NSGA-II and Powell Optimized Inverse Design of MAO Coatings.

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Learn more: PMC Disclaimer | PMC Copyright Notice ACS Omega . 2026 Apr 1;11(14):22110–22124. doi: 10.1021/acsomega.5c13340 Search in PMC Search in PubMed View in NLM Catalog Add to search NSGA-II and Powell Optimized Inverse Design of MAO Coatings Dajun Zhai Dajun Zhai † School of Intelligent Manufacturing & Transportation, Chongqing Vocational Institute of Engineering, Chongqing 402260, China Find articles by Dajun Zhai † , Side Ou Side Ou ‡ School of Intelligent Science and Engineering, Chengdu Neusoft University, Chengdu 611844, China Find articles by Side Ou ‡ , Anting Liang Anting Liang ‡ School of Intelligent Science and Engineering, Chengdu Neusoft University, Chengdu 611844, China Find articles by Anting Liang ‡ , Guoping Lu Guoping Lu † School of Intelligent Manufacturing & Transportation, Chongqing Vocational Institute of Engineering, Chongqing 402260, China Find articles by Guoping Lu † , Haimei Lin Haimei Lin § China Unicom Hunan Branch, Changsha 410021, China Find articles by Haimei Lin § , Xuedong Lin Xuedong Lin † School of Intelligent Manufacturing & Transportation, Chongqing Vocational Institute of Engineering, Chongqing 402260, China Find articles by Xuedong Lin †, * Author information Article notes Copyright and License information † School of Intelligent Manufacturing & Transportation, Chongqing Vocational Institute of Engineering, Chongqing 402260, China ‡ School of Intelligent Science and Engineering, Chengdu Neusoft University, Chengdu 611844, China § China Unicom Hunan Branch, Changsha 410021, China * E-mail: [email protected] . Received 2025 Dec 19; Accepted 2026 Mar 24; Revised 2026 Mar 23; Collection date 2026 Apr 14. © 2026 The Authors. Published by American Chemical Society This article is licensed under CC-BY-NC-ND 4.0 PMC Copyright notice PMCID: PMC13084377  PMID: 42004366 Abstract Microarc oxidation (MAO), a key surface modification technique for in situ ceramic coating growth on valve metals, is hindered by stochastic plasma discharge dynamics that induce substantial property variability, impeding quality assurance, and industrial scalability. Existing empirical models fail to capture this nonlinearity due to small-sample constraints inherent to MAO process development. Here, we present a modular hybrid inverse design framework integrating (i) a composite deep variational autoencoder (ComDeep-VAE) for physics-aware data augmentation and (ii) Powell-optimized surrogate modeling with NSGA-II multiobjective optimization, establishing a generalizable platform extensible to mechanical integrity characterization and manufacturing system analytics. The ComDeep-VAE reconstructs high-dimensional process-parameter spaces while preserving experimentally validated statistical distributions, reducing the predictive mean absolute error by 60.8% (thickness) and 72.3% (porosity) relative to raw-data baselines using limited trials. The surrogate model achieves R 2 = 0.948 (thickness) and 0.902 (porosity), exceeding conventional benchmarks. For inverse design, multiobjective optimization navigates trade-offs between deposition efficiency and barrier performance, achieving theoretical convergence (errors <2 μm, <0.5%) within 750–1000 evaluations for target specifications (8.0 μm, 21% porosity). Experimental validation across contrasting targets (7.5 μm/32% and 13.5 μm/17% porosity) confirms practical reliability (relative errors 6.0% and 5.6%) within intrinsic MAO variability (±5–15%), substantiating that the framework resolves stochastic discharge effects through variational inference-based uncertainty quantification. This work establishes a scalable computational platform for intelligent coating design, with explicit extension pathways to adhesion strength optimization, substrate topography engineering, dynamic process control, and Overall Equipment Effectiveness (OEE) modeling, thereby bridging data-driven optimization with mechanistic process understanding to accelerate industrial adoption. 1. Introduction Microarc oxidation (MAO) has emerged as a pivotal surface engineering technique for the in situ growth of high-performance ceramic coatings on valve metals via electrochemical microdischarges. − These coatings exhibit exceptional multifunctionality, combining outstanding wear resistance, superior corrosion protection, excellent dielectric properties, and remarkable thermal stability, rendering them indispensable for aerospace components, biomedical implants, and critical automotive applications. − Despite these advances, critical challenges persist regarding both the fundamental coating formation mechanism and the reliable industrial translation of this technology. Key bottlenecks include inconsistent oxide layer performance and complex, highly nonlinear process–property correlations that collectively undermine the predictability of coating characteristics. − Although contemporary research heavily emphasizes empirical parameter optimization and mechanistic analysis, a pronounced scarcity of systematic studies aimed at establishing high-precision predictive models hinders the transition from phenomenological understanding to quantitative design-led engineering. The intrinsic complexity of MAOa process governed by multifield coupling spanning electrochemistry, plasma physics, and thermodynamics − renders conventional trial-and-error experimentation inadequate for deconvoluting intricate parameter interactions. This inherent limitation underscores the pressing need for robust data-driven modeling frameworks. Recently, machine learning (ML) and deep learning (DL) have demonstrated considerable potential for performance prediction in materials science. − However, their application to surface engineering is universally constrained by the small-data set challenge: the high cost and time-intensive nature of experimental data acquisition, compounded by complex parameter coupling and stringent optimization requirements, severely restricts the availability of large, high-fidelity data sets. , This data scarcity often leads to models plagued by low accuracy, overfitting, and poor generalizability when trained using traditional single-model architectures. To address data limitations, data augmentation techniquesparticularly those leveraging generative models such as Variational Autoencoders (VAEs)have gained traction for expanding training sets while preserving the statistical integrity of the original data distribution. , Nevertheless, the practical efficacy and limitations of such methods, particularly their ability to enhance physical diversity and external generalization within physically constrained systems, demand rigorous, context-specific validation. Focusing specifically on the MAO process, this study first systematically evaluates a ComDeep-VAE data augmentation framework tailored for its highly dimensional, small-sample regime. Concurrently, strategic model selection remains paramount. The field has increasingly adopted ensemble learning to enhance the robustness and predictive reliability. Among these, voting ensemble models stand out for synthesizing predictions from multiple base estimators, effectively