A benchmark suite of intracellular Boolean model variants and multiscale simulations for computational biology Marco Masera2 , Riccardo Smeriglio1 , Roberta Bardini1 , Alessandro Savino1 , Stefano Di Carlo1 1
Department of Control and Computer Engineering, Politecnico di Torino, Turin, Italy
arXiv:2606.18215v1 [cs.DB] 16 Jun 2026
2
Department of Life Sciences and Systems Biology, University of Turin, Turin, Italy
Correspondence: Roberta Bardini, Riccardo Smeriglio ([email protected], [email protected])
March 2026 Abstract We present PhysiBench, an open resource for developing and evaluating computational methods in systems biology including a benchmark suite of 612 executable intracellular Boolean regulatory network variants and a dataset of 120,000 time-resolved multiscale stochastic simulations. The benchmark models are derived from seven published Boolean networks spanning cell-cycle control, developmental patterning, cancer signaling, immune response, and cell-fate decisions, and are executable in the PhysiBoSS/PhysiCell multiscale simulation framework. Model variants are generated through mutation-based model construction, online behavioral filtering, and offline sensitivity evaluation. The simulation dataset is produced from 60 selected models under systematically sampled stimulation protocols and fixed model-level initial configurations. Each trajectory is linked to its model identifier, input-parameter file, stochastic seed, and cell-level output file. PhysiBench supports direct simulation, surrogate modeling, data-driven inference, simulation-based optimization, and comparative benchmarking. Technical validation includes file-integrity and executability checks, graph-based structural diversity analyses, and behavioral heterogeneity assessment from multiscale simulation outputs.
1
Background & Summary
Computational systems biology increasingly relies on simulation-based workflows to study, predict, and control complex biological processes. Two methodological areas are especially dependent on reusable simulation resources. The first is optimization via simulation, where search algorithms repeatedly simulate a biological model to identify parameters, perturbations, or stimulation protocols that produce a desired behavior. Practical examples include calibrating uncertain model parameters against observed dynamics or searching for stimulation and treatment schedules that drive a simulated cell population toward a target outcome 4;6;7 . The second is surrogate modeling, where statistical or machine-learning emulators are trained to approximate computationally expensive mechanistic simulations and predict their outputs at reduced cost. Practical examples include training fast predictors of population growth, spatial organization, or cell-fate trajectories from simulation inputs, so that downstream optimization or uncertainty analysis can be performed without repeatedly running full costly simulations 2;3 . Although these fields address different tasks, they share a common need: controlled biological simulation benchmarks that are executable, reproducible, diverse, and paired with well-defined input spaces 1;5 . Comparable benchmark resources have already accelerated method development in other scientific domains. Datasets such as PDEBench 8–10 , WeatherBench 11–13 , and The Well 14;15 provide standardized simulation data, controlled tasks, and reusable evaluation settings for physics, climate modeling, and scientific machine learning. Systems biology lacks an equivalent resource for the development of simulation-based methods. Existing computational biology resources play important complementary roles: BioModels, BioSimulators, and BioSimulations 23–25 , PhysiBoSS-Models 26 ,
1
Boolean model repositories 27;28 , and PhysiCell datasets 29 support model sharing, simulator discovery, reproducible execution, or specific simulation studies. What they do not provide is a controlled benchmark built around families of related executable biological models, embedded in a common multiscale framework, and paired with large numbers of systematically generated stochastic trajectories. This gap limits both optimization and surrogate-modeling research in systems biology. Researchers developing optimization via simulation methods need executable biological models that can be repeatedly run under controlled, comparable conditions. Researchers developing surrogate models need large, paired input-output datasets with enough variation to test whether emulators can learn nonlinear, stochastic, multiscale dynamics. In the absence of such resources, methods are often evaluated on ad hoc examples, making it difficult to compare algorithms, assess robustness, or reproduce benchmark conditions. A further obstacle is that building multiscale hybrid models by hand is resource-intensive, requiring manual curation, domain expertise, and harmonization across modeling formalisms 21 ; this motivates pipelines that instead generate diverse regulatory variants automatically by systematically evolving a baseline logic 22 . Here we present PhysiBench, a controlled in silico benchmark resource designed to address this gap. The name reflects the resource’s foundation in the PhysiBoSS/PhysiCell ecosystem 18–20 , where intracellular Boolean regulation is coupled to cell-level and spatial multiscale simulation. PhysiBench consists of a benchmark suite of 612 executable intracellular Boolean regulatory models, and a dataset of 120,000 time-resolved stochastic multiscale simulations generated from 60 selected models (Figure 1). The model suite provides a controlled family of related regulatory models executable in a shared framework, while the simulation dataset provides paired input-output trajectories generated under systematically varied initial conditions and stimulation protocols.
Figure 1: Overview of the resource, including a benchmark suite of 612 variant intracellular Boolean models embedded in a shared multiscale framework, for use by methods that generate dynamic data on demand, and a dataset of 120,000 precomputed multiscale simulations under controlled inputs, for use by methods that operate on time-resolved trajectories. Together, they provide inputs and reference trajectories for surrogate modeling, parameter estimation, simulation-based optimization, and benchmarking of controlled stimulation-protocol workflows.
2
The two components support complementary uses: the executable model suite enables methods that require simulations on demand, whereas the precomputed trajectories support surrogate modeling, emulator evaluation, data-driven inference, and comparative benchmarking. Shared identifiers and explicit input-parameter files link models, simulation inputs, and outputs, allowing the resource to be used either as executable benchmark problems or as a structured dataset for supervised learning. PhysiBench is biologically motivated but methodologically oriented. The Boolean regulatory models are derived from published networks spanning cell-cycle control, developmental patterning, cancer signaling, immune response, and cell-fate decisions, but the released variants and simulations are controlled in silico benchmarks rather than calibrated representations of specific biological systems. This design provides realistic biological structure and multiscale stochastic dynamics 16;17 while preserving the reproducibility, scale, and controlled variation needed for systematic method development in computational systems biology.
