Physics-informed machine learning framework integrating solid solution strengthening theory for accelerated hardness prediction in high-entropy alloys

Abstract

High-entropy alloys (HEAs) exhibit exceptional stability in extreme environments, yet their expansive design space presents a “curse of dimensionality” for traditional discovery methods. While machine learning (ML) offers a data-driven paradigm for material screening, the scarcity of experimental data often results in overfitting and limited physical interpretability. To address these challenges, this study proposes a hybrid physics-informed machine learning (Hybrid PIML) framework for accelerated hardness prediction. By integrating classical solid solution strengthening theory with a residual learning artificial neural network (ANN), the model explicitly embeds the physical coupling of shear modulus and lattice distortion (G·δr2/3) as prior knowledge. This approach ensures predictions adhere to metallurgical principles while significantly outperforming benchmark algorithms, achieving a coefficient of determination (R2) of 0.976 and reducing the root mean square error (RMSE) by approximately 43%. SHapley Additive exPlanations (SHAP) analysis confirms that physics-enhanced features dominate the decision-making process, validating the model’s internalization of strengthening mechanisms. Furthermore, the research elucidates a phase-dependent non-linear correlation between hardness and yield strength, correcting the failure of the classical Tabor formula in work-hardening face-centered cubic (FCC) alloys. Finally, a high-throughput virtual screening funnel based on this framework successfully identified optimized non-equiatomic candidates within the refractory Co-Cr-Ti-Mo-W system. This work establishes a precise, physically consistent pathway for inverse material design under data-constrained conditions.