mitigating overfitting, reducing variance, and substantially improving generalizationattributes crucial for navigating the complexity of materials data. This paradigm has demonstrated success across diverse domains: Fu et al. reported an IN-voting model achieving exceptional accuracy (0.9846) for slope stability prediction; Abbas et al. integrated gradient boosting (GB), random forest (RF), and weighted voting for high-fidelity prediction of concrete mechanical properties ( R 2 up to 0.973); and Wang et al. employed a hybrid soft-voting ensemble to enhance rockburst intensity forecasting. Further validation comes from liquefaction susceptibility assessments and fault detection studies, consistently affirming the superiority of ensemble voting over individual classifiers. Despite these demonstrated successes, the application of advanced voting ensemble frameworks to predict MAO coating properties remains conspicuously absent from the literature. Existing efforts have not fully addressed the modeling challenges posed by the intricate, nonlinear relationships between MAO process parameters and coating characteristics, particularly with respect to multiscale feature coupling and inverse process optimization. This gap critically impedes the intelligent development and widespread industrial adoption of MAO technology. To bridge this gap, we introduce an integrated methodology that synergistically combines a ComDeep-VAE data enhancement strategy with a Powell-optimized voting ensemble framework. The ComDeep-VAE is designed to extract physically meaningful features and generate statistically consistent synthetic data from limited experimental data, directly tackling the small-data challenge. The subsequent Powell-voting mechanism optimally integrates multiple ML paradigms on this enhanced data set to model the complex MAO process–property landscape. Furthermore, by incorporating NSGA-II multiobjective optimization, we establish an inverse design framework for intelligent process parameter optimization to achieve tailored coating characteristics. This comprehensive approach not only promises enhanced prediction accuracy but also enables coordinated multiobjective coating optimization, offering a novel pathway for the intelligent advancement and robust industrial deployment of MAO technology. 2. Materials and Methods MAO experiments were conducted on Φ12 mm × 6 mm Ti6Al4V alloy samples (Baoji Titanium Industry Co., Ltd., China) with the nominal composition (wt %): Ti (bal.), 6.1 Al, 4.1 V, 0.3 Fe, 0.2 O, and 0.015 H. An integrated MAO platform was developed, featuring: (1) a programmable alternating polarity power supply (0–750 V, 0–5 A), (2) a closed-loop electrolyte circulation system with ±1 °C temperature control, and (3) a liquid-cooled anodizing reactor, detailed in Figure . Treatments were performed in an alkaline electrolyte containing 5 g/L Na 2 SiO 3 ·9H 2 O, 10 g/L Na 3 PO 4 ·12H 2 O, and 5 g/L KF. Parameters included: current 0.2–0.5 A (5–12.5 A/dm 2 ), pulse width 250–400 μs at 10% duty cycle, duration 1–9 min, and electrolyte temperature 5–20 °C. Table details the complete experimental protocol, listing the parameter sets and the corresponding results obtained. 1. Open in a new tab (a) Voltage–time response recorded during the MAO process. (b) Schematic illustration of the integrated MAO platform. (c) Schematic of the anodizing reactor equipped with an electrolyte circulation system. (d) Schematic diagram outlining the characterization procedure. 1. Governing Equations and Parameter Definitions for MAO Coating Characterization. Category Formula Parameters Charge transfer Q = J · A · t 1 J : current density (A/dm 2 ); A : sample area (0.0113 dm 2 , Φ12 mm disc); t : oxidation time (s); Q : total charge (C) Coating mass m a c t = A s · h · ( 1 − P ) · ρ e f f 2 A s : substrate area (1.13 cm 2 ); h : thickness (cm, h μm × 10 –4 ); P : porosity (%); ρ eff : effective density (3.40 g/cm 3 ) Theoretical mass m t h = Q · M / n · F 3 M : molar mass of TiO 2 (79.866 g/mol); n = 4 (electrons for Ti → TiO 2 ); F : Faraday constant (96,485 C/mol) Deposition efficiency η = m a c t / m t h × 100 % 4 η: ratio of actual to theoretical mass (%) Charge utilization η c = η b · f c · f v 5 η b : base efficiency (15%, accounting for gas evolution); f c : current density factor (0.6–0.9); f v : voltage factor (0.6–1.2, CV mode) Film stress σ = σ b · f ϕ · f p · f c + σ t h 6 σ b : base stress (−50 to – 500 MPa, thickness-dependent); f ϕ : phase factor (1.0–1.5, anatase/rutile); f p : porosity factor (1–0.008 P ); f c : current factor (0.9–1.2); σ th : thermal stress (CTE mismatch) Substrate curvature κ = − 6 ( 1 − ν s ) t f · σ f / E s · t s 2 7 ν s : Poisson’s ratio (0.34); t f : film thickness (m); σ f : film stress (Pa); E s : elastic modulus (110 GPa); t s : substrate thickness (6 mm) Open in a new tab Transient voltage was recorded using a power supply, while discharge phenomena were captured via high-speed imaging (Phantom VEO710L, Vision Research Inc.). Coating thickness was measured with a calibrated eddy-current thickness gauge (DUALSCOPE MP0, Fischer, Germany; accuracy ± 0.1 μm) following the nondestructive testing procedure outlined in ASTM D7091-22 (“Standard Practice for Nondestructive Measurement of Dry Film Thickness of Nonmagnetic Coatings Applied to Ferrous Metals and Nonmagnetic, Nonconductive Coatings Applied to Non-Ferrous Metals”). Surface morphologies were characterized by field-emission scanning electron microscopy (FE-SEM) (MIRA4 LMH, TESCAN, Czech Republic) at 20 kV with sample preparation and imaging protocols adhering to ASTM E3-11(2021) (“Standard Guide for the Preparation of Metallographic Specimens”). Porosity quantification was performed through computer-assisted digital image analysis of backscattered electron micrographs captured at 500× magnification, adhering to the standard practice described in ASTM E2109-01(2022) (“Standard Test Methods for Determining Area Percentage Porosity in Thermal Sprayed Coatings”) with a minimum of ten fields of view analyzed per sample cross-section to ensure statistical reliability. The deposition efficiency and film stress were subsequently calculated using established methodologies grounded in the MAO literature, with all governing equations and parameter definitions summarized in Table . The deposition efficiency was determined based on Faraday’s law of electrolysis according to eq , where the actual coating mass calculated from measured thickness and porosity is normalized against the theoretical mass determined from the total charge passed. The total charge was calculated following eq as a function of the current density, sample area, and oxidation time. The theoretical mass was subsequently obtained using the Faraday equation accounting for the molar mass of TiO 2 and the electron transfer number ( n = 4 for Ti → TiO 2 ). , It is well documented that MAO processes suffer from significant charge loss due to oxygen gas evolution at the anode, with literature reports indicating that only ∼15% of the total charge density is utilized for oxide formation. Consequently, the charge utilization efficiency was incorporated using empirical correction factors for current density