Machine learning-enabled prediction and optimization of hardness for Nb-Ti-V-Zr refractory high entropy alloy

Abstract

High entropy alloy (HEA) design strategies have been limited to experimental trial-and-error approaches. However, due to the vast compositional space of HEAs, efficiently discovering new HEAs with exceptional performance using trial-and-error methodology is time-consuming and challenging. In this work, a machine learning (ML) framework was introduced for Nb-Ti-V-Zr refractory HEA (RHEA) design. This framework aims to streamline the design of Nb-Ti-V-Zr RHEA with a focus on improving hardness. This framework encompasses data collection, feature construction, four-step feature selection, and training of different ML models, followed by Fisher material pattern recognition and SHAP feature analysis. For the first time, three key features, including the atomic size difference (δ), the configurational entropy of mixture (Smix), and the average deviation of electronegativity (AdE) were identified as the most significant compositional factors impacting the hardness of Nb-Ti-V-Zr RHEA. Furthermore, the Support Vector Regression (SVR) model with a polynomial kernel was the best-trained model for hardness prediction compared to other ML models trained and tested in this work. The coefficient of determination (R) was 0.85 for the testing set and 0.91 for 5-fold cross-validation, while the root mean square error (RMSE) values were 0.9 and 0.74, respectively. Moreover, it was observed that high-hardness samples follow a particular combination of key features, providing important optimization insights. Finally, the analysis of key features revealed the negative effect of AdE, the positive effect of Smix, and the hybrid effect of δ on hardness.