣ neural ␣ network ␣ with ␣ atomic - cluster - expansion - style ␣ many - body ␣ messages " ; mlips : hasFunctionalForm entity : mace - functional - form - batatia2024mp0 ; mlips : hasHyperparameter mlips : bodyOrder , mlips : cutoffRadius , mlips : learningRate , mlips : numAngularBasis , mlips : numEpochs , mlips : numFeatures , mlips : numLayers , mlips : numRadialBasis , entity : hp - mlp - hidden - batatia2024mp0 ; mlips : hasImplementation entity : mace - impl - batatia2024mp0 ; mlips : hasLossFunction entity : mace - huber - loss - batatia2024mp0 ; mlips : hasTrainingAlgorithm entity : amsgrad - batatia2024mp0 ; mlips : supportsSimulation mlips : GeometryOptimization , mlips : MolecularDynamics , mlips : NudgedElasticBand , mlips : PhononCalculation . entity : amsgrad - batatia2024mp0 a mls : Algorithm ; rdfs : label " AMSGrad ␣ variant ␣ of ␣ Adam ␣ ( beta_1 =0.9 , ␣ beta_2 =0.999 , ␣ epsilon =1 e -8) ␣ with ␣ EMA ␣ learning - rate ␣ schedule ␣ ( decay ␣ 0.99999) ␣ and ␣ gradient ␣ clipping ␣ ( max - norm ␣ 100) " . entity :hp - mlp - hidden - batatia2024mp0 a mlips : Hyperparameter ; rdfs : label " MACE - MP -0 ␣ readout ␣ MLP ␣ architecture " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : string ; mlips : hyperparameterName " mlp_hidden " ; mlips : isHyperparameterOf entity : MACE - MP -0 .

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entity : mace - functional - form - batatia2024mp0 a mlips : FunctionalForm ; rdfs : label " MACE : ␣ equivariant ␣ message - passing ␣ graph ␣ tensor ␣ network ␣ ( e3nn ) . ␣ Two ␣ layers ␣ of ␣ higher - order ␣ equivariant ␣ messages ␣ built ␣ from ␣ sums ␣ of ␣ two - body ␣ permutation invariant ␣ polynomials ␣ in ␣ a ␣ spherical ␣ basis ; ␣ tensor - decomposition ␣ parameterisation ; ␣4- body ␣ messages ␣ per ␣ layer ␣ ( correlation ␣ order ␣ 3) ; ␣ ZBL ␣ repulsive ␣ pair ␣ potential ␣ at ␣ close ␣ range ␣ with ␣ Agnesi ␣ distance ␣ transform ; ␣ energy ␣ is ␣ the ␣ sum ␣ of ␣ per - atom ␣ contributions , ␣ forces ␣ and ␣ stresses ␣ by ␣ auto - differentiation . ␣ The ␣ MACE - MP -0 b3 ␣ release ␣ is ␣ the ␣ L =1 ␣ ( medium - sized ) ␣ variant ␣ in ␣ 128 x0e ␣ + ␣ 128 x1o ␣ irreps . " . entity : mace - huber - loss - batatia2024mp0 a mlips : LossFunction ; rdfs : label " Weighted ␣ Huber ␣ loss ␣ on ␣ energy , ␣ forces , ␣ and ␣ stresses ␣ with ␣ weights ␣ ( lambda_E ,␣ lambda_F , ␣ lambda_sigma ) =(1 , ␣ 10 , ␣ 10) ␣ and ␣ Huber ␣ deltas ␣ ( delta_E , ␣ delta_F , ␣ delta_sigma ) =(0.01 , ␣ 0.01 , ␣ 0.01) ; ␣ the ␣ force ␣ Huber ␣ delta ␣ is ␣ conditional , ␣ decreasing ␣ step - wise ␣ from ␣ 1.0 ␣ to ␣ 0.1 ␣ as ␣ the ␣ per - atom ␣ force ␣ magnitude ␣ increases ␣ from ␣ 0 ␣ to ␣ 300 ␣ eV /A" . entity : mace - impl - batatia2024mp0 a mlips : Implementation ; mlips : implementedIn mlips : MACE ; mlips : isImplementationOf entity : MACE - MP -0 ; mlips : version " MACE - MP -0 b3 " .