and voltage mode, consistent with reported values of 15–45% for constant voltage and 30–90% for constant current operation. , The residual film stress was estimated using a semiempirical approach according to eq , which integrates thickness-dependent baseline values with correction factors for phase composition (anatase/rutile ratio), porosity, and process parameters, supplemented by a thermal stress term accounting for the coefficient of thermal expansion mismatch between the coating and Ti6Al4V substrate. , This approach yields stress values within the literature-reported range of −1530 to +720 MPa for MAO TiO 2 coatings. , The substrate curvature was subsequently calculated via the Stoney equation ( eq ) to quantify the mechanical interaction between the film and substrate. All material constants employed in these calculations, including density, elastic modulus, and thermal expansion coefficients, are provided in Table , while the complete set of calculated and measured results for all experimental conditions is presented in Table 2. Material Constants. Parameter Symbol Value Unit Density (anatase/rutile) ρ anatase /ρ rutile 3.89/4.25 g/cm 3 Ti6Al4V elastic modulus E s 110 GPa Ti6Al4V Poisson’s ratio ν s 0.34  Coefficient of thermal expansion α s /α anatase /α rutile 8.6/5.8/7.8 10 –6 K –1 Open in a new tab 3. A Subset of Experimental Data from MAO Samples . No. J (A/dm 2 ) τ (μs) t (min) T (°C) η (%) σ (MPa) R p (Ω·cm 2 ) h (μm) φ (%) 1 7.5 300 3 10 60.40 –159.76 0.0490 5.775 14.054 2 10 350 7 15 17.11 –163.20 0.0467 5.683 22.995 3 12.5 400 9 20 14.60 –74.748 0.0616 7.500 20.006 4 5 300 3 10 51.31 –244.86. 0.0294 3.566 21.183 5 7.5 350 7 10 53.07 –161.68 0.0471 14.10 27.832 6 10 400 9 15 17.28 –342.79 0.0618 7.470 23.945 7 12.5 350 7 10 29.93 –141.72 0.0180 12.42 22.978 8 5 400 9 5 36.68 –76.864 0.1237 8.211 26.577 9 7.5 250 3 15 25.27 –41.620 0.0858 2.540 18.244 10 10 300 1 10 26.84 –354.46 0.0432 1.240 20.947 ... ... ... ... ... ... ... ... ... ... Open in a new tab a The key parameters in this study are defined as follows: J denotes current density, τ represents pulse width, t indicates time, T stands for temperature, η is defined as the deposition efficiency in percentage, σ is defined as the film stress in MPa, R p is defined as the polarization resistance in Ω·cm 2 , h corresponds to thickness, and φ signifies porosity. 3. Experimental Results and Analysis 3.1. MAO Coating Morphology Figure presents the surface SEM morphology of the MAO coating prepared on the samples. The coating exhibits numerous crater-like pores with diameters ranging from 2–10 μm, formed during Stage III and hereafter referred to as “micro-arc pores”. Additionally, a significant number of smaller pores (<2 μm in diameter) are observed, formed during Stage II and designated as “sparking pores” in this study. 2. Open in a new tab Surface morphologies of MAO coatings on the samples. The scale bars of SEM images for each sample are identical. Statistical analysis reveals significant variations in the number density of both sparking pores and microarc pores among the 30 samples, which directly correspond to distinct surface pore characteristics. Quantitative characterization was conducted: surface porosity was measured using Image-Pro Plus software, and the obtained data have been systematically compiled in Table . Cross-sectional morphologies of representative samples were examined to validate the structural variations associated with surface porosity differences. Figure presents cross-sectional SEM images of six representative specimens (Samples 9, 12, 13, 17, 24, and 26), which were subsequently used to validate the predictive performance of the developed model. The micrographs reveal distinct coating–substrate interfaces across the specimen set with substantial variations in coating thickness. Sample 9 exhibits a relatively compact coating with minimal interfacial irregularities, whereas Sample 26 demonstrates pronounced coating thickening, extensive internal porosity, and microcracks penetrating toward the substrate. These cross-sectional observations validate the quantitative porosity metrics in Table and provide direct structural evidence linking surface porosity to subsurface coating architecture. The heterogeneous coating growth behavior captured in these micrographs highlights the critical need for predictive models capable of correlating process parameters with coating porosity, thereby enabling controlled MAO coating synthesis. 3. Open in a new tab Cross-sectional SEM micrographs of MAO coatings on validation specimens 9, 12, 13, 17, 24, and 26. 3.2. Multimodal Diagnostics of Process–Property Relationships in MAO To systematically elucidate the influence mechanisms of MAO process parameters on coating properties, this study establishes a multilevel sensitivity analysis framework. First, a statistical distribution analysis is employed to characterize the distributional properties of each performance indicator. Subsequently, we combine machine learning with response surface methodology to reveal the nonlinear regulatory patterns of key parameters. Finally, interactions among multiple parameters are quantified through correlation matrix analysis, providing a quantitative basis for the synergistic optimization of coating performance. Analysis of the probability density distributions in Figure a–e reveals marked heterogeneity among the performance parameters: Deposition efficiency exhibits pronounced right-skewness (skewness = 3.333) and leptokurtosis (kurtosis = 12.660), indicating a data concentration in the low-value region with occasional extreme high-efficiency events. In contrast, film stress and porosity both exhibit left-skewed, platykurtic distributions (skewness = −0.817 and −0.232; kurtosis = −0.342 and −0.517, respectively), indicating concentration at lower absolute values with relatively uniform dispersion. The near-symmetric distribution of coating thickness (skewness = 0.403) and the moderately right-skewed nature of polarization resistance (skewness = 1.063, kurtosis = 0.470) further indicate concurrent optimization potential for these properties within specific parameter intervals. Notably, the polarization resistance displays a substantial coefficient of variation (55.6%), underscoring its significant sensitivity to process fluctuations. This statistical characterization establishes a quantitative foundation for subsequent parameter sensitivity analysis. 