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

The multiobjective 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 (ML) suffer from low efficiency and severe overfitting under typical “small-sample” constraints, often recommending nonphysical 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 nonstationary 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 nonphysical 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 artificial intelligence (AI)-driven surface engineering and high-performance coating development.