Q8 – Hyperparameter settings. Reported settings: cutoff 𝑟𝑐 = 6.0 Å, 2 message-passing layers, 𝑙 max = 3, correlation order 3, 128 channels, 10 radial Bessel basis functions, 3×64 SiLU readout MLP, initial learning rate 10−3 , 100 epochs. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - correlation - order -3 - batatia2024mp0 a mlips : HyperparameterSetting ; rdfs : label " body ␣ order ␣ = ␣ 3 ␣ for ␣ MACE - MP -0 b3 ␣ ( medium ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : bodyOrder ; mlips : isSettingOf entity : run - mace - mp -0 - batatia2024mp0 ; mlips : settingValue 3 . entity : setting - initial - lr -1 e -3 - batatia2024mp0 a mlips : HyperparameterSetting ; rdfs : label " learning ␣ rate ␣ = ␣ 0.001 ␣ for ␣ MACE - MP -0 b3 ␣ ( medium ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : learningRate ; mlips : isSettingOf entity : run - mace - mp -0 - batatia2024mp0 ; mlips : settingValue 0.001 . entity : setting - lmax -3 - batatia2024mp0 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ angular ␣ basis ␣ functions ␣ = ␣ 3 ␣ for ␣ MACE - MP -0 b3 ␣ ( medium ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : numAngularBasis ; mlips : isSettingOf entity : run - mace - mp -0 - batatia2024mp0 ; mlips : settingValue 3 . entity : setting - mlp - hidden -3 x64 - batatia2024mp0 a mlips : HyperparameterSetting ; rdfs : label " MACE - MP -0 ␣ readout ␣ MLP ␣ architecture ␣ = ␣ 3 x64 ␣ SiLU ␣ for ␣ MACE - MP -0 b3 ␣ ( medium ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter entity : hp - mlp - hidden - batatia2024mp0 ; mlips : isSettingOf entity : run - mace - mp -0 - batatia2024mp0 ; mlips : settingValue " 3 x64 ␣ SiLU " . entity : setting - num - channels -128 - batatia2024mp0 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ features ␣ = ␣ 128 ␣ for ␣ MACE - MP -0 b3 ␣ ( medium ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : numFeatures ; mlips : isSettingOf entity : run - mace - mp -0 - batatia2024mp0 ; mlips : settingValue 128 . entity : setting - num - epochs -100 - batatia2024mp0 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ epochs ␣ = ␣ 100 ␣ for ␣ MACE - MP -0 b3 ␣ ( medium ) ␣ training ␣ run ␣ on ␣ MPtrj " ;

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mlips : forHyperparameter mlips : numEpochs ; mlips : isSettingOf entity : run - mace - mp -0 - batatia2024mp0 ; mlips : settingValue 100 . entity : setting - num - layers -2 - batatia2024mp0 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ layers ␣ = ␣ 2 ␣ for ␣ MACE - MP -0 b3 ␣ ( medium ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : numLayers ; mlips : isSettingOf entity : run - mace - mp -0 - batatia2024mp0 ; mlips : settingValue 2 . entity : setting - num - radial - bessel -10 - batatia2024mp0 a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ radial ␣ basis ␣ functions ␣ = ␣ 10 ␣ for ␣ MACE - MP -0 b3 ␣ ( medium ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : numRadialBasis ; mlips : isSettingOf entity : run - mace - mp -0 - batatia2024mp0 ; mlips : settingValue 10 . entity : setting - rcut -6 - batatia2024mp0 a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 6 ␣ for ␣ MACE - MP -0 b3 ␣ ( medium ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - mace - mp -0 - batatia2024mp0 ; mlips : settingValue 6 .

Q9 – MLIP run and trained model. A single training run on MPtrj produces the MACE-MP-0b3 medium foundation model. Training compute is reported on the run. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - mace - mp -0 - batatia2024mp0 a mlips : TrainedModel ; rdfs : label " MACE - MP -0 b3 ␣ medium ␣ foundation ␣ model " . entity : run - mace -mp -0 - batatia2024mp0 a mlips : MLIPRun ; rdfs : label " MACE - MP -0 b3 ␣ ( medium ) ␣ training ␣ run ␣ on ␣ MPtrj " ; mlips : appliesMethod entity : MACE - MP -0 ; mlips : hasHyperparameterSetting entity : setting - correlation - order -3 - batatia2024mp0 , entity : setting - initial - lr -1 e -3 - batatia2024mp0 , entity : setting - lmax -3 batatia2024mp0 , entity : setting - mlp - hidden -3 x64 - batatia2024mp0 , entity : setting - num channels -128 - batatia2024mp0 , entity : setting - num - epochs -100 - batatia2024mp0 , entity : setting - num - layers -2 - batatia2024mp0 , entity : setting - num - radial - bessel -10 batatia2024mp0 , entity : setting - rcut -6 - batatia2024mp0 ; mlips : produces entity : model - mace - mp -0 - batatia2024mp0 ; mlips : runsOn entity : ds - MPtrj - batatia2024mp0 .

Q10 – Benchmark results. Test-set MAEs on the MPtrj held-out split: 18 meV/atom on energy and 39 meV/Å on force components. Many additional zero-shot out-of-distribution evaluations (organic-molecule MD, MOF flexibility, protein side-chain stability) are reported but not encoded as separate BenchmarkResult instances. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - mae - energy - batatia2024mp0 a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 18 ␣ [ millielectronvolt ␣ per ␣ atom ] " , " Test ␣ MAE ␣ on ␣ energy ␣ per ␣ atom ␣ ( MPtrj ␣ held - out , ␣ MACE - MP -0 ␣ medium ) " ;