4. Open in a new tab (a–e) Hyperbolic normal distribution curves of membrane stress, porosity, thickness, deposition efficiency, and polarization resistance. (f, g, i, j, and k) 3D response surfaces showing the variation of deposition efficiency, polarization resistance, thickness, membrane stress, and porosity as a function of temperature and time. (h) Pearson correlation matrix of all studied parameters. Random Forest analysis identified process time and temperature as dominant factors across all five performance indicators. Three-dimensional response surfaces ( Figure f–j) reveal critical parameter–property relationships: (i) deposition efficiency peaks at 156.9% under low-temperature, short-duration conditions (5 °C, 1 min), driven by kinetically favorable nucleation; (ii) polarization resistance reaches a maximum of 0.151 Ω·cm 2 at low-temperature, short-duration conditions (5 °C, 1 min), coinciding with maximal deposition efficiency, suggesting a strong coupling between deposition kinetics and electrochemical barrier properties; (iii) film stress becomes increasingly compressive (−354.5 MPa) with prolonged processing at intermediate temperatures (7 min, 5 °C), governed by defect annihilation and phase transformation kinetics. Multiparameter correlation analysis elucidates key mechanistic couplings: the strong time–thickness ( r = 0.631) and time–porosity ( r = 0.544) correlations indicate cumulative structural development, while the negative temperature–efficiency correlation ( r = −0.667) reflects thermally activated dissolution competing with deposition. The pronounced time–temperature interaction for efficiency (−0.644) signifies a transition from kinetic-limited to diffusion-limited growth regimes. Notably, the polarization resistance exhibits weak correlations with both time ( r = 0.118) and temperature ( r = 0.098), suggesting its dependence on localized microstructural features rather than global process parameters. Integration of these insights identifies two primary process windows: (i) high-efficiency/high-barrier regime (1–7 min, 5–10 °C), optimizing deposition rate, porosity, and polarization resistance simultaneously; and (ii) low-stress regime (1–3 min, 5–15 °C), minimizing film stress while maintaining moderate barrier performance (polarization resistance ∼ 0.108 Ω·cm 2 ). The former represents a synergistic zone where rapid, kinetically controlled deposition yields dense, protective coatings, while the latter offers a compromise for stress-sensitive applications requiring dimensional stability. 4. Modeling and Prediction Analysis 4.1. Construction of the ComDeep-VAE Framework In machine learning applications with limited data sets, variational autoencoders (VAEs) have been employed to augment training data through statistically consistent synthetic sample generation, thereby improving model generalization. , Specifically, the encoder maps input data to a stochastic latent space via variational inference, enabling robust feature extraction, while the decoder reconstructs samples from latent representations, jointly optimizing reconstruction fidelity and distributional alignment. Compared with deterministic autoencoders, VAEs exhibit superior capabilities in probabilistic generative modeling, latent space regularization, and generalization to unseen data. To address the high-dimensional, small-sample challenges inherent to MAO process data, we propose ComDeep-VAE (Composite Deep Variational Autoencoder), a hierarchical architecture integrating multiscale feature extraction with physics-informed latent constraints. The proposed architecture is schematically illustrated in Figure . The mathematical formulation comprises three interconnected modules (see Table for notation): 5. Open in a new tab Schematic of the ComDeep-VAE architecture. 4. Nomenclature of the ComDeep-VAE Mathematical Framework. Symbol Parameter Symbol Parameter x Input Data Vector g i Decoder Layer Output θ enc Encoder Parameters ∂ L ∂ h Gradient W 1 , W 2 , W 5 , W σ , W i Weight Matrices I ( x ; z ) Mutual Information μ Mean Vector H ( x ) Entropy log σ 2 Log-Variance Vector D KL KL Divergence z Latent Code ε Perturbation Noise BN Batch Normalization λ L2 Regularization Weight α GELU Slope x̂ Decoded Output Open in a new tab (a) Feature Encoding and Structured Latent Space Module: This module collaboratively optimizes the information flow from input data to latent representations through adaptive compression and information-theoretic constraints, which are mathematically formulated in eqs and μ , log ⁡ σ 2 = f e n c ( x ; θ e n c ) = W σ ( G E L U ( B N ( W 2 ( G E L U ( B N ( W 1 x ) ) ) ) ) ) 8 I ( x ; z ) = H ( x ) − Ε [ log ⁡ p ( x | z ) ] + β D K L ( q ( z | x ) ∥ p ( z ) ) 9 (b) Training Dynamics Optimization Module: This module ensures stable and effective model training through balanced objective formulation and normalized optimization dynamics, as formalized in eqs and L K L ( β ) = − 1 2 × ∑ ( 1 + log ⁡ σ 2 − μ 2 − σ 2 ) , β = 0.01 10 ∂ L ∂ h = ∂ L ∂ h n ∏ i = 0 n − 1 ( ∂ h i + 1 ∂ h i ) × α i × B N ′ ( h i ) 11 (c) Decoding and Generalization Enhancement Module: This module enhances output reconstruction quality and model robustness through multiscale decoding and adversarial training, as defined in eqs and x̂ = W 5 · g 4 · g 3 ( z ) , g i = D r o p o u t ( G E L U ( B N ( W i ) ) ) 12 L t o t a l = Ε [ ∥ x − f d e c ( f e n c ( x ) + ε ) ∥ 2 ] + β D K L + λ ∥ θ ∥ 2 13 The proposed ComDeep-VAE architecture implements a parameter-efficient topology (37,100 trainable parameters) optimized for low-data regimes. As depicted in Figure , the parameter budget is asymmetrically allocated across three functional components: The encoder network (54% of parameters) compresses high-dimensional process inputs into a four-dimensional probabilistic latent manifold (compression ratio 4:1), leveraging batch normalization and GELU nonlinearities to stabilize variational inference. The latent distribution is regularized via β-weighted Kullback–Leibler divergence to enforce distributional alignment with the prior. The decoder (12.5% of parameters) employs a mirror-symmetric multilayer perceptron with dropout regularization ( p = 0.1), exploiting the information bottleneck principle to achieve high-fidelity reconstruction despite constrained capacity. An intermediate adaptive feature projection layer (33.4% of parameters) mediates a nonlinear transformation between the encoding and latent representations. This allocation strategy, coupled with a composite loss objective (reconstruction error + L2 parameter regularization, λ = 0.001), ensures robust latent representation learning under stringent data limitations. 6. Open in a new tab Intra-architectural parameter allocation of the ComDeep-VAE framework. ComDeep-VAE’s internal parameters were optimized via a two-stage hierarchical protocol. Stage one employed stochastic exploration (random search) to identify optimal architectural and regularization parameters, excluding activation functions from the search space ( Table ). Stage two selected the activation function by evaluating convergence dynamics and predictive metrics across eight candidate nonlinearities, conditional on stage-one optima. 5. Architectural Parameters of the ComDeep-VAE. Hyperparameter Best parameters Hyperparameter Best parameters Encoder_dims [192, 96] Weight_decay 1 × 10 –6 Latent_dim 64 Batch_size 32 Decoder_dims [32, 64] Epochs 300 Dropout 0.1 Beta 0.01 Open in a new tab Quantitative benchmarking establishes GELU as the optimal nonlinearity, yielding a minimal reconstruction error of 0.0738substantially outperforming Sigmoid (0.0882), LeakyReLU (0.1014), and ELU (0.1096) with relative improvements ranging from 16.4–67.8% ( Table ). Conventional saturating nonlinearities exhibit manifest limitationsspecifically gradient vanishing and optimization instabilityundermining their suitability for deep variational architectures. Mish exhibits pronounced overfitting, evidenced by its elevated reconstruction error (0.1507), attributable to excessive representational capacity relative to the constrained data set scale. Collectively, these findings corroborate GELU’s superior equilibrium between expressive power and optimization stability. 