Deep learning for high-entropy alloys: Phase prediction and feature interpretability through hyperparameter optimization

Abstract

High-entropy alloys (HEAs), characterized by multi-principal elements and high configurational entropy, exhibit exceptional mechanical, thermal, and corrosion-resistant properties, making them promising candidates for aerospace, energy, and biomedical applications. However, predicting their phase formation—single-phase solid solutions, multi-phase solid solutions, or intermetallic compounds—remains challenging due to the interplay of thermodynamic and atomic-scale parameters. This study leverages deep neural networks (DNNs) to predict HEA phases using six compositional features: entropy of mixing (ΔS_mix), enthalpy of mixing (ΔH_mix), atomic size difference ( $\delta$ ), thermodynamic stability ( $\mathrm{\Omega }$ ) parameter, valence electron concentration (VEC), and electronegativity difference (Δχ). The optimized DNN architecture (three hidden layers with 128–128–64 neurons) achieved 78.6% accuracy and 78.5% F1-score, outperforming shallow models. SHapley Additive explanation (SHAP) analysis revealed ΔH_mix and Δχ as dominant features, where exothermic mixing (negative ΔH_mix) and moderate Δχ favored single-phase solid solution and Multiphase solid solution, while low ΔS_mix and high $\delta$ promoted intermetallic phase formation. Thermodynamic stability ( $\mathrm{\Omega }$ ) and VEC further distinguished phase regimes, with $\mathrm{\Omega }$ ≥ 1.1 and VEC 8–10 favoring FCC/BCC solid solutions. Hyperparameter tuning highlighted the critical role of learning rate (optimal 0.001–0.0001) and model depth, where deeper networks (3 layers) enhanced performance but risked overfitting with limited data. These insights enable targeted alloy development, balancing entropy-driven stabilization and atomic-scale effects, and provide a framework for integrating computational tools in materials discovery.