2
Methods
PhysiBench contains two linked outputs: a benchmark suite of 612 executable intracellular Boolean regulatory network variants and a dataset of 120,000 time-resolved multiscale simulation trajectories generated from 60 selected models. The Methods are organized around these two outputs: construction of the benchmark model suite and generation of the trajectory dataset. Throughout this section, a simulation context refers to the non-model inputs required to define one PhysiBoSS run: the initial cell-population configuration and the external stimulation protocol. The stimulation protocol specifies the stimulation duration, stimulation period, and four spatial boundary values defining the external signal field over the two-dimensional simulation domain. Given a model, a context, and a stochastic seed, the corresponding simulation run is fully specified. The components included in the simulation context, and the run-specific metadata recorded separately, are summarized in Table 1. Table 1: Components of the simulation context and run-specific metadata.
Component
Included in a simulation context?
Description
Initial cell-population configuration Stimulation duration Stimulation period Spatial boundary values Model identifier
Yes
Defines the starting spatial arrangement, density, and related initial-condition parameters.
Yes
Stochastic seed
No
Duration of the external signal applied through the model input node. Periodicity of the external stimulation signal. Four boundary values defining the external signal field over the two-dimensional simulation domain. Specifies which candidate or selected model is evaluated. Recorded separately to reproduce each stochastic simulation run.
Yes Yes No
The context schema and context files used at each workflow stage are listed in the GitHub repository (see Section 7).
2.1
Construction of the benchmark model suite
The benchmark-suite workflow starts from seven published source models, assigns each model a common PhysiBoSS/PhysiCell interface, generates stochastic model variants, and applies two filtering steps to retain executable, nonredundant, and input-responsive variants (Figure 2).
3
Figure 2: Overview of the pipeline. Starting from seven reference intracellular Boolean regulatory network models, benchmark suite construction proceeds through three stages: (1) mutation-based generation of candidate models, (2) online behavioral evaluation, and (3) offline sensitivity evaluation. This produces a benchmark suite of 612 variant intracellular Boolean regulatory network models. A subsequent model selection step retains 60 models to increase coverage of diverse dynamical regimes for simulation dataset generation. In the second phase, simulations are executed under fixed simulator settings and controlled variations in initial conditions and stimulation protocols, producing 120,000 time-resolved multiscale stochastic simulations.
4
2.1.1
Source Boolean models and common simulation interface
Seven published PhysiBoSS-compatible Boolean regulatory network models are used as starting points for benchmark construction. They are selected because they are open source, executable in the PhysiBoSS/MaBoSS ecosystem, documented in previous studies, and cover distinct biological processes and network architectures. The source models are summarized in Table 2. Table 2: Published Boolean regulatory network models used as source models for benchmark construction. Source model
Short description
Mammalian cell-cycle restriction-point model Drosophila segment-polarity model EGF/TNF signaling model
Mammalian cell-cycle restriction-point control.
Gastric cancer signaling model
Regulatory mechanisms associated with gastric cancer signaling. Immune-cell activation and macrophage response states. Regulatory mechanisms associated with prostate cancer signaling. TNF-induced cell-fate decisions.
Macrophage activation model Prostate cancer signaling model TNF cell-fate model
Developmental patterning in the Drosophila segment-polarity network. Signaling responses to EGF and TNF stimulation.
Reference 30;31
32–34
35;36 37;38
39;40
41;42
43;44
Before variant generation, each reference model is prepared for use in a common multiscale simulation workflow. This preparation focused on two requirements. First, each model is checked for syntactic validity and provided with compatible MaBoSS .bnd and .cfg files. Second, each model is assigned the same high-level simulation interface, allowing all variants to be controlled and observed consistently during PhysiBoSS/PhysiCell simulations. The prepared model files and interface assignments are released and documented in the repository (See Section 7). The common interface consists of one intracellular input node and three intracellular output nodes. The input node acts as the single controllable signal through which the external stimulation protocol is passed from the PhysiCell environment to the intracellular model. The three output nodes are read by the multiscale simulator and used to connect intracellular regulatory dynamics to cell-level behavior, including survival, proliferation, and death. This interface was introduced to standardize benchmarks. It should not be interpreted as a biological claim that the selected nodes are validated receptors, phenotypic markers, or therapeutic readouts for the corresponding source systems. 2.1.2
Generation of model variants
Model variants are generated by applying stochastic modifications to the seven prepared reference models. The goal was to create families of related but distinct intracellular regulatory networks that could all be executed through the same PhysiBoSS/PhysiCell interface. For each candidate variant, one reference model is copied and modified by a sequence of random mutation operations. These operations changed the regulatory logic of the model while preserving the common simulation interface. The single input node and the three output nodes assigned to each reference model were protected from mutation, removal, or reassignment. This ensured that every accepted variant could be controlled by the same external stimulation protocol and observed through the same intracellular outputs during multiscale simulation. The released mutation operators are summarized in Table 3.
5
Table 3: Mutation operators used to generate Boolean model variants.
Mutation operator
Used in released generation
Effect on the model
switch Selects two nodes with defined logic and swaps their logical nodes expressions. logic replace Selects a binary logical operator within a node rule and replaces it logical with another operator. operator replace Selects a node appearing inside a logical expression and replaces it node with another node. inside logic negate Selects a subexpression within a logical rule and adds or removes a subexpressionlogical negation. add input Adds an additional input node to the logical rule of a selected node to logic by combining it with the existing expression through a randomly chosen operator. add new Creates a new regulatory node with a random initial value and node random logical rule, then connects it to existing logic. randomize Replaces the logical rule of a selected node with a newly generated node logic random expression built from existing nodes. randomize Randomizes one model parameter by assigning it a value sampled parameter uniformly between 0 and 1.