6. Performance Comparison of Different Activation Functions. Activation Performance Activation Performance GELU 0.0738 ELU 0.1096 Sigmoid 0.0882 ReLU 0.1106 Swish 0.0998 Tanh 0.1238 LeakyReLU 0.1014 Mish 0.1507 Open in a new tab Leveraging optimally configured ComDeep-VAE parameters, we synthetically expanded the training corpus 15-fold via latent space sampling. Downstream predictive modelstrained independently on raw versus augmented data setswere rigorously evaluated on held-out test data to quantify augmentation efficacy. Figure quantifies the augmentation-induced performance gains. Panels (a)–(b) contrast Mean Absolute Error (MAE) distributions for thickness and porosity predictions across model architectures (decision trees, multilayer perceptrons, gradient boosting), demonstrating systematically reduced prediction errors under augmented training regimes. Panel (c) visualizes error reduction magnitudes via a bivariate scatter analysis, revealing consistent performance enhancements across all model-target combinations. Panel (d) aggregates these findings, documenting a mean error reduction of 66.5%comprising a 72.3% improvement in porosity prediction and 60.8% in thickness prediction. These findings corroborate that ComDeep-VAE effectively alleviates overfitting in low-data regimes, enhances latent feature discriminability, and establishes a statistically robust augmentation protocol for high-dimensional process optimization in surface engineering. 7. Open in a new tab (a) Comparative analysis of error metrics for thickness predictions across models trained on distinct data sets. (b) Comparative analysis of error metrics for porosity predictions across models trained on distinct data sets. (c) Scatter plot comparison of error reduction across evaluation metrics. (d) Overall comparison of aggregate error reduction performance. Notwithstanding these empirical validations, explicit delineation of methodological boundaries remains essential for governing model applicability. To preempt concerns regarding physical diversity constraints, we emphasize that ComDeep-VAE operates strictly within statistical interpolation boundaries, eschewing unconstrained physical extrapolation. Specifically, the variational posterior learns to approximate the empirical joint probability distribution of the original high-dimensional process data; , synthetic samples thus constitute statistically plausible interpolations confined to the observed distributional support, distinct from unvalidated hypothetical physical regimes. Consistent with established theoretical frameworks, , generative augmentation strategies necessitate strict confinement of reliable predictions to the training data envelope. Concerning external validity, an independent test set evaluation substantiates statistical generalizability to in-distribution unseen data, establishing internal methodological validity. Prospective transferability to dissimilar material systems or alternative processing regimes theoretically depends on the VAE-learned latent space’s capacity to encode transferable physical representations abstracted from material-specific instantiations. We explicitly acknowledge that rigorous cross-system validation constitutes an imperative avenue for future inquiry. Collectively, these considerations position the present contribution as a rigorously internally validated computational framework equipped with methodological foundations for prospective external extension rather than a domain-agnostic universal predictor. 4.2. Construction of the Powell-Voting Model Voting ensembles have demonstrated substantial efficacy in predictive modeling across heterogeneous domains, − attributable to their capacity for aggregating heterogeneous base learners and mitigating generalization error through variance reduction. Nevertheless, ensemble efficacy hinges critically on the optimal weight allocation among constituent base learners. To address this optimization challenge, we employ Powell’s conjugate direction method for determining globally optimal weight configurations across the ensemble constituents. Model-specific extraction protocols elucidate internal architectures: decision trees via top-down path enumeration, multilayer perceptrons via layerwise weight-bias decomposition, and meta-ensembles via aggregated base-learner statistics. Comprehensive architectural specifications are collated in Table . 7. Architectural Parameters of the Machine Learning Models. Gradient Boosting MLP Decision Tree N_estimators = 200 Total_parameters = 8961 Leaves = 342 Learning_rate = 0.1 Layers = 3 Depth = 18 Max_depth = 3 Architecture = [128, 64, 1] Node_count = 683 Avg_tree_depth = 3 Activation_function = ReLU Min_samples_leaf = 1 Min_samples_split = 2 Solver = Adam Min_samples_split = 2 Open in a new tab Mathematical formulations governing the three base learners and the integrated ensemble predictor are systematically derived below. (a) Gradient Boosting: The Gradient Boosting model adopted in this work is conFigd with the following key hyperparameters: number of iterations M = 200, and learning rate η = 0.1. The model is constructed via a forward stagewise additive strategy, mathematically defined as follows: f 0 ( x ) = a i g min γ ⁡ ∑ i = 1 n L ( y i , γ ) 14 f m ( x ) = f m − 1 ( x ) + η · h m ( x ) 15 f G r a d i e n t B o o s t i n g ( x ) = f 0 ( x ) + η ∑ m = 1 200 h m ( x ) 16 Here, f 0 denotes the initial constant model, and h m ( x )­represents the weak learner (a decision tree) fitted at the m -th iteration. (b) Multilayer Perceptron (MLP): The MLP designed in this study employs a fully connected architecture with a hidden layer configuration of (128, 64), utilizing the ReLU activation function. The parameter dimensions of the network layers are specifically conFigd as follows: weight matrices W (1) ∈ R 128×4 , W (2) ∈ R 64×128 , W (3) ∈ R 1×64 ; bias vectors b (1) ∈ R 128 , b (2) ∈ R 64 , b (3) ∈ R 1 . The forward propagation process is formally defined as z ( 1 ) = W ( 1 ) x + b ( 1 ) , a ( 1 ) = Re L U ( z ( 1 ) ) 17 z ( 2 ) = W ( 2 ) a ( 1 ) + b ( 2 ) , a ( 2 ) = Re L U ( z ( 2 ) ) 18 f M L P ( x ) = W ( 3 ) a ( 2 ) + b ( 3 ) 19 (c) Decision Tree: The Decision Tree model constructed in this work, after pruning and optimization, yields a final structure parametrized by a total of 683 nodes, of which 342 are leaf nodes. The model partitions the feature space into 342 ( M = 342) mutually exclusive regions. Its prediction function is expressed as f D e c i s i o n T r e e ( x ) = ∑ m = 1 342 c m · Ι Ι ( x ∈ R m ) 20 Where R m denotes the m -th region, c m is the representative value of the target variable for samples within that region, and Π(·) is the indicator function. (d) Powell-Voting: The final ensemble prediction f emsemble of the proposed Powell-Voting model is formulated as a weighted average of the predictions from the three base learners. The weight vector w = [ w D e c i s i o n T r e e , w Grad i e n t B o o s t i n g , w M L P ] T , satisfying the constraint Σ w i = 1. Consequently, the final predictive output of the ensemble is formally given by f e n s e m b l e ( x ) = − 0.1122 · f D e c i s i o n T r e e ( x ) + 0.585 · f M L P ( x ) + 0.5272 · f G r a d i e n t B o o s t i n g ( x ) 21 We evaluate model predictive performance using the Coefficient of Determination ( R 2 ), defined as R 2 = 1 − ∑ i = 1 n ( y i − ŷ i ) 2 ∑ i = 1 n ( y i − y̅ ) 2 22 M A E = 1 n ∑ i = 1 n | y i − ŷ i | 23 In this formulation: y i represents the ground-truth value of the i -th sample in the test set, ŷ i denotes the predicted value output by the model for the corresponding sample, y̅ is the mean of all ground-truth values in the test set. Figure and Table benchmark the generalization performance of four predictive architectures for bimodal coating characterization (porosity and thickness). A pronounced performance hierarchy emerges, rooted in architectural and mechanistic disparities. 