Phase prediction in high-entropy alloys through uncertainty sampling and symbolic classification-based parameter discovery

Data imbalance represents critical challenges for data-driven approaches in materials data modeling. In the present work, active learning models were developed to mitigate data imbalance in phase selection of high-entropy alloys (HEAs). Three alloy phase classifiers were established based on three datasets containing 149 features: one classifier evaluated the glass-forming ability of alloys; another distinguished among SS, SS + IM, and IM; and the third differentiated BCC, FCC, BCC + FCC, and HCP phases. Sample distribution bias was effectively alleviated through the combined application of multistage feature selection, active learning, cost-sensitive strategies, cluster analysis, and ensemble learning. Model performance was further validated through experimental synthesis and independent external datasets, demonstrating robust predictive capability. SHAP analysis and symbolic classification identified a novel phase selection parameter that enabled precise discrimination between BCC and FCC phases. A committee-based active learning framework was further constructed to enhance classification accuracy under sparse data conditions, thereby advancing data-driven strategies for alloy development. This framework provides a general and efficient solution for improving machine learning modeling when dealing with sparse and imbalanced materials data.