Yes
Yes
Yes
Yes Yes
Yes Yes No
Mutation settings were chosen to favor local changes in regulatory logic while preventing uncontrolled network growth. Operators that add new nodes were assigned a low probability, and each mutation lineage was limited to at most 45 added nodes. This limit was introduced as a computational safeguard rather than a biological assumption: it allowed substantial expansion of the reference networks while preventing unbounded network growth that would reduce tractability, comparability across variants, and traceability to the source models. After mutation, each candidate was checked for compatibility with the MaBoSS and PhysiBoSS execution formats. Candidates that failed these checks were discarded. The number of mutation operations applied to each candidate is adjusted during generation to balance local exploration and broader search. When generation produced acceptable variants, fewer mutations are applied to subsequent candidates, encouraging exploration near successful models. When candidates are repeatedly rejected, more mutations are applied, increasing the chance of discovering distinct behaviors. The mutation depth is bounded between 10 and 2,000 operations. The mutation code, configuration file, and generated-model manifest are released and documented in the repository (See Section 7). 2.1.3
Online behavioral filtering
Each valid candidate model is evaluated immediately after generation to reduce redundancy in the model suite. The candidate is simulated under a fixed set of 48 stimulation protocols while holding the initial cell configuration constant. For each protocol, the final six recorded time points are retained, and the number of alive cells is extracted. These values are concatenated across the 48 protocols to form a population-level behavioral signature for the candidate. The exact 48 online-evaluation protocol definitions and the sampled parameter space are provided in the GitHub repository (see Section 7). The candidate’s signature is compared with the signatures of models already accepted into the provisional suite. Similarity is measured using Pearson correlation 45 between behavioral signatures; candidates are accepted only when their maximum correlation with the accepted pool was below 0.85. Candidates whose behavior is too similar to previously accepted models are discarded, whereas candidates 6
with sufficiently distinct population dynamics are retained. This online filtering step produces 2,122 candidate variants from the seven reference architectures, as summarized in Table 4. 2.1.4
Offline sensitivity filtering
The online filtering step removes candidates that were behaviorally redundant with previously accepted models. Offline sensitivity filtering then removes candidates that are executable but weakly responsive to controlled changes in simulation inputs. For this step, each candidate model is simulated once across 215 released contexts. This produces, for each model, a set of outputs spanning controlled variation in initial conditions and stimulation protocols. The purpose of this step is not to evaluate biological realism, but to retain models whose multiscale behavior changed detectably across the sampled input space. For every simulation, nine output summaries are computed. These summaries measured total alive-cell count and spatial organization of the alive-cell population with respect to circular and square target regions, including shifted and distribution-weighted variants. For each model and each output summary, variability across the 215 contexts is quantified using the standard deviation and coefficient of variation. A model is retained only when every output summary met both thresholds: standard deviation greater than 30.0 and coefficient of variation greater than 0.2. This rule removes models that are executable but insensitive to the sampled input conditions. The output summaries, their code-level identifiers, the workflow scripts and configuration files are provided in the repository (See Section 7). After offline filtering, 612 Boolean regulatory network variants are retained as the released benchmark suite. The number of retained variants differs across reference families because some source architectures generated more diverse multiscale behaviors under the mutation and filtering procedure, as summarized in Table 4. Table 4: Candidate variants retained after online behavioral filtering and offline sensitivity filtering for each source model family.
Source model Mammalian cell-cycle restriction-point model Drosophila segment-polarity model EGF/TNF signaling model Gastric cancer signaling model Macrophage activation model Prostate cancer signaling model TNF cell-fate model Total
Variants after online filtering
Variants retained after offline filtering
204
56
226 263 48 45 51 1,285 2,122
84 103 15 15 18 321 612
The main hyperparameters used for benchmark-suite construction are summarized in Table 5 to support reproducibility. The full configuration files and execution environment are described in the GitHub repository (see Section 7). Table 5: Main hyperparameters used for benchmark-suite construction. Focus
Hyperparameter
Value
Mutation-based generation Mutation-based generation Mutation-based generation Mutation-based generation Mutation-based generation Mutation-based generation
Evaluation protocols per behavioral signature Final time steps retained per protocol Novelty threshold Mutation depth, initial and minimum Mutation depth, maximum Adaptive decay factor after candidate acceptance
48 6 0.15 10 2,000 × 0.75
7
Table 5: Main hyperparameters used for benchmark-suite construction. Focus
Hyperparameter
Value
Mutation-based generation Mutation operator distribution Mutation operator distribution Mutation operator distribution Mutation operator distribution Mutation operator distribution Mutation operator distribution Mutation operator distribution Mutation operator distribution Network constraints Network constraints
Adaptive growth factor after candidate rejection switch nodes logic
× 1.5 0.15
replace logical operator
0.26
replace node inside logic
0.228
negate subexpression
0.25
add input to logic
0.01
add new node
0.002
randomize node logic
0.1
randomize parameter
0 (disabled)
Maximum new nodes per lineage Maximum network size after interface standardization Simulation contexts per model Output summaries Minimum standard deviation Minimum coefficient of variation MaBoSS pseudorandom seed Maximum candidates tested Generated models before offline filtering Models retained after offline filtering
45 63
Offline filtering Offline filtering Offline filtering Offline filtering Offline filtering Pipeline termination Pipeline termination Pipeline termination
2.2
215 9 30.0 0.2 37 200,000 2,122 612
Generation of the multiscale trajectory dataset
The trajectory-dataset workflow starts from the 612-model benchmark suite, selects 60 models to increase coverage of variable and extreme simulation behaviors, and simulates each selected model under 2,000 controlled contexts. 2.2.1
Selection of models for dataset generation
A subset of 60 models was selected from the 612-model benchmark suite to increase coverage of diverse and informative simulation behaviors while keeping dataset generation computationally tractable. Thirty models are selected for high variability in alive-cell-count outputs across sampled contexts. Pairwise correlations 45 are used to reduce redundancy: when two selected models produce highly correlated response profiles, the model with lower variability is replaced by the next eligible candidate. A second group of 30 models is selected for strong outlier behavior, based on the frequency and magnitude of extreme output responses across contexts. Outlier responses were identified using the modified z-score, with values above 3.5 in absolute value classified as outliers. Models selected by the first criterion were excluded from the second criterion, ensuring that the two groups were disjoint. The two complementary selection groups used to choose the final 60 models for simulationdataset generation are summarized in Table 6.
8
Table 6: Model-selection groups used to choose the 60 benchmark models for simulation-dataset generation.
Selection group
Number of models Selection criterion
Redundancy control
Highvariability models
30
Largest standard deviation in alive-cell-count outputs across sampled contexts.
Outlierresponse models
30
Total selected for dataset generation
60
Highest outlier-strength scores, capturing both the frequency and severity of extreme responses. Complementary coverage of broadly variable and rare or extreme behaviors.
Pairwise correlations were checked; when correlation exceeded 0.85, the lower-variability model was replaced by the next eligible candidate. Models selected by the high-variability criterion were excluded so that the groups remained disjoint. Selection groups were kept disjoint.