8. Open in a new tab Comparative visualization of predictive performance for coating porosity and thickness across heterogeneous machine learning models: (a) Powell-Voting ensemble predictions for porosity; (b) Powell-Voting ensemble predictions for thickness; (c) Multilayer Perceptron (MLP) predictions for porosity; (d) MLP predictions for thickness; (e) Decision Tree (DT) predictions for porosity; (f) DT predictions for thickness; (g) Gradient Boosting (GB) predictions for porosity; (h) GB predictions for thickness. Corresponding coefficient of determination ( R 2 ) metrics for training and test sets are annotated within each subplot. 8. Model Performance Comparison for Thickness and Porosity Prediction. Thickness Porosity Model Train ( R 2 ) Test ( R 2 ) Mean Train (MAE) Test (MAE) Mean MLP 0.969 0.861 0.915 0.959 0.784 0.872 DT 1.000 0.643 0.822 1.000 0.394 0.697 GB 0.997 0.883 0.940 0.991 0.795 0.893 Ours 0.987 0.908 0.948 0.977 0.826 0.902 Open in a new tab The Powell-optimized voting ensemble ( Figure a–b) exhibits superior generalization robustness, attaining peak test R 2 values (thickness: 0.908; porosity: 0.826) and optimal mean metrics (0.948 and 0.902, respectively). The minimal train–test R 2 discrepancy indicates an optimal complexity–generalization equilibrium. In marked contrast, the decision tree ( Figure e–f) exhibits pronounced overfitting: perfect training fidelity ( R 2 = 1.000) but substantially degraded test performance (thickness R 2 = 0.643; porosity R 2 = 0.394), yielding minimal generalization. Gradient boosting ( Figure g–h) and the multilayer perceptron ( Figure c–d) demonstrate intermediate capabilities, with the former consistently being suboptimal relative to the Powell-optimized ensemble. The Powell-ensemble’s robustness stems from structural meta-learning: integrating heterogeneous structural priorsdecision tree paths, neural weight patterns, and ensemble statisticsinto a unified meta-representation. This complementary synthesis mitigates constituent deficiencies: decision tree variance, multilayer perceptron local optima susceptibility, and gradient boosting error accumulation, thereby achieving superior predictive stability and generalization. 4.3. Inverse Materials Design This study establishes a closed-loop inverse design framework for predictive control of MAO processing, enabling simultaneous optimization of coating thickness and architected porosity-two mutually constrained performance attributesthrough physics-informed parameter space exploration. The algorithmic workflow, encompassing forward prediction and inverse optimization modules, is schematically depicted in Figure . 9. Open in a new tab Schematic diagram of the inverse design framework/structure. The inverse design is cast as a constrained multiobjective optimization problem solved via NSGA-II (Nondominated Sorting Genetic Algorithm II), with MAO process parameters (current density, electrolyte temperature, pulse width, treatment duration) serving as decision variables and coating attributes as competing objectives. Objective functions quantifying coating thickness and porosity, together with parameter bounds defining the feasible search space for the four decision variables, are elaborated below; nomenclature is presented in Table . 9. Architectural Parameters of the NSGA-II Optimization Framework. Symbol Parameter Symbol Parameter P Population solution space M Objective dimension n p Domination count f m ( i ) Objective function value S p Dominated set β Expansion factor F k k -th Pareto front η c Distribution index ≺ Pareto dominance relation p Parent individual d i Crowding distance c l , c u Decision space boundaries Open in a new tab (a) Fast Nondominated Sorting and Elite Selection: F 1 = { p ∈ P | n p = 0 } 24 F k = { q ∈ ∪ p ∈ F k − 1 S p | n q − | { r ∈ F k − 1 | r ≺ q } | = 0 } 25 p ≺ q ⇔ ∀ i : f i ( p ) ≤ f i ( q ) ∧ ∃ j : f j ( p ) < f j ( q ) 26 (b) Crowding Distance and Diversity Preservation: d i = ∑ m = 1 M f m ( i + 1 ) − f m ( i − 1 ) f m max − f m min 27 (c) Simulated Binary Crossover and Adaptive Search: β = ( 1 + 2 η c + 1 · min ( p − c l , c u − p ) ) 1 / η c + 1 , c 1 , 2 = 0.5 [ ( 1 ± β ) p 1 + ( 1 ∓ β ) p 2 ] 28 To experimentally validate the practical efficacy of the proposed inverse design framework, a systematic experimental campaign was conducted targeting predetermined coating property benchmarks. The optimization objectives were defined as target coating thickness (8.0 μm) and porosity (21%), with the multiobjective search constrained within bounded ranges for four critical process parameters: current density (5–25 A/dm 2 ), pulse duration (300–450 μs), oxidation duration (1–15 min), and electrolyte temperature (5–25 °C). The NSGA-II-based inverse design framework exhibited robust convergence characteristics for multiobjective optimization of MAO coatings, as substantiated by comprehensive convergence diagnostics ( Figure ). The composite objective function stabilized beyond 500 generation cycles ( Figure a), with independent convergence of thickness and porosity deviations to <2 μm and <0.5%, respectively, within 750–1000 generations ( Figure b–c). Design space sampling ( Figure d) and PCA-projected optimization trajectories ( Figure h; cumulative variance explained: PC1 33.0%, PC2 27.6%) revealed convergence toward an optimal parameter subspace (current density: 15–20 A/dm 2 , pulse duration: 380–420 μs). Pareto frontier analysis ( Figure e) quantified the intrinsic thickness–porosity trade-off, identifying a Pareto-optimal solution set with optimal trade-off performance characterized by absolute deviations of 1.5 μm (thickness) and 0.2% (porosity) from target values. Response surface analysis ( Figure f–g) elucidated the antagonistic coupling between the current density and pulse duration in governing coating properties. Variable importance analysis of the NSGA-II-generated Pareto-optimal set ( Figure i) revealed electrolyte temperature and pulse duration as the dominant determinants of the thickness–porosity trade-off, with normalized importance scores of 0.493 and 0.329, respectively (collectively 82.2%). The convergence trajectory ( Figure j) demonstrated generational stability, supporting solution reliability. 