Interpretable machine learning methods to predict the mechanical properties of ABX3 perovskites

Abstract

This paper proposes the utility of interpretable ensemble learning models for predicting the mechanical properties (bulk, shear and Young moduli) of ABX₃ perovskite compounds with the A, B, and X referring to the 3 elements that make the cubic 3-dimensional framework of the perovskite compounds. These models consist of 3 ensemble learning techniques namely CatBoost, Random Forest, and XGBoost. To expand the feature space, robust first-principles density functional theory calculations were used to generate some of the input features, namely elastic constants, density, volume per atom, and ground state energy per atom. The order of the input feature ranking that influences the machine learning (ML) model decisions was then determined. For this, we performed correlation analysis on the multi-dimensional input feature space, suppressed features with high collinearity, and selected features with limited correlation. We trained the three ensemble learning techniques on the desired vectorial input feature representation to predict the mechanical properties. Furthermore, we employed the Shapley Additive Explanations (SHAP) algorithm for analysing the intrinsic decision-making rationality of the ensemble learning models. We measured the performance in the context of the error metrics and coefficient of determination, R². The results show that XGBoost outperforms other approaches when predicting the shear modulus or Young modulus of the perovskite compounds yielding the least error metrics and the highest R² value (0.97) in the testing phase. However, both CatBoost and Random Forest outperformed XGBoost when attempting to predict the bulk modulus in the testing phase. The deficiency of the XGBoost in predicting the bulk modulus can be ascribed to an overfitting problem which can occur when the ML model gives accurate predictions for training data but not for test data. Furthermore, the SHAP algorithm provides an insight into the order of feature importance (from highest to lowest). Additionally, we conducted a post-analysis using a holistic ranking to analyse the relative importance of the SHAP feature impact comprehension for the examined ensemble learning techniques. Our findings indicate that the elastic constants are the most important input features influencing the predictive decision of the ensemble learning models.