Machine-Learning-Driven Prediction of Formation Energy and Compositional Design for IrRuRhMoW High-Entropy Alloys

Formation energy is a critical parameter for evaluating the thermodynamic stability of high-entropy alloys (HEAs), offering essential guidance for alloy composition design and performance optimization. In this study, we present an efficient prediction framework that integrates machine learning (ML) with density functional theory (DFT) to investigate the formation energy of IrRuRhMoW HEAs. Using the special quasi-random structure (SQS) method, we constructed face-centered cubic supercell models containing 108 atoms and generated a data set of formation energies across various atomic ratios. A descriptor system comprising 14 features across three categories, compositional, statistical, and thermodynamic, was developed. Four ML methods, ridge regression, random forest, extreme gradient boosting, and artificial neural networks, were systematically evaluated for their predictive performance. Among them, the ridge regression model demonstrated the best performance in terms of prediction accuracy, stability, and generalization. Feature importance analysis revealed that mixing enthalpy, mean square deviation of atomic radius, average relative atomic mass, and the atomic fractions of Ru and Ir elements play dominant roles in predicting formation energy. Through stepwise forward feature selection, we constructed a simplified model with only 7 key features, achieving high prediction precision with a mean absolute error (MAE) of 0.00562 ± 0.00007 eV/atom on the independent test set. Prediction across the full compositional space revealed key trends: increasing the proportions of Mo and W favors lowering the formation energy, while higher proportions of Ru and Rh increase it. These findings offer theoretical insights for optimizing the composition of IrRuRhMoW HEAs and demonstrate the potential of ML approaches for efficiently predicting the thermodynamic stability of alloys.