Predicting and understanding the ductility of BCC high entropy alloys via knowledge-integrated machine learning

Despite the fact that body-centered cubic high entropy alloys (BCC HEAs) exhibit exceptional strengthening mechanisms over a wide temperature range, their application is often hindered by poor room temperature ductility. Consequently, the accurate prediction of BCC HEAs′ ductility becomes critical in alloy design but is challenged by the intricate nature of these alloy systems. In this study, a comprehensive machine learning (ML) strategy with integrated material knowledge is proposed to address this problem. By referring to plasticity theories, thermodynamics as well as atomic properties, we develop a set of cost-effective material descriptors with various mathematical forms such as averaging, mismatching, maximum-minimum ranging and averaging as binary pairs for HEAs. These descriptors are proved to effectively incorporate material knowledge into ML modelling. They also offer potential alternatives to those obtained from costly first principles calculations. Classification and regression tasks are conducted to predict the ductility of BCC HEAs, and Gradient boosting algorithm exhibiting the best performance for both tasks is eventually selected. The established optimized models achieve high predictive accuracies exceeding 0.85. Through feature engineering, five key features related to valence electron concentration (VEC) and atomic size are screened out. These features lay the foundation for explicit formulae developed via Symbolic Classification, enabling the straightforward numerical prediction of BCC HEAs′ ductility. These key features are further analyzed by an interpretable ML method and compared against experimental and computational plasticity factors, elucidating their influences on various plasticity mechanisms. An in-depth exploration of why the proposed ML models outperform conventional plasticity criteria for HEAs is also presented. This study highlights an effective knowledge-integrated ML approach in predicting material properties resulting from complex mechanisms, with a particular focus on HEAs that often exhibit sparse data.