Interpretable Machine Learning Model-Based Phase Prediction for Refractory High-Entropy Alloys

Abstract:

Five machine learning (ML) approaches, i.e. K-Nearest Neighbor (KNN), Support Vector Machine (SVM), Decision Tree (DT), Random Forest (RF) and Artificial Neural Network (ANN) were used to classify and to predict the combination of phases, i.e. solid solutions (SS) and mixed solid solution and intermetallic (SS+IM) in refractory high-entropy alloys (RHEAs). Five input characteristic phase predicting parameters and 139 RHEAs were selected to train these models. Results show that ANN model has the highest accuracy of 90.72%. Experimental results of 9 quaternary and (TiVTa)_xCr_1–x RHEAs verify the accuracy of prediction and indicate that RF and ANN can predict more accurately, successfully predicting 11 SS and 3 SS+IM. SHAP (SHapley Additive exPlanations) model was used to interpret the ANN model which exhibits the highest accuracy and to investigate the contribution of each feature to phase formation. The order of importance of five features is enthalpy of mixing (ΔH_mix), atomic size difference (δ), valence electron concentration (VEC), entropy of mixing (ΔS_mix), and electronegativity difference (Δχ), where the mean SHAP value of ΔH_mix is approximately 5 times higher than that of ?χ and 4 times higher than that of ΔS_mix. Less negative ΔH_mix, smaller δ and VEC may contribute to the formation of SS in RHEAs.