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mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - mae - energy - batatia2024mp0 ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 18 . entity : metric - mae - force - batatia2024mp0 a mlips : AccuracyMetric ; rdfs : label " MAE ␣ of ␣ Force ␣ = ␣ 39 ␣ [ millielectronvolt ␣ per ␣ angstrom ] " , " Test ␣ MAE ␣ on ␣ force ␣ components ␣ ( MPtrj ␣ held - out , ␣ MACE - MP -0 ␣ medium ) " ; mlips : hasUnit mlips : MilliEV - PER - ANGSTROM ; mlips : isMetricOf entity : result - mae - force - batatia2024mp0 ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : MAE ; mlips : metricValue 39 . entity : result - mae - energy - batatia2024mp0 a mlips : BenchmarkResult ; rdfs : label " MACE - MP -0 b3 ␣ medium ␣ foundation ␣ model ␣ on ␣ Materials ␣ Project ␣ Trajectory ␣ coverage ␣( foundation - model ␣ scope , ␣ 89 ␣ elements ) ␣ in ␣ Batatia ␣ et ␣ al . ␣ (2024) : ␣ MACE - MP -0 ␣ foundation ␣ model " ; mlips : evaluatesModel entity : model - mace - mp -0 - batatia2024mp0 ; mlips : hasAccuracyMetric entity : metric - mae - energy - batatia2024mp0 ; mlips : isResultOf entity : study - batatia2024mp0 ; mlips : targetMaterial entity : mat - MP - universal - batatia2024mp0 . entity : result - mae - force - batatia2024mp0 a mlips : BenchmarkResult ; rdfs : label " MACE - MP -0 b3 ␣ medium ␣ foundation ␣ model ␣ on ␣ Materials ␣ Project ␣ Trajectory ␣ coverage ␣( foundation - model ␣ scope , ␣ 89 ␣ elements ) ␣ in ␣ Batatia ␣ et ␣ al . ␣ (2024) : ␣ MACE - MP -0 ␣ foundation ␣ model " ; mlips : evaluatesModel entity : model - mace - mp -0 - batatia2024mp0 ; mlips : hasAccuracyMetric entity : metric - mae - force - batatia2024mp0 ; mlips : isResultOf entity : study - batatia2024mp0 ; mlips : targetMaterial entity : mat - MP - universal - batatia2024mp0 . entity : study - batatia2024mp0 mlips : hasResult entity : result - mae - energy - batatia2024mp0 , entity : result - mae - force batatia2024mp0 .

Q11 – Computational resources. Reported: 2,600 GPU-hours of training on 40–80 NVIDIA H100 GPUs across 10–20 nodes; inference scaling on a single A100 80GB GPU (∼ns/day for a 1000-atom system; weak scaling to 32,000 atoms on 64 GPUs at 0.1 ns/day). Wall-clock training duration, peak memory, and explicit per-atom inference time are not reported. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - mace - mp -0 - batatia2024mp0 mlips : inferenceHardware " Single ␣ NVIDIA ␣ A100 ␣ 80 GB ␣ GPU : ␣ ~ ns / day ␣ for ␣ 1000 - atom ␣ system ; ␣ weak ␣ scaling ␣ to ␣ 32 ,000 ␣ atoms ␣ on ␣ 64 ␣ GPUs ␣ at ␣ 0.1 ␣ ns / day " . entity : run - mace -mp -0 - batatia2024mp0 mlips : gpuHours 2600 ; mlips : trainingHardware " 40 -80 ␣ NVIDIA ␣ H100 ␣ GPUs ␣ across ␣ 10 -20 ␣ nodes " .

Q12 – Gaps. The most consequential gaps are: out-of-distribution use (TrainedModel is applied zero-shot to organics, MOFs, a protein, and gas-phase chemistry far beyond the MPtrj training set, but the ontology has no concept for "deployment domain" distinct from the training MaterialSystem); explicit DFT settings that vary by MP task (energy cutoff, k-mesh) are not surfaced; and the foundation model’s three released sizes (small/medium/large) plus the L=1/L=2 variants are not encoded as separate TrainedModel instances. The training duration in wall-clock time is also not reported, only GPU hours.

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Wang et al. (2024): efficient MTP for defects in Ni–Al alloys Note on paper-id: this corpus entry is filed under the upstream paper-id nitol2024nial, but the actual authors of the encoded paper are Wang et al. (Shenyang National Laboratory for Materials Science). The CORPUS.md substitution table notes that the original Nitol 2025 Ti-Al-V PRMaterials paper is journal-only with no arXiv preprint and was substituted with this earlier Ni–Al MTP work.