Together, these two criteria retained models with broadly variable responses and rare or extreme responses. The selected model identifiers, selection scores, and model-selection script are released with the workflow (See Section 7). 2.2.2
Sampling of simulation contexts
For each selected model, 2,000 contexts are generated using the shared context definition introduced above. For each protocol parameter, ten evenly spaced candidate values are generated over the configured range. Stimulation duration is sampled between 5 and 200 simulation-time units, stimulation period between 5 and 800 simulation-time units, and each spatial boundary value between 0 and 10. The resulting grid is filtered to retain only protocols in which the stimulation period was greater than or equal to the stimulation duration. The remaining protocols are randomly shuffled, and 2,000 contexts are retained for each selected model. Contexts are sampled independently for each model, so the exact set of stimulation protocols differs between models. The sampled dataset-generation contexts and the sampling script are released with the repository (See Section 7). The parameter ranges and sampling rules used to generate stimulation protocols for simulationdataset construction are summarized in Table 7. Table 7: Parameter ranges and sampling rules used to generate simulation contexts.
Parameter or rule
Candidate values
Stimulation duration
10 evenly spaced values
Stimulation period
10 evenly spaced values
xmin boundary value xmax boundary value ymin boundary value
10 evenly spaced values 10 evenly spaced values 10 evenly spaced values
Range or value
Constraint or sampling rule
5–200 simulationtime units 5–800 simulationtime units 0–10
None beyond grid sampling.
0–10
None beyond grid sampling.
0–10
None beyond grid sampling.
9
Stimulation period must be greater than or equal to stimulation duration. Stimulation period must be greater than or equal to stimulation duration.
Table 7: Parameter ranges and sampling rules used to generate simulation contexts.
Parameter or rule
Candidate values
ymax boundary value Protocol grid
10 evenly spaced values 1,000,000 combinations before filtering
Retained contexts
2,000 per selected model
2.2.3
Range or value
Constraint or sampling rule
0–10
None beyond grid sampling.
Six parameters with 10 candidate values each 120,000 total simulations across 60 models
Invalid protocols with stimulation period shorter than stimulation duration were removed.
Valid protocols were randomly shuffled and retained independently for each model.
Multiscale simulation execution
All simulations are executed in the PhysiBoSS/PhysiCell framework 19;20 . Each cell contains an independent MaBoSS Boolean network instance that is updated asynchronously during the simulation 18 . The intracellular input node receives the external stimulation signal from the PhysiCell environment, and the intracellular output nodes are propagated back to the cell-based layer to modulate cell behavior. This coupling allows intracellular regulatory dynamics, cell-level decisions, spatial interactions, and environmental fields to evolve jointly. For each of the 60 selected models, 2,000 independent simulations runs produce 120,000 timeresolved multiscale stochastic simulations. Each simulation was assigned a unique stochastic seed recorded with its input parameters. Simulator-level settings were held fixed for a given Boolean model, including intracellular update settings, maximum simulation time, cell mechanics parameters, microenvironmental diffusion and decay parameters, boundary conditions, and PhysiBoSS coupling settings. Therefore, variation in the released dataset arises from controlled differences in initial conditions and stimulation protocols, together with the intrinsic stochasticity of the multiscale simulator. The final multiscale trajectory dataset is summarized in Table 8. Table 8: Summary of the multiscale simulation dataset generated from the selected benchmark models. Dataset quantity or setting
Value or description
Selected models Simulations per selected model Total simulations Stochastic seed Controlled variation Fixed model-specific settings
60 2,000 120,000 One recorded seed per simulation Initial conditions and stimulation protocols Intracellular update settings, maximum simulation time, cell mechanics, microenvironmental diffusion and decay, boundary conditions, and PhysiBoSS coupling settings x position, y position, z position, and current phase
Recorded cell-level variables
The fixed PhysiBoSS/PhysiCell configuration files used for simulation execution are released with the workflow (See Section 7). Each simulation output records the cell population over time. For each recorded time point, the released files include cell-level spatial coordinates and cell-cycle phase information, allowing users to reconstruct spatial trajectories and compute additional population-level summaries. Each simulation is linked to an input-parameter file containing the sampled stimulation protocol and 10
to model-level initial-configuration metadata. Together with the model identifier and stochastic seed recorded in the manifest, these records provide the information required to reproduce the run. The trajectory manifest links each simulation output to its model identifier, sampled context, stochastic seed, input-parameter file, and output file.
2.3
Resource organization and reproducibility
The released repository provides the model files, context files, simulation configurations, trajectory manifest, filtering scripts, and workflow documentation needed to reproduce the benchmark-suite construction and dataset-generation workflow (see Section 7). This organization allows the resource to be used either as an executable benchmark suite or as a precomputed trajectory dataset.
3
Data Records
The PhysiBench resource as an open-access record including the benchmark model suite and the multiscale trajectory dataset [Repository/DOI: add record]. The benchmark suite contains the 612 executable intracellular Boolean regulatory network variants. The trajectory dataset contains 120,000 time-resolved multiscale simulations generated from 60 selected benchmark models. The two records can be reused independently or linked through shared model identifiers. The two linked components of the PhysiBench resource are summarized in Table 9. Table 9: Main components of the released PhysiBench resource.
Component
Content
Number of records
Benchmark model suite Multiscale trajectory dataset
Variant intracellular Boolean regulatory network models compatible with PhysiBoSS Time-resolved multiscale simulation outputs generated from 60 selected benchmark models under controlled parameterizations
612 models 120,000 simulations
3.1
Storage footprint <50 MB 23 GB
Benchmark model suite
The benchmark model suite contains 612 model variants organized by reference family and model identifier. Each model is provided as a MaBoSS-compatible pair of files: a .bnd file defining the regulatory nodes, logical rules, and transition rates, and a .cfg file specifying simulation settings. The minimum reusable unit is one model variant, identified by the triplet <reference model, variant ID, model ID>. A manifest file, variant models manifest.json, indexes all 612 models and records the reference model, variant identifier, and model identifier for each entry. This manifest allows users to programmatically enumerate models, filter by reference family, and link selected models to the simulation dataset. The main fields of the benchmark-suite manifest are summarized in Table 10. Table 10: Main fields of the benchmark model-suite manifest. Field
Description
reference model variant ID model ID bnd file cfg file
Source reference family from which the variant was generated. Variant identifier within the reference family. Model identifier used to link benchmark models and simulation outputs. Path to the MaBoSS .bnd file. Path to the MaBoSS .cfg file.
