Physics-Informed Explainable Hybrid Machine Learning and True Pareto-Optimal Inverse Design for Strength–Conductivity Optimization of High-Performance Cu–Cr–X Copper Alloys

Abstract

High-performance Cu–Cr–X copper alloys face an inherent trade-off between mechanical strength and electrical conductivity. This study develops a physics-informed, interpretable machine-learning framework for their optimization and inverse design. A literature-derived dataset of 3017 experimental records was compiled, with 2302 records retained after preprocessing and reliability filtering. Metallurgically motivated descriptors, including Aging Severity, Cold Work Index, Cr–Aging interaction, Zener-pinning and Hall–Petch proxies, and source reliability, were incorporated. Random Forest, Extra Trees, XGBoost, and CatBoost were evaluated using a leakage-free 10-fold out-of-fold stacking framework. The stacking model achieved R 2 = 0.895, MAE = 17.3, and RMSE = 48.7, compared with R 2 values of 0.781, 0.802, 0.837, and 0.857, respectively, for the four base learners. SHAP analysis highlighted Cu, Cr, source reliability, aging-related variables, and precipitation-related descriptors as important predictors. Pareto-based inverse screening identified candidates with predicted Strength Index values exceeding 520 and approaching 580, with conductivity reaching approximately 95 %IACS. The framework provides a data-driven route for narrowing the Cu–Cr–X design space, while the predicted candidates require experimental validation.