10. Open in a new tab (a) Objective function convergence. (b) Thickness convergence with the CI. (c) Porosity convergence with CI. (d) Design space sampling distribution. (e) Pareto frontier of thickness vs porosity error. (f) Thickness response surface. (g) Porosity response surface. (h) PCA-projected optimization trajectory. (i) Variable importance correlation. (j) Error evolution over evaluations. The physical origins underlying these machine-learning correlations warrant mechanistic interpretation to contextualize data-driven insights within established MAO discharge physics. Empirical parametric analysis ( Figure ) examines these relationships. Pulse duration governed energy delivery dynamics: intermediate durations (320–410 μs, Category D) yielded maximal coating thickness ( Figure a), attributable to balanced energy input and thermal dissipation, whereas prolonged durations (>410 μs, Category E) exacerbated pore coalescence, plausibly via localized thermal accumulation ( Figure b). Electrolyte temperature exerted dual effects: elevated temperatures enhanced ionic mobility and interfacial reaction kinetics yet concurrently intensified discharge thermal energy, promoting electrolyte vaporization and gas evolution, thereby increasing coating porosity. This trade-off was manifest in the divergent trends of Figure d–e, wherein elevated temperature conditions produced thicker yet more porous coatings. Three-dimensional response surfaces ( Figure c, f) mapped the interactive parameter space, revealing an optimal processing window at moderate temperatures and intermediate pulse durations, wherein rapid solidification kinetics suppressed defect formation and refined the coating microstructure. These observations confirm that the NSGA-II framework captures physically grounded process–structure relationships inherent to MAO discharge behavior, extending beyond mere statistical correlations. 11. Open in a new tab Effect of pulse width on coating thickness (a) and porosity (b); temperature dependence of thickness (d) and porosity (e); 3D response surfaces of thickness (c) and porosity (f) as functions of temperature and pulse width. 4.4. Experimental Validation and Application To experimentally validate the predictive fidelity of the inverse design framework for MAO coating fabrication, two sets of target-driven validation experiments were conducted under rigorously controlled process conditions. The primary objective entailed the experimental realization of Pareto-optimal process parameter setsidentified via multiobjective optimization for prescribed coating performance metricsthrough direct implementation in MAO processing. This validation strategy systematically quantified the predictive accuracy and robustness of the inverse design framework in realizing target coating architectures with quantifiable microstructural and functional attributes. 4.4.1. Targeted Performance and Inverse Design Two distinct coating performance targets were established to rigorously evaluate the inverse design strategy. Target I aimed for a moderately thick, highly porous coating (7.5 μm, 32% porosity), while Target II specified a denser, thicker coating (13.5 μm, 17% porosity), thereby testing the framework’s ability to navigate contrasting property landscapes. To achieve these targets, our validated process-performance surrogate model was coupled with a multiobjective optimization algorithm. The algorithm performed a global search within defined parameter boundscurrent density [5, 25] A/dm 2 , pulse width [200, 450] μs, treatment time [1, 15] min, and electrolyte temperature [5, 25] °Cminimizing the composite error between model predictions and the fixed targets. This inverse solving process yielded two optimal parameter combinations, designated as Sets I and II, with the optimized values reported in Table . 10. Pareto-Optimal Process Parameters and Inverse-Design Validation. Category Parameter Set I (Target I) Set II (Target II) Unit Targets Thickness target 7.5 13.5 μm Porosity target 32 17 % Process Current density 15.12 13.70 A/dm 2 Pulse width 202.8 202.4 μs Time 14.99 7.907 min Temperature 15.80 5.006 °C Predictions Thickness 8.06 13.13 μm Porosity 28.79 18.66 % Experiments Thickness 8.03 ± 0.57 12.69 ± 0.67 μm Porosity 30.91 ± 0.27 19.17 ± 0.31 % Open in a new tab 4.4.2. Experimental Setup and Process The MAO experiments were conducted in a dedicated reactor featuring a bipolar pulsed power supply and an electrolyte thermostatic circulation system. The electrolyte composition was maintained consistent with that employed for the construction of the surrogate model database. The experimental protocols were executed in strict accordance with the parametric configurations specified by Optimized Parameter Set I and Optimized Parameter Set II. For each parameter set, a minimum of seven replicate experiments ( n ≥ 7) were conducted to rigorously evaluate process stability and ensure statistical reliability of the data. 4.4.3. Analysis of Control Precision via Inverse Design The inverse design framework exhibits robust predictive fidelity, manifested by the quantitative concordance between computationally optimized parameters and experimentally validated metrics ( Table ). For Target I, the predicted coating thickness (8.06 μm) deviates merely +0.4% from the experimental mean (8.03 ± 0.57 μm), well within one standard deviation. The predicted porosity (28.79%) agrees with the measured value (30.91 ± 0.27%) within 6.9% relative error, consistent with the framework’s predictive tolerance. This high-porosity architecture is corroborated by cross-sectional SEM imaging ( Figure a), confirming an 8.0 μm-thick coating exhibiting surface roughness and interconnected pore networks. 12. Open in a new tab Cross-sectional SEM micrographs of the fabricated MAO coatings. (a) Target I, exhibiting a porous morphology. (b) Target II, showing a denser and thicker microstructure. For Target II, the framework accurately prescribed process parameters, yielding a thicker, denser coating architecture. The predicted thickness (13.13 μm) exhibits a +3.5% deviation from the measured value (12.69 ± 0.67 μm), marginally exceeding the experimental uncertainty bounds. Although the model predicts a reduction in porosity (18.66% versus 28.79% for Target I), the absolute predicted value deviates by merely −2.7% from the experimentally achieved porosity of 19.17 ± 0.31%. These predictions are microstructurally corroborated by cross-sectional SEM imaging ( Figure b), revealing a substantially denser, more uniform morphology throughout the ∼13 μm coating thickness. Aggregated across both targets, the predictions yield mean absolute percentage errors of 6.0% for thickness and 5.6% for porosity. These error magnitudes are comparable to the characteristic 5–15% process variability inherent to MAO, , which arises from stochastic microdischarge events that introduce localized microstructural inhomogeneities ( Figure ). The consistency between computational predictions, experimental measurements, and microstructural characterization supports the utility of this inverse design framework for microarc oxidation coatings, enabling a rational strategy to achieve target thickness–porosity combinations. 