Q1 – Bibliographic identification. Wang, Liu, Zhu, Liu, Ma, Chen, Sun, and Chen present an efficient moment tensor potential for defects in Ni–Al alloys, with a genetic-algorithm-optimised tensor-contraction scheme. arXiv:2411.01282. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . < https :// orcid . org /0000 -0002 -5904 -6578 > a schema : Person ; schema : familyName " Chen " ; schema : givenName " Yun " ; schema : identifier < https :// orcid . org /0000 -0002 -5904 -6578 > ; schema : name " Yun ␣ Chen " . < https :// orcid . org /0000 -0003 -4962 -7691 > a schema : Person ; schema : familyName " Liu " ; schema : givenName " Peitao " ; schema : identifier < https :// orcid . org /0000 -0003 -4962 -7691 > ; schema : name " Peitao ␣ Liu " . < https :// orcid . org /0009 -0000 -2049 -1829 > a schema : Person ; schema : familyName " Wang " ; schema : givenName " Jiantao " ; schema : identifier < https :// orcid . org /0009 -0000 -2049 -1829 > ; schema : name " Jiantao ␣ Wang " . < https :// orcid . org /0009 -0009 -7643 -8723 > a schema : Person ; schema : familyName " Ma " ; schema : givenName " Hui " ; schema : identifier < https :// orcid . org /0009 -0009 -7643 -8723 > ; schema : name " Hui ␣ Ma " . entity : article - nitol2024nial a schema : ScholarlyArticle ; schema : author < https :// orcid . org /0000 -0002 -5904 -6578 > , < https :// orcid . org /0000 -0003 -4962 -7691 > , < https :// orcid . org /0009 -0000 -2049 -1829 > , < https :// orcid . org /0009 -0009 -7643 -8723 > , entity : person - Sun - nitol2024nial , entity : person - Zhu nitol2024nial ; schema : datePublished " 2024 " ^^ xsd : gYear ; schema : name " Efficient ␣ Moment ␣ Tensor ␣ Machine - Learning ␣ Interatomic ␣ Potential ␣ for ␣ Accurate ␣ Description ␣ of ␣ Defects ␣ in ␣ Ni - Al ␣ Alloys " ; schema : sameAs < https :// doi . org /10.48550/ arXiv .2411.01282 > . entity : person - Sun - nitol2024nial a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " ; schema : familyName " Sun " ; schema : givenName " Yan " ; schema : name " Yan ␣ Sun " . entity : person - Zhu - nitol2024nial a schema : Person ; rdfs : comment " No ␣ ORCID ␣ found ␣ via ␣ Crossref ␣ / ␣ arXiv ␣ API ␣ as ␣ of ␣ 2026 -05 -04. " ; schema : familyName " Zhu " ; schema : givenName " Heyu " ; schema : name " Heyu ␣ Zhu " .

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entity : study - nitol2024nial a mlips : BenchmarkStudy ; rdfs : label " Wang ␣ et ␣ al . ␣ (2024) : ␣ efficient ␣ MTP ␣ for ␣ defects ␣ in ␣ Ni - Al ␣ alloys " ; mlips : reportedIn entity : article - nitol2024nial .

Q2 – Material system. The MTP covers fcc Ni and L12 -Ni3 Al, the Ni/Ni3 Al interface, and their defect environments (vacancies, vacancy clusters, antisites, GSF supercells). We model this as a single MaterialSystem with the defect detail in materialClass. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : mat - NiAl - nitol2024nial a mlips : MaterialSystem ; rdfs : comment " Wikidata ␣ Q7028279 ␣ ( ' nickel ␣ aluminide ') ␣ covers ␣ the ␣ Ni3Al ␣ intermetallic ␣ specifically , ␣ which ␣ is ␣ the ␣ dominant ␣ target ␣ of ␣ this ␣ paper ' s ␣ MTP . ␣ The ␣ broader ␣ Ni - Al ␣ binary ␣ alloy ␣ has ␣ no ␣ dedicated ␣ Wikidata ␣ entry ␣ as ␣ of ␣ 2026 -04 -28. " ; rdfs : label "Ni - Al ␣ binary ␣ alloy ␣ ( fcc ␣ Ni ␣ and ␣ L1_2 - Ni3Al ␣ phases ␣ plus ␣ their ␣ interface ␣ and ␣ defects )" ; mlips : chemicalFormula " Ni - Al " ; mlips : materialClass " Binary ␣ intermetallic ; ␣ fcc ␣ Ni ␣ ( Fm -3 m ) ,␣ L1_2 - Ni3Al ␣ ( Pm -3 m ) ,␣ Ni / Ni3Al ␣ interface ; ␣ with ␣ vacancies , ␣ vacancy ␣ clusters , ␣ antisites , ␣ and ␣ generalised ␣ stacking - fault ␣ ( GSF ) ␣ defects " ; mlips : sameAsWikidata < http :// www . wikidata . org / entity / Q7028279 > .

Q3 – Reference calculation method. Reference data come from DFT calculations. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - nitol2024nial a mlips : DFTCalculation .

Q4 – Reference settings. DFT uses VASP with PAW, PBE GGA, a 400 eV plane-wave cutoff, and Monkhorst–Pack k-point meshes with ∼0.2 Å−1 spacing. Convergence: total energy 1 meV/atom, SCF 10−6 eV, ionic-force 0.01 eV/Å. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : dft - nitol2024nial mlips : hasDFTSettings entity : dft - settings - nitol2024nial . entity : dft - settings - nitol2024nial a mlips : DFTSettings ; mlips : energyCutoff 400 ; mlips : kPointMesh " Monkhorst - Pack ␣ with ␣k - point ␣ spacing ␣ ~0.2 ␣ A ^ -1; ␣ total ␣ energies ␣ converged ␣ to ␣ 1 ␣ meV / atom ; ␣ SCF ␣ convergence ␣ 1e -6 ␣ eV ; ␣ ionic - relaxation ␣ force ␣ convergence ␣ 0.01 ␣ eV / A " ;

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mlips : pseudopotentialType mlips : PAW ; mlips : usedDFTCode mlips : VASP ; mlips : xcFunctional mlips : PBE .