11
3.2
Multiscale trajectory dataset
The simulation dataset contains 120,000 time-resolved multiscale simulations generated from 60 selected benchmark models, with 2,000 simulations per selected model. The minimum reusable unit is one simulation, identified by the quadruplet <reference model, variant ID, model ID, simulation ID>. A manifest file, multiscale simulations manifest.json, indexes all simulations and links each simulation to its parent model through the fields reference model, variant ID, model ID, and simulation ID. The corresponding input-parameter and cell-data files are organized under the same model-specific directory structure.
3.3
Simulation-context metadata
Each PhysiBoSS simulation run is specified by a Boolean regulatory model, a stochastic seed, an initial cell-population configuration, and a stimulation protocol. The stimulation protocol is stored in the corresponding input parameters file, whereas the initial configuration is defined at model level in initial positions.json and is shared by simulations associated with the same model ID. The released input-parameter files retain the field names treatment duration and treatment period; throughout the manuscript, these fields are described as stimulation duration and stimulation period. The field names follow the released configuration files. The fields defining model-level initial configurations and simulation-level stimulation protocols are summarized in Table 11. Table 11: Fields used to define initial configurations and stimulation protocols in the simulation dataset. Field
Source
type
initial positions.json Geometry of the initial cell population, such as circle or square. initial positions.json Center coordinates of the initial cell population. initial positions.json Fraction of candidate lattice positions occupied by cells. initial positions.json Simulated cell type identifier. initial positions.json Initial-cell sampling mode, such as sparse or contour. initial positions.json Radius for circular initializations or half-side length for square initializations. input parameters Periodicity of the external stimulation signal, in simulation time units. input parameters Duration of each stimulation interval, in simulation time units. input parameters Boundary values defining the external stimulation field over the two-dimensional simulation domain.
center density cell type mode length treatment period treatment duration TNF dirichlet xmin, TNF dirichlet xmax, TNF dirichlet ymin, TNF dirichlet ymax
3.4
Description
Cell-data output files
Time-resolved cellular outputs are stored in compressed cell data files. Each file contains the saved time points for one simulation. At each saved time point, the released records contain the cell positions and the corresponding cell-cycle or death-state annotation, which are sufficient to reconstruct spatial trajectories and compute population-level summaries. The core fields used in this manuscript are: • time: simulation time, expressed in simulation time units;
12
• x positions: x coordinates of the simulated cells; • y positions: y coordinates of the simulated cells; • z positions: z coordinates of the simulated cells; • current phase: PhysiCell cell-cycle or death-state phase associated with each cell. Spatial coordinates follow the PhysiCell unit convention and are reported in micrometers. Simulation times, saved intervals, stimulation periods, and stimulation durations are reported in simulation time units. The current phase field follows the PhysiCell integer phase encoding used in the released simulations: live cells are encoded as 14, apoptotic cells as 100, and necrotic states as 101, 102, or 103. Additional PhysiCell-derived quantities, when present in exported simulation outputs, follow the corresponding PhysiCell unit conventions.
3.5
Directory organization
The benchmark suite and trajectory dataset are organized by shared model identifiers. The expected directory organization is: benchmark_suite/ |-- variant_models_manifest.json |-- <reference_model>_<variant_ID>_<model_ID>/ | |-- model.bnd | `-- model.cfg `-- ... simulation_dataset/ |-- multiscale_simulations_manifest.json |-- initial_positions.json |-- <reference_model>_<variant_ID>_<model_ID>/ | `-- data/ | |-- input_parameters/ | | |-- input_parameters_<simulation_ID>.json | | `-- ... | `-- cell_data/ | |-- cell_data_<simulation_ID>.json.gz | `-- ... `-- ... Time-resolved simulation outputs are stored as compressed JSON files (.json.gz) and can be parsed using standard JSON libraries after decompression. The input parameters files are JSON metadata records associated with individual simulations. The manifests provide the primary entry point for programmatic access, filtering, and linking between benchmark models, initial configurations, simulation inputs, stochastic seeds, and trajectory outputs.
4
Technical Validation
The resource is validated through three complementary checks: file integrity and executability, structural diversity of the benchmark models, and behavioral heterogeneity of the multiscale outputs. These checks assess whether the released files are complete, readable, executable in the intended simulation framework, and diverse with respect to the structural and behavioral metrics reported below.
13
4.1
Resource integrity and executability
For the benchmark suite, all 612 model directories are checked for the expected .bnd and .cfg files. Each model is verified to be syntactically valid, fully specified, and compatible with the PhysiBoSS execution format. The benchmark manifest is cross-checked against the directory structure to confirm that each listed model identifier corresponds to an available model directory and that no duplicate model identifiers are present. For the simulation dataset, multiscale simulations manifest.json is checked against the released directory structure to verify the presence of 120,000 simulation records, corresponding to 2,000 simulations for each of the 60 selected benchmark models. For each simulation record, the corresponding input-parameter file and cell-data file are verified to be present and parsable with standard JSON libraries, with decompression applied where required. Input-parameter files are checked for the required stimulation-protocol fields, and the manifest is checked for the metadata required to link each simulation to its model identifier, initial configuration, stochastic seed, and trajectory output. Executability is assessed by running representative PhysiBoSS simulations from the released model and configuration files without model-specific adaptation. These checks confirm that the benchmark suite can be used as an executable collection of intracellular Boolean regulatory network models and that the simulation dataset is consistently indexed, readable, and linked to the corresponding model and input records.
4.2
Structural diversity of the benchmark suite
Structural diversity is assessed using graph-based distance measures to verify that mutation-based generation produced distinct regulatory structures rather than minor syntactic variants. Boolean update rules are converted into graph representations, and each model is mapped to a directed signed graph whose edges encode regulatory dependencies and polarity. Three complementary graph distances are computed using the netrd 46 and networkx 47 Python libraries: DeltaCon 48 , Ipsen–Mikhailov distance 49 , and Quantum Jensen–Shannon divergence 50 . The metrics are first evaluated on control sets generated by permuting node labels of selected reference models while preserving topology. All three metrics assign lower distances to permuted instances of the same model than to structurally distinct models, supporting robustness to node relabeling and sensitivity to structural differences (Figure 3).
Figure 3: Pairwise structural distances computed on the Control Set used to validate the graphbased similarity metrics. Panels show heatmaps of (a) DeltaCon, (b) Ipsen-Mikhailov distance, and (c) Quantum Jensen-Shannon divergence computed on one original reference model and a set of shuffled versions of it, for each reference model. Darker blocks along the diagonal correspond to shuffled instances derived from the same reference model and indicate lower distances than those observed between different source models.
