A physics-informed active learning framework for the inverse design of vacuum coatings

The multi-objective optimization of Physical Vapor Deposition (PVD), as a predominant modality of vacuum coating, is indispensable for surface engineering, yet its optimization is bottlenecked by the conflict between experimental efficiency and data scale. Traditional trial-and-error and purely data-driven machine learning suffer from low efficiency and severe overfitting under typical "small-sample" constraints, often recommending non-physical or unsafe parameters. To address these challenges, this study proposes a closed-loop Physics-Informed Active Learning (PIAL) framework integrating three core modules: physics-enhanced feature engineering, a Physics-Regularized Heteroscedastic Neural Network (PR-HNN), and a risk-aware dual-point batch acquisition strategy. By embedding fundamental sputtering kinetics into the PR-HNN via continuous partial derivative constraints, the model is softly regularized toward physically plausible monotonic and saturating trends within the investigated CoCrFeNiTi magnetron sputtering process window, while effectively quantifying non-stationary experimental noise. Experimental results demonstrate that physics-based regularization reduces the generalization error of the PR-HNN by 41% compared to purely data-driven baselines, effectively eliminating non-physical fluctuations in sparse data regions. Guided by the risk-aware acquisition function, the framework progressively expanded the initial Pareto front through three closed-loop iterations. The PIAL-optimized coatings achieved a peak hardness of approximately 13.4 GPa and a minimum wear depth of 0.25 μm, while maintaining robust corrosion resistance. This methodology establishes a highly efficient, physically interpretable, and safe paradigm for AI-driven surface engineering and high-performance coating development.