Q5 – Training dataset. The training set has 8,450 configurations: 6,092 from on-the-fly activelearning during AIMD plus 2,358 added through D-optimality active-learning cycles. Energies, forces, and stresses are covered. Provenance is published. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :ds - NiAl - nitol2024nial a mlips : TrainingDataset ; rdfs : label "Ni - Al ␣ MTP ␣ training ␣ set : ␣ 8450 ␣ configurations ␣ (6092 ␣ from ␣ on - the - fly ␣ active ␣ learning ␣ during ␣ AIMD ␣ + ␣ 2358 ␣ added ␣ through ␣D - optimality ␣ active - learning ␣ cycles ) " ; mlips : coversMaterial entity : mat - NiAl - nitol2024nial ; mlips : coversProperty mlips : Energy , mlips : Forces , mlips : Stresses ; mlips : datasetProvenance mlips : Published ; mlips : hasDFTCalculation entity : dft - nitol2024nial ; mlips : numConfigurations 8450 ; mlips : wasRunBy entity : run - mtp - NiAl - nitol2024nial .

Q6 – Sampling strategies. Three strategies were combined: on-the-fly active learning during AIMD heating from 700 to 1600 K (kernel-based Bayesian regression in VASP, NPT with Langevin thermostat + Parrinello–Rahman barostat); D-optimality active learning (configurations with extrapolation grade > 5 during 200 ps MD trajectories are added; iterations continue until the threshold is no longer exceeded); and defect-prototype enumeration (an independent 815-configuration validation set was constructed from the same prototypes). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity :d - optimality - active - learning - nitol2024nial a mlips : SamplingStrategy ; rdfs : comment " Second - pass ␣ active ␣ learning : ␣ 200 ␣ ps ␣ MD ␣ trajectories ␣ with ␣ the ␣ current ␣ MTP ␣ are ␣ screened ␣ for ␣ configurations ␣ whose ␣ extrapolation ␣ grade ␣ exceeds ␣ 5; ␣ selected ␣ configurations ␣ have ␣ their ␣ DFT ␣ energies , ␣ forces , ␣ and ␣ stresses ␣ computed ␣ and ␣ added ␣ to ␣ the ␣ training ␣ set ; ␣ the ␣ MTP ␣ is ␣ refitted ; ␣ iterations ␣ continue ␣ until ␣ no ␣ configurations ␣ exceed ␣ the ␣ threshold . ␣ Adds ␣ 2358 ␣ configurations . " ; rdfs : label "D - optimality ␣ active ␣ learning ␣ ( Shapeev ' s ␣ generalised ␣D - optimality ␣ criterion )" . entity : defect - prototype - sampling - nitol2024nial a mlips : SamplingStrategy ; rdfs : comment " Initial ␣ configurations ␣ span ␣ fcc ␣ Ni , ␣ L1_2 - Ni3Al , ␣ the ␣ Ni / Ni3Al ␣ interface , ␣ GSF ␣ supercells ␣ of ␣ Ni ␣ and ␣ Ni3Al , ␣ plus ␣ combinations ␣ with ␣ vacancies , ␣ vacancy ␣ clusters ,␣ and ␣ antisite ␣ defects ; ␣ an ␣ independent ␣ validation ␣ set ␣ of ␣ 815 ␣ configurations ␣ was ␣ constructed ␣ from ␣ the ␣ same ␣ prototypes . " ; rdfs : label " Defect - prototype ␣ enumeration " . entity :ds - NiAl - nitol2024nial mlips : samplingStrategy entity :d - optimality - active - learning - nitol2024nial , entity : defect - prototype - sampling - nitol2024nial , entity : on - the - fly - aimd - sampling nitol2024nial . entity :on - the - fly - aimd - sampling - nitol2024nial a mlips : SamplingStrategy ;

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Hernández et al. rdfs : comment " First - pass ␣ training - set ␣ generation : ␣ on - the - fly ␣ Bayesian - regression ␣ active ␣ learning ␣ during ␣ AIMD ␣ heating ␣ from ␣ 700 ␣ to ␣ 1600 ␣ K ␣ at ␣ ambient ␣ pressure ␣ ( NPT , ␣ Langevin ␣ thermostat ␣ + ␣ Parrinello - Rahman ␣ barostat ) . ␣ Yields ␣ 6092 ␣ reference ␣ configurations . " ; rdfs : label "On - the - fly ␣ active ␣ learning ␣ during ␣ AIMD ␣ ( kernel - based ␣ Bayesian ␣ regression ␣ in ␣ VASP )" .

