An interpretable machine learning framework for predicting Curie temperature of lead-based piezoelectric ceramics

Lead-based perovskite piezoelectric ceramics exhibit tunable Curie temperatures through sophisticated compositional design, which is critical for high-temperature applications. However, predicting T c remains challenging owing to complex compositional spaces. Herein, we develop an interpretable machine learning framework leveraging published experimental data to guide the chemical design of lead-based piezoelectric ceramics. Our methodology involves: (1) exhaustive screening of feature combinations to minimize cross-validation errors, (2) Bayesian optimization of hyperparameters to reduce model error and improve predictive accuracy ( R 2 >0.98), and (3) Shapley Additive Explanations and partial dependence analysis to