14
The validated metrics are then applied to the full benchmark suite. Pairwise distances are computed within and across reference-model families (Figure 4). Across the three metrics, average within-family distances are slightly lower than, but comparable to, between-family distances, with within-to-between distance ratios ranging from 0.76 to 0.85. This indicates that the mutation process generates structurally diverse models while preserving traceable relationships to their source architectures.
Figure 4: Pairwise structural distances across the curated Boolean model collection. Panels show heatmaps of (a) DeltaCon, (b) Ipsen-Mikhailov distance, and (c) Quantum Jensen-Shannon divergence computed for all filtered models. The matrices summarize structural variability in the released dataset both within and across reference Boolean model families.
4.3
Behavioral heterogeneity of the simulation dataset
Behavioral heterogeneity is assessed from multiscale simulation outputs generated during offline evaluation and model selection. This analysis tests whether the benchmark models induce diverse responses under controlled variation in initial conditions and stimulation protocols. Across selected models, the average correlation between output-response profiles is 0.06015, indicating low redundancy and largely independent response profiles. Rare or extreme behaviors are quantified using the outlier-strength measure used during model selection. Outlier-strength values span several orders of magnitude, with a maximum of approximately 1.07 × 104 , a mean of 42.44, and quartiles of 0.45, 6.40, and 18.79. Together, these analyses indicate that the dataset captures both smooth and highly irregular multiscale response regimes.
4.4
Scope and limitations
PhysiBench is an in silico benchmark resource intended for computational method development and evaluation. It is appropriate for workflows such as surrogate modeling, parameter estimation, simulation-based optimization, sensitivity analysis, and algorithmic comparison. Although the source networks are derived from published biological regulatory models, the released variants are synthetic constructs generated by stochastic mutation and filtering. They have not been independently calibrated or validated against experimental data and should not be used to infer biological mechanisms, predict cell-line-specific responses, or draw conclusions about pharmacological efficacy, toxicity, or therapeutic scheduling in real biological systems. Several modeling assumptions define the scope of the resource. The Boolean formalism represents intracellular signaling through discrete switch-like transitions and does not capture graded signal transduction, continuous dose-response relationships, or kinetic effects that may be important in specific biological applications. PhysiBoSS simulations are executed in a two-dimensional
15
spatial domain, so three-dimensional tissue architecture, extracellular matrix mechanics, and outof-plane diffusion are not represented. The external stimulation protocol is implemented as an abstract input to the intracellular network and should not be interpreted as a mechanistic model of drug exposure, pharmacokinetics, receptor binding, or dose-dependent pharmacological action. These limitations define the intended scope of the resource rather than limiting its use as a controlled benchmark. Users requiring biological predictive accuracy for a specific system should independently select, calibrate, and validate an appropriate model before drawing biological or experimental conclusions.
5
Usage Notes
The resource supports three main reuse modes: direct execution of benchmark models, analysis of the precomputed trajectory dataset, and regeneration or extension of the dataset using the workflow released in the repository. Executable examples are maintained in the GitHub repository rather than embedded in the manuscript, so that commands, paths, and software requirements remain synchronized with the released code (See Section 7). The benchmark model suite can be used directly as a collection of MaBoSS/PhysiBoSS-compatible intracellular regulatory models. Example scripts for loading the model manifest, selecting models by reference family, and launching a PhysiBoSS simulation are provided in the repository (see Section 7). Users may also modify input nodes, output mappings, or simulation parameters for exploratory computational workflows, provided that biological interpretation is supported by independent calibration and validation. The trajectory dataset can be used for downstream tasks such as surrogate modeling, datadriven inference, sensitivity analysis, and simulation-based optimization. Example scripts for reading the simulation manifest, loading paired input-parameter and cell-data files, filtering simulations by context parameters, and computing population-level summaries are provided in the repository (see Section 7).. The full construction workflow is reproducible through the released Snakemake pipeline (See Section 7). The workflow includes rules for reference-model preparation, mutation-based generation, online behavioral filtering, offline sensitivity filtering, model selection, structural validation, and simulation-data extraction. Users can execute the complete workflow or run individual stages to regenerate selected components or extend the dataset with additional simulation contexts. The workflow supports local execution, containerized environments, and remote execution on highperformance computing systems through the configuration files provided in the repository.
6
Data Availability
The PhysiBench resource, including the benchmark model suite,comprising 612 variant Boolean regulatory network models compatible with PhysiBoSS, and multiscale trajectory dataset, comprising 120,000 time-resolved PhysiBoSS simulation outputs generated from 60 selected models under controlled parameterizations, is publicly available as an open-access record in the Politecnico di Torino institutional repository 51 . The record is released under an open license and can be reused independently or together through their shared model identifiers.
7
Code Availability
All custom code developed to construct, validate, and reuse the resource is publicly available in the GitHub repository 52 . The repository includes scripts and workflows to reproduce model generation, online behavioral filtering, offline sensitivity filtering, model selection, technical validation analyses, simulation-data extraction, and example downstream reuse workflows. The repository also records the software versions and execution environment used for dataset generation, including PhysiBoSS/PhysiCell, MaBoSS, Python dependencies, Snakemake, and container definitions where applicable. Links to the benchmark-suite and simulation-dataset records are provided in the repository README.