Q7 – MLIP method, components, implementation. The method is a Moment Tensor Potential with a genetic-algorithm-optimised tensor-contraction scheme: rank of moment tensors limited to 4 (𝜇 ≤ 3) and a redefined level lev(𝑀𝜇,𝜈 ) = 2𝜇 + 𝜈 + 1 with maximum-level threshold 2,653. Loss is weighted MSE on energy/forces/stresses with weights 1:0.01:0.005. Fitting is two-step: linear optimisation on minimal then full basis with shared radial functions, followed by 5,000 L-BFGS iterations and a least-squares refinement. Implementation: MLIP package with custom tensor-contraction extensions. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . mlips : bodyOrder mlips : isHyperparameterOf entity : MTP - nitol2024nial . mlips : cutoffRadius mlips : isHyperparameterOf entity : MTP - nitol2024nial . mlips : momentLevel mlips : isHyperparameterOf entity : MTP - nitol2024nial . mlips : numRadialBasis mlips : isHyperparameterOf entity : MTP - nitol2024nial . entity : MTP - nitol2024nial a mlips : MLIPMethod ; rdfs : label " Moment ␣ Tensor ␣ Potential ␣ with ␣ optimised ␣ tensor - contraction ␣ scheme ␣ ( Wang ␣ et ␣ al .␣ 2024) " ; mlips : hasDescriptor mlips : MomentTensorDescriptor ; mlips : hasFunctionalForm entity : mtp - functional - form - nitol2024nial ; mlips : hasHyperparameter mlips : bodyOrder , mlips : cutoffRadius , mlips : momentLevel , mlips : numRadialBasis , entity : hp - num - linear - params - nitol2024nial ; mlips : hasImplementation entity : mlip - package - nitol2024nial ; mlips : hasLossFunction entity : mtp - loss -1 -001 -0005 - nitol2024nial ; mlips : hasTrainingAlgorithm entity : lbfgs - nitol2024nial ; mlips : supportsSimulation mlips : GeometryOptimization , mlips : MolecularDynamics , mlips : NudgedElasticBand , mlips : PhononCalculation . entity :hp - num - linear - params - nitol2024nial a mlips : Hyperparameter ; rdfs : label " MTP ␣ linear - parameter ␣ count ␣ ( after ␣ GA - optimised ␣ contractions ) " ; mlips : candidateForVocabulary mlips : Hyperparameter ; mlips : hyperparameterDatatype xsd : integer ; mlips : hyperparameterName " num_linear_params " ; mlips : isHyperparameterOf entity : MTP - nitol2024nial . entity : lbfgs - nitol2024nial a mls : Algorithm ; rdfs : label " Two - step ␣ fitting : ␣ ( i ) ␣ initial ␣ linear ␣ coefficients ␣ on ␣ a ␣ minimal ␣ basis ␣ followed ␣ by ␣ linear ␣ optimisation ␣ on ␣ the ␣ full ␣ basis ␣ with ␣ shared ␣ radial ␣ functions ; ␣ ( ii )␣L - BFGS ␣ for ␣ 5000 ␣ iterations ␣ followed ␣ by ␣ a ␣ least - squares ␣ linear ␣ refinement " . entity : mlip - package - nitol2024nial a mlips : Implementation ; mlips : implementedIn mlips : MLIP ; mlips : isImplementationOf entity : MTP - nitol2024nial . entity : mtp - functional - form - nitol2024nial a mlips : FunctionalForm ; rdfs : label " MTP ␣ moment - tensor ␣ polynomial ␣ with ␣ genetic - algorithm - optimised ␣ tensor ␣ contractions ; ␣ rank ␣ of ␣ moment ␣ tensors ␣ limited ␣ to ␣ 4 ␣ ( mu ␣ <= ␣ 3) ␣ and ␣ the ␣ redefined ␣ level ␣ lev ( M_ { mu , nu }) ␣ = ␣ 2* mu ␣ + ␣ nu ␣ + ␣ 1 ␣ with ␣ maximum - level ␣ threshold ␣ 2653 " . entity : mtp - loss -1 -001 -0005 - nitol2024nial

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a mlips : LossFunction ; rdfs : label " Weighted ␣ MSE ␣ on ␣ energy , ␣ forces , ␣ and ␣ stresses ␣ with ␣ weights ␣ 1 ␣ : ␣ 0.01 ␣ : ␣ 0.005 " .

Q8 – Hyperparameter settings. Reported settings: cutoff radius 𝑟𝑐 = 5.4 Å, maximum level 2,653, 8 radial-basis functions, maximum body order 5, total of 2,653 linear basis parameters. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : setting - levmax -2653 - nitol2024nial a mlips : HyperparameterSetting ; rdfs : label " MTP ␣ moment ␣ level ␣ = ␣ 2653 ␣ for ␣ MTP ␣ training ␣ run ␣ (2653 ␣ basis ␣ set , ␣ r_cut =5.4 ␣ A ) ␣ on ␣ the ␣Ni - Al ␣ training ␣ set " ; mlips : forHyperparameter mlips : momentLevel ; mlips : isSettingOf entity : run - mtp - NiAl - nitol2024nial ; mlips : settingValue 2653 . entity : setting - max - body - order -5 - nitol2024nial a mlips : HyperparameterSetting ; rdfs : label " body ␣ order ␣ = ␣ 5 ␣ for ␣ MTP ␣ training ␣ run ␣ (2653 ␣ basis ␣ set , ␣ r_cut =5.4 ␣ A ) ␣ on ␣ the ␣ Ni - Al ␣ training ␣ set " ; mlips : forHyperparameter mlips : bodyOrder ; mlips : isSettingOf entity : run - mtp - NiAl - nitol2024nial ; mlips : settingValue 5 . entity : setting - num - linear - params -2653 - nitol2024nial a mlips : HyperparameterSetting ; rdfs : label " MTP ␣ linear - parameter ␣ count ␣ ( after ␣ GA - optimised ␣ contractions ) ␣ = ␣ 2653 ␣ for ␣ MTP ␣ training ␣ run ␣ (2653 ␣ basis ␣ set , ␣ r_cut =5.4 ␣ A ) ␣ on ␣ the ␣ Ni - Al ␣ training ␣ set " ; mlips : forHyperparameter entity : hp - num - linear - params - nitol2024nial ; mlips : isSettingOf entity : run - mtp - NiAl - nitol2024nial ; mlips : settingValue 2653 . entity : setting - num - radial -8 - nitol2024nial a mlips : HyperparameterSetting ; rdfs : label " number ␣ of ␣ radial ␣ basis ␣ functions ␣ = ␣ 8 ␣ for ␣ MTP ␣ training ␣ run ␣ (2653 ␣ basis ␣ set , ␣ r_cut =5.4 ␣ A ) ␣ on ␣ the ␣ Ni - Al ␣ training ␣ set " ; mlips : forHyperparameter mlips : numRadialBasis ; mlips : isSettingOf entity : run - mtp - NiAl - nitol2024nial ; mlips : settingValue 8 . entity : setting - rcut -5 _4 - nitol2024nial a mlips : HyperparameterSetting ; rdfs : label " cutoff ␣ radius ␣ = ␣ 5.4 ␣ for ␣ MTP ␣ training ␣ run ␣ (2653 ␣ basis ␣ set , ␣ r_cut =5.4 ␣ A ) ␣ on ␣ the ␣Ni - Al ␣ training ␣ set " ; mlips : forHyperparameter mlips : cutoffRadius ; mlips : isSettingOf entity : run - mtp - NiAl - nitol2024nial ; mlips : settingValue 5.4 .