5. Conclusion The inherent stochasticity of plasma discharges during MAO induces substantial variability in coating properties, posing critical challenges for industrial process control and quality assurance. To address these challenges, we develop a hybrid inverse design framework integrating Powell multiobjective optimization with ComDeep-VAE data augmentation, enabling coupled prediction of coating thickness and surface porosity. Based on these findings, we conclude: (1) Statistical heterogeneity analysis reveals right-skewed, leptokurtic deposition efficiency contrasting with left-skewed, platykurtic film stress and porosity, while polarization resistance demonstrates substantial sensitivity to process fluctuations (CV = 55.6%) with moderate right-skewness (skewness = 1.063). Random Forest identifies time and temperature as dominant factors, with 3D response surfaces delineating two critical process windows: a high-efficiency/high-barrier regime (1–7 min, 5–10 °C) simultaneously maximizing deposition efficiency (50.1%) and polarization resistance (0.151 Ω·cm 2 ), and a low-stress/structural-integrity regime (1–3 min, 5–15 °C) minimizing film stress (−64.1 MPa) while maintaining substantial barrier performance (0.108 Ω·cm 2 ) for stress-sensitive applications. (2) The ComDeep-VAE framework establishes a variational inference-based augmentation protocol tailored for small-sample, high-dimensional data sets in surface engineering, reducing predictive errors by 66.5% relative to baseline models via uncertainty-bounded interpolations within the experimentally characterized parameter space. The methodology incorporates explicitly defined operational boundaries, providing a benchmark for prospective validation across alternative substrate alloys. (3) The hybrid prediction model achieves coefficients of determination ( R 2 ) of 0.948 for thickness and 0.902 for porosity, substantially exceeding the performance of conventional regression algorithms (e.g., Multilayer Perceptron, Decision Tree). (4) This study establishes an experimentally validated inverse design framework for MAO coatings, integrating multiobjective optimization with surrogate modeling. Numerical convergence analysis for target specifications (8.0 μm thickness, 21% porosity) achieves absolute discrepancies below 2 μm and relative errors below 0.5% within 750–1000 function evaluations, identifying optimal processing windows of 15–20 A/dm 2 current density and 380–420 μs pulse duration. Experimental validation across contrasting targets (7.5 μm/32% and 13.5 μm/17% porosity) confirms practical reliability, with mean absolute percentage errors of 6.0% and 5.6%falling within the intrinsic MAO process variability of 5–15%. The concordance between computational convergence metrics and experimental validation substantiates that the framework effectively resolves property trade-offs inherent to stochastic discharge dynamics, thereby bridging data-driven optimization with mechanism-guided engineering for intelligent coating design. 6. Outlook While the present framework establishes a validated inverse design methodology for MAO coating fabrication, its current implementation focuses on static electrical parameter optimization under standardized substrate conditions. The modular architecture of our hybrid platformcomprising ComDeep-VAE augmentation and multiobjective surrogate modelingprovides explicit extension pathways to address the critical manufacturing metrics highlighted: (1) Mechanical integrity characterization. The current optimization targets (thickness, porosity, polarization resistance) will be expanded through multitask Gaussian process regression to incorporate quantitative mechanical responses. Systematic nanoindentation (hardness, modulus) and instrumented scratch testing (adhesion strength, fracture toughness) will establish structure–property correlations across the parametrized process space. These data will train augmented surrogate models enabling Pareto optimization for load-bearing applications, with adhesion strength serving as a hard constraint rather than an objective function to ensure interfacial reliability. (2) Substrate topography engineering. Standardized surface preparation (Ra < 0.4 μm) in this study isolated electrical effects. Future work will treat substrate roughness (Ra, Rz, Rsk) as a controllable preprocess variable, employing physics-informed neural networks to model roughness-dependent discharge initiation kinetics and coating nucleation density. This integration will identify optimal texture regimes that enhance mechanical interlocking without compromising dielectric breakdown uniformity. (3) Temporal efficiency via dynamic optimization. While static process windows (1–7 min) were identified, coating formation time reduction requires transition from batchwise parameter selection to trajectory optimization. We are developing reinforcement learning (RL) controllers utilizing real-time optical emission spectroscopy (OES) feedbackspecifically monitoring Mg I 285.2 nm and O I 777.4 nm emission intensitiesto dynamically adjust pulse duration and current density during deposition. This closed-loop approach targets a 30–40% reduction in processing time while maintaining thickness/porosity specifications through early termination criteria based on predictive convergence. (4) Manufacturing system analytics. Industrial scalability necessitates quantitative Overall Equipment Effectiveness (OEE) modeling beyond laboratory optimization. We will integrate availability losses (electrolyte maintenance, electrode degradation), performance efficiency (actual vs theoretical deposition rate), and quality rates (first-pass yield) into the digital twin framework. This requires the acquisition of industrial MAO line operational data to parametrize stochastic failure models, enabling predictive maintenance scheduling and throughput optimization. These extensions leverage the uncertainty quantification capabilities inherent to our ComDeep-VAE architecture, positioning the framework as a generalizable platform for the autonomous manufacturing of functional ceramic coatings. The progression from static inverse design to dynamic, self-correcting process control represents the critical next step toward industrial deployment. Acknowledgments This study was supported by the following funds: (1) Chongqing Vocational Institute of Engineering (Grant No. 2024KJB0102: “Study on AI-Driven Innovative Device for Microarc Oxidation”), Dajun Zhai; (2) Science and Technology Research Project of Chongqing Municipal Education Commission (Grant No. KJQN202303417), Guoping Lu. Conceptualization, D.Z.; Data curation, H.L.; Formal analysis, D.Z. and S.O.; Investigation, D.Z.; Methodology, D.Z. and S.O.; Project administration, X.L.; Resources, A.L.; Software, S.O. and G.L.; Validation, G.L.; Writingoriginal draft, D.Z. and S.O.; Writingreview and editing, A.L. and X.L. All authors will be updated at each stage of manuscript processing, including submission, revision, and revision reminder, via e-mails from our system or the assigned Assistant Editor. The authors declare no competing financial interest. References Pan M., Ye J., Sun C., Zhang S., Ling M., Liu J., Wang Y., Sun L.. 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