16
References [1] Cascarano, A., Mur-Petit, J., Hernandez-Gonzalez, J., Camacho, M., de Toro Eadie, N., Gkontra, P., Chadeau-Hyam, M., Vitria, J., and Lekadir, K. Machine and deep learning for longitudinal biomedical data: a review of methods and applications. Artificial Intelligence Review, 56(Suppl 2):1711–1771 (2023). https://doi.org/10.1007/s10462-023-10561-w [2] Abrate, M. P., Smeriglio, R., Bardini, R., Savino, A., and Di Carlo, S. Fast and accurate LSTM meta-modeling of TNF-induced tumor resistance in vitro. In Proceedings of the 2024 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 6194–6201 (2024). https://doi.org/10.1109/BIBM62325.2024.10822769 [3] K. A. Norton, D. Bergman, H. V. Jain, and T. Jackson, “Advances in surrogate modeling for biological agent-based simulations: trends, challenges, and future prospects,” Journal of Mathematical Biology, vol. 92, no. 1, p. 6, 2026. [4] Ponce-de-León, M., Montagud, A., Akasiadis, C., Schreiber, J., Ntiniakou, T., and Valencia, A. Optimizing dosage-specific treatments in a multiscale model of tumor growth. Frontiers in Molecular Biosciences, 9:836794 (2022). https://doi.org/10.3389/fmolb.2022.836794 [5] Bardini, R. and Di Carlo, S. Computational methods for biofabrication in tissue engineering and regenerative medicine—a literature review. Computational and Structural Biotechnology Journal, 23:601–616 (2024). https://doi.org/10.1016/j.csbj.2023.12.035 [6] Castrignano, A., Bardini, R., Savino, A., and Di Carlo, S. A methodology combining reinforcement learning and simulation to optimize the in silico culture of epithelial sheets. Journal of Computational Science, 76:102226 (2024). https://doi.org/10.1016/j.jocs.2024.102226 [7] Giannantoni, L., Bardini, R., and Di Carlo, S. A methodology for co-simulationbased optimization of biofabrication protocols. In Proceedings of the International WorkConference on Bioinformatics and Biomedical Engineering, pp. 179–192 (2022). Springer. https://doi.org/10.1007/978-3-031-07802-6 17 [8] Takamoto, M., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pflüger, D. & Niepert, M. PDEBench: An Extensive Benchmark for Scientific Machine Learning. In: Advances in Neural Information Processing Systems 36 (NeurIPS 2022), Datasets and Benchmarks Track. Available at: https://papers.neurips.cc/paper_files/paper/2022/file/ 0a9747136d411fb83f0cf81820d44afb-Paper-Datasets_and_Benchmarks.pdf Accessed: 24 March 2026. [9] PDEBench Project. PDEBench: An Extensive Benchmark for Scientific Machine Learning. GitHub repository. Available at: https://github.com/pdebench/PDEBench Accessed: 24 March 2026. [10] Takamoto, M., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pflüger, D. & Niepert, M. PDEBench Datasets. DaRUS dataset. doi:10.18419/DARUS-2986. Available at: https:// darus.uni-stuttgart.de/dataset.xhtml?persistentId=doi:10.18419/darus-2986 Accessed: 24 March 2026. [11] Rasp, S., Düben, P. D., Scher, S., Weyn, J. A., Mouatadid, S. & Thuerey, N. WeatherBench: A Benchmark Data Set for Data-Driven Weather Forecasting. Journal of Advances in Modeling Earth Systems 12, e2020MS002203 (2020). doi:10.1029/2020MS002203. Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020MS002203 Accessed: 24 March 2026. [12] Pangeo Data. WeatherBench: A benchmark dataset for data-driven weather forecasting. GitHub repository. Available at: https://github.com/pangeo-data/WeatherBench Accessed: 24 March 2026.
17
[13] Google Research. WeatherBench 2: A benchmark for the next generation of data-driven global weather models. GitHub repository. Available at: https://github.com/google-research/ weatherbench2 Accessed: 24 March 2026. [14] Ohana, R. et al. The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning. Advances in Neural Information Processing Systems 37, 44989–45037 (2024). Available at: https://openreview.net/forum?id=00Sx577BT3 Accessed: 24 March 2026. [15] Polymathic AI. The Well: 15TB of Physics Simulations. GitHub repository. Available at: https://github.com/PolymathicAI/the_well Accessed: 24 March 2026. [16] Alsalloum, G. A., Al Sawaftah, N. M., Percival, K. M., and Husseini, G. A. Digital twins of biological systems: A narrative review. IEEE Open Journal of Engineering in Medicine and Biology (2024). https://doi.org/10.1109/OJEMB.2024.3426916 [17] Bardini, R., Politano, G., Benso, A., and Di Carlo, S. Multi-level and hybrid modeling approaches for systems biology. Computational and Structural Biotechnology Journal, 15:396–402 (2017). https://doi.org/10.1016/j.csbj.2017.05.001 [18] Stoll, G., Caron, B., Viara, E., Dugourd, A., Zinovyev, A., Naldi, A., et al. MaBoSS 2.0: an environment for stochastic Boolean modeling. Bioinformatics, 33(14):2226–2228 (2017). https://doi.org/10.1093/bioinformatics/btx123 [19] Letort, G., Montagud, A., Stoll, G., Heiland, R., Barillot, E., Macklin, P., et al., and Calzone, L. PhysiBoSS: a multiscale agent-based modeling framework integrating physical dimension and cell signalling. Bioinformatics, 35(7):1188–1196 (2019). https://doi.org/10.1093/bioinformatics/bty766 [20] Calzone, L., Noël, V., Barillot, E., Kroemer, G., and Stoll, G. modeling signaling pathways in biology with MaBoSS: From one single cell to a dynamic population of heterogeneous interacting cells. Computational and Structural Biotechnology Journal, 20:5661–5671 (2022). https://doi.org/10.1016/j.csbj.2022.09.034 [21] Ruscone, M., Tsirvouli, E., Checcoli, A., Turei, D., Barillot, E., Saez-Rodriguez, J., et al. NeKo: a tool for automatic network construction from prior knowledge. PLOS Computational Biology, 21(9):e1013300 (2025). https://doi.org/10.1371/journal.pcbi.1013300 [22] Ouellet, M., Kim, J. Z., Guillaume, H., Shaffer, S. M., Bassett, L. C., and Bassett, D. S. Breaking reflection symmetry: evolving long dynamical cycles in Boolean systems. New Journal of Physics, 26(2):023006 (2024). https://doi.org/10.1088/1367-2630/ad1b5a [23] Malik-Sheriff, R. S., Glont, M., Nguyen, T. V., Tiwari, K., Roberts, M. G., Xavier, A., et al., and Hermjakob, H. BioModels—15 years of sharing computational models in life science. Nucleic Acids Research, 