Q9 – MLIP run and trained model. A single fitting run on the 8,450-configuration training set produces the optimised Ni–Al MTP. Training hardware (96 CPU cores) is recorded on the run. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - mtp - NiAl - nitol2024nial a mlips : TrainedModel ; rdfs : label " Optimised ␣ MTP ␣ for ␣ Ni - Al ␣ alloys ␣ (2653 ␣ basis ␣ set , ␣ 5.4 ␣ A ␣ cutoff ) " . entity : run - mtp - NiAl - nitol2024nial

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Hernández et al. a mlips : MLIPRun ; rdfs : label " MTP ␣ training ␣ run ␣ (2653 ␣ basis ␣ set , ␣ r_cut =5.4 ␣ A ) ␣ on ␣ the ␣ Ni - Al ␣ training ␣ set " ; mlips : appliesMethod entity : MTP - nitol2024nial ; mlips : hasHyperparameterSetting entity : setting - levmax -2653 - nitol2024nial , entity : setting - max - body - order -5 - nitol2024nial , entity : setting - num - linear - params -2653 nitol2024nial , entity : setting - num - radial -8 - nitol2024nial , entity : setting - rcut -5 _4 nitol2024nial ; mlips : produces entity : model - mtp - NiAl - nitol2024nial ; mlips : runsOn entity : ds - NiAl - nitol2024nial .

Q10 – Benchmark results. Validation RMSEs on the 815-configuration validation set: 1.64 meV/atom on energy, 0.028 eV/Å on force components, 0.09 GPa on stress components. @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : metric - rmse - energy - nitol2024nial a mlips : AccuracyMetric ; rdfs : label " RMSE ␣ of ␣ Energy ␣ ( metric ␣ property ) ␣ = ␣ 1.64 ␣ [ millielectronvolt ␣ per ␣ atom ] " , " Validation ␣ RMSE ␣ on ␣ energy ␣ per ␣ atom ␣ ( Ni - Al ␣ validation ␣ set , ␣ 815 ␣ configs ) " ; mlips : hasUnit mlips : MilliEV - PER - ATOM ; mlips : isMetricOf entity : result - rmse - energy - nitol2024nial ; mlips : metricProperty mlips : EnergyProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 1.64 . entity : metric - rmse - force - nitol2024nial a mlips : AccuracyMetric ; rdfs : label " RMSE ␣ of ␣ Force ␣ = ␣ 0.028 ␣ [ EV - PER - ANGSTROM ] " , " Validation ␣ RMSE ␣ on ␣ force ␣ components ␣ ( Ni - Al ␣ validation ␣ set ) " ; mlips : hasUnit unit : EV - PER - ANGSTROM ; mlips : isMetricOf entity : result - rmse - force - nitol2024nial ; mlips : metricProperty mlips : ForceProperty ; mlips : metricType mlips : RMSE ; mlips : metricValue 0.028 . entity : metric - rmse - stress - nitol2024nial a mlips : AccuracyMetric ; rdfs : label " Validation ␣ RMSE ␣ on ␣ stress ␣ components ␣ ( Ni - Al ␣ validation ␣ set ) " ; mlips : hasUnit unit : GigaPA ; mlips : isMetricOf entity : result - rmse - stress - nitol2024nial ; mlips : metricType mlips : RMSE ; mlips : metricValue 0.09 . entity : result - rmse - energy - nitol2024nial a mlips : BenchmarkResult ; rdfs : label " Optimised ␣ MTP ␣ for ␣ Ni - Al ␣ alloys ␣ (2653 ␣ basis ␣ set , ␣ 5.4 ␣ A ␣ cutoff ) ␣ on ␣ Ni - Al ␣ binary ␣ alloy ␣ ( fcc ␣ Ni ␣ and ␣ L1_2 - Ni3Al ␣ phases ␣ plus ␣ their ␣ interface ␣ and ␣ defects ) ␣ in ␣ Wang ␣ et ␣ al . ␣ (2024) : ␣ efficient ␣ MTP ␣ for ␣ defects ␣ in ␣ Ni - Al ␣ alloys " ; mlips : evaluatesModel entity : model - mtp - NiAl - nitol2024nial ; mlips : hasAccuracyMetric entity : metric - rmse - energy - nitol2024nial ; mlips : isResultOf entity : study - nitol2024nial ; mlips : targetMaterial entity : mat - NiAl - nitol2024nial . entity : result - rmse - force - nitol2024nial a mlips : BenchmarkResult ; rdfs : label " Optimised ␣ MTP ␣ for ␣ Ni - Al ␣ alloys ␣ (2653 ␣ basis ␣ set , ␣ 5.4 ␣ A ␣ cutoff ) ␣ on ␣ Ni - Al ␣ binary ␣ alloy ␣ ( fcc ␣ Ni ␣ and ␣ L1_2 - Ni3Al ␣ phases ␣ plus ␣ their ␣ interface ␣ and ␣ defects ) ␣ in ␣ Wang ␣ et ␣ al . ␣ (2024) : ␣ efficient ␣ MTP ␣ for ␣ defects ␣ in ␣ Ni - Al ␣ alloys " ; mlips : evaluatesModel entity : model - mtp - NiAl - nitol2024nial ; mlips : hasAccuracyMetric entity : metric - rmse - force - nitol2024nial ; mlips : isResultOf entity : study - nitol2024nial ; mlips : targetMaterial entity : mat - NiAl - nitol2024nial . entity : result - rmse - stress - nitol2024nial a mlips : BenchmarkResult ;

