Accelerating Bulk Modulus Design of High-Entropy Alloys Through Explainable Machine Learning and SHAP-Driven Insights

Abstract

This work presents an interpretable machine learning (ML) system that uses composition- and physics-based descriptors to predict the bulk moduli of high-entropy alloys (HEAs). Extra Trees, Random Forest, Gradient Boosting, AdaBoost, and LightGBM are five ensemble ML algorithms that were systematically shaped and refined by hyperparameter fine-tuning. With a test R2 of about 0.852 and an RMSE and MAE of about 5.49 GPa and 1.5 GPa, respectively, Extra Tree outperformed the other optimized models, indicating good generalization capacity for untested HEA compositions. The computational efficiency results showed that LightGBM had the fastest prediction speed (~4.24 ms), whereas Extra Trees had the shortest training time (~17.3 s). The majority of the optimized models had statistically equal prediction performance (p > 0.05), according to statistical validation using paired t-test analysis, even though residual error distributions for the Extra Tree model established consistent and unbiased predictions. To enhance the interpretability of the model, SHAP-based explainable analysis was performed, which included SHAP importance, dependence, and waterfall plots. The SHAP results revealed that the primary determinants impacting bulk modulus behavior in HEAs were Zr content, mean electronegativity, Al content, bond strength, and melting-temperature-related parameters. The proposed framework enables the rapid identification and design of next-generation HEAs by permitting precise and computationally efficient bulk modulus prediction, as well as physically significant insights into descriptor–property connections.