48(D1):D407–D415 (2020). https://doi.org/10.1093/nar/gkz1055 [24] Vaginay, A., Boukhobza, T., and Smaı̈l-Tabbone, M. From quantitative SBML models to Boolean networks. Applied Network Science, 7(1):73 (2022). https://doi.org/10.1007/s41109022-00473-8 [25] Shaikh, B., Smith, L. P., Vasilescu, D., Marupilla, G., Wilson, M., Agmon, E., Agnew, H., Andrews, S. S., Anwar, A., Beber, M. E., et al. BioSimulators: a central registry of simulation engines and services for recommending specific tools. Nucleic Acids Research, 50(W1):W108– W114 (2022). https://doi.org/10.1093/nar/gkac231 [26] Noel, V., Ruscone, M., Heiland, R., Montagud, A., Valencia, A., Barillot, E., Macklin, P., and Calzone, L. PhysiBoSS-Models: A database for multiscale models. arXiv preprint arXiv:2508.05550 (2025). https://arxiv.org/abs/2508.05550 [27] Pastva, S., Šafránek, D., Beneš, N., Brim, L. & Henzinger, T. Repository of logically consistent real-world Boolean network models. bioRxiv. Available at: https://www.biorxiv.org/ content/10.1101/2023.06.12.544361v1.full Accessed: 24 March 2026. 18
[28] Sybila. Biodivine Boolean Models (BBM) Benchmark Dataset. GitHub repository. Available at: https://github.com/sybila/biodivine-boolean-models Accessed: 24 March 2026. [29] Rocha, H. L. Parameter Sensitivity in Tumor Models: Dataset from PhysiCell Simulations. Zenodo dataset. doi:10.5281/zenodo.14590312. Available at: https://zenodo.org/records/ 14590312 Accessed: 24 March 2026. [30] Fauré, A., Naldi, A., Chaouiya, C., and Thieffry, D. Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinformatics 22(14), e124–e131 (2006). https://doi.org/10.1093/bioinformatics/btl210 [31] Fauré, A. Restriction point control of the mammalian cell cycle. Gene Interaction Network simulation (GINsim) Model Repository. Available at: https://ginsim.github.io/models/ 2006-mammal-cell-cycle/ Accessed: 23 March 2026. [32] Albert, R. and Othmer, H. G. The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. Journal of Theoretical Biology 223(1), 1–18 (2003). [33] Stoll, G., Bischofberger, M., Rougemont, J., and Naef, F. Stabilizing patterning in the Drosophila segment polarity network by selecting models in silico. Biosystems 102(1), 3–10 (2010). [34] MaBoSS Project. Drosophila Patterning. MaBoSS model repository. Available at: https: //maboss.curie.fr/ Accessed: 23 March 2026. [35] Chaouiya, C., Bérenguier, D., Keating, S. M., Naldi, A., Van Iersel, M. P., Rodriguez, N., et al. SBML qualitative models: a model representation format and infrastructure to foster interactions between qualitative modeling formalisms and tools. BMC Systems Biology 7(1), 135 (2013). [36] BioModels. Chaouiya2013 - EGF and TNFalpha mediated signalling pathway. BioModels Database, BIOMD0000000562. Available at: https://www.ebi.ac.uk/biomodels/ BIOMD0000000562 Accessed: 23 March 2026. [37] Flobak, Å., Baudot, A., Remy, E., Thommesen, L., Thieffry, D., Kuiper, M., and Lægreid, A. Discovery of drug synergies in gastric cancer cells predicted by logical modeling. PLoS Computational Biology 11(8), e1004426 (2015). [38] PhysiBoSS. gastric cancer. PhysiBoSS boolean-models repository. Available at: https:// github.com/PhysiBoSS/boolean-models/tree/main/gastric_cancer Accessed: 23 March 2026. [39] Niarakis, A., Ostaszewski, M., Mazein, A., Kuperstein, I., Kutmon, M., Gillespie, M. E., et al., and the COVID-19 Disease Map Community. Drug-target identification in COVID-19 disease mechanisms using computational systems biology approaches. Frontiers in Immunology, 14:1282859 (2024). https://doi.org/10.3389/fimmu.2023.1282859 [40] PhysiBoSS-COVID. boolean network. pb4covid19 repository. Available at: https://gitlab.lcsb.uni.lu/computational-modeling-and-simulation/pb4covid19/ -/tree/master/data/boolean_network Accessed: 23 March 2026. [41] Montagud, A., Béal, J., Tobalina, L., Traynard, P., Subramanian, V., Szalai, B., et al. Patientspecific Boolean models of signalling networks guide personalised treatments. eLife 11, e72626 (2022). [42] PhysiBoSS. prostate cancer. PhysiBoSS boolean-models repository. Available at: https: //github.com/PhysiBoSS/boolean-models/tree/main/prostate_cancer Accessed: 23 March 2026.
19
[43] Calzone, L., Tournier, L., Fourquet, S., Thieffry, D., Zhivotovsky, B., Barillot, E., and Zinovyev, A. Mathematical modeling of cell-fate decision in response to death receptor engagement. PLoS Computational Biology 6(3), e1000702 (2010). [44] PhysiBoSS. tnf cell fate. PhysiBoSS boolean-models repository. Available at: https:// github.com/PhysiBoSS/boolean-models/tree/main/tnf_cell_fate Accessed: 23 March 2026. [45] Benesty, J., Chen, J., Huang, Y., and Cohen, I. Pearson correlation coefficient. In Noise Reduction in Speech Processing, pp. 1–4 (2009). Springer. https://doi.org/10.1007/978-3-64200296-0 5 [46] McCabe, S., Torres, L., LaRock, T., Haque, S. A., Yang, C. H., Hartle, H., and Klein, B. netrd: A library for network reconstruction and graph distances. arXiv preprint arXiv:2010.16019 (2020). [47] Hagberg, A., Swart, P. J., and Schult, D. A. Exploring network structure, dynamics, and function using NetworkX. Los Alamos National Laboratory Technical Report LA-UR-08-05495 (2008). [48] Koutra, D., Vogelstein, J. T., and Faloutsos, C. DeltaCon: A principled massive-graph similarity function. In Proceedings of the 2013 SIAM International Conference on Data Mining, 162–170 (2013). [49] Jurman, G., Riccadonna, S., Visintainer, R., and Furlanello, C. Biological network comparison via Ipsen–Mikhailov distance. arXiv preprint arXiv:1109.0220 (2011). [50] Nielsen, F. On a variational definition for the Jensen–Shannon tion of distances based on the information radius. Entropy 23(4), https://doi.org/10.3390/e21050485
symmetriza464 (2021).
[51] Masera, M., Smeriglio, R., Bardini, R., Savino, A., Di Carlo, S. PhysiBench. PhysiBench resource. Available at: https://drive.cloud.polito.it/index.php/s/pefzfJpnZZiRMWY Accessed: 16 June 2026. [52] PhysiBench GitHub repository. PhysiBench GitHub repository. GitHub repository. Available at: https://github.com/smilies-polito/PhysiBench Accessed: 16 June 2026.
20