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rdfs : label " Optimised ␣ MTP ␣ for ␣ Ni - Al ␣ alloys ␣ (2653 ␣ basis ␣ set , ␣ 5.4 ␣ A ␣ cutoff ) ␣ on ␣ Ni - Al ␣ binary ␣ alloy ␣ ( fcc ␣ Ni ␣ and ␣ L1_2 - Ni3Al ␣ phases ␣ plus ␣ their ␣ interface ␣ and ␣ defects ) ␣ in ␣ Wang ␣ et ␣ al . ␣ (2024) : ␣ efficient ␣ MTP ␣ for ␣ defects ␣ in ␣ Ni - Al ␣ alloys " ; mlips : evaluatesModel entity : model - mtp - NiAl - nitol2024nial ; mlips : hasAccuracyMetric entity : metric - rmse - stress - nitol2024nial ; mlips : isResultOf entity : study - nitol2024nial ; mlips : targetMaterial entity : mat - NiAl - nitol2024nial . entity : study - nitol2024nial mlips : hasResult entity : result - rmse - energy - nitol2024nial , entity : result - rmse - force nitol2024nial , entity : result - rmse - stress - nitol2024nial .

Q11 – Computational resources. Training and inference hardware are reported as 96 CPU cores (Intel Xeon Platinum 9242 @ 2.30 GHz); the model achieves ∼241 s for 105 MD steps on a 2,048-atom Ni3 Al supercell. Wall-clock training duration, peak memory, and explicit per-atom inference time are not reported (no GPUs are used). @base < http :// example . org / > . @prefix rdf : < http :// www . w3 . org /1999/02/22 - rdf - syntax - ns # > . @prefix rdfs : < http :// www . w3 . org /2000/01/ rdf - schema # > . @prefix xsd : < http :// www . w3 . org /2001/ XMLSchema # > . @prefix schema : < https :// schema . org / > . @prefix mls : < http :// www . w3 . org / ns / mls # > . @prefix unit : < http :// qudt . org / vocab / unit / > . @prefix mlips : < https :// w3id . org / mlips # > . @prefix entity : < https :// w3id . org / mlips / entity / > . entity : model - mtp - NiAl - nitol2024nial mlips : inferenceHardware " 96 ␣ CPU ␣ cores ␣ ( Intel ␣ Xeon ␣ Platinum ␣ 9242 ␣ @ ␣ 2.30 ␣ GHz ) : ␣ 100 ,000 ␣ MD ␣ steps ␣ on ␣ a ␣ 2048 - atom ␣ Ni3Al ␣ supercell ␣ take ␣ ~241 ␣ s " . entity : run - mtp - NiAl - nitol2024nial mlips : trainingHardware " 96 ␣ CPU ␣ cores ␣ ( Intel ␣ Xeon ␣ Platinum ␣ 9242 ␣ @ ␣ 2.30 ␣ GHz ) " .

Q12 – Gaps. Beyond Q11, the genetic-algorithm-driven tensor-contraction search that distinguishes this MTP from the standard Shapeev formulation is not first-class in the ontology (recorded only in the FunctionalForm label). The two-step linear-then-L-BFGS fitting procedure is captured in hasTrainingAlgorithm via prose; the ontology has no concept for multi-stage training. Many downstream defect-property comparisons (vacancy formation energies, GSF curves, point-defect migration barriers) are reported as derived figures rather than encoded as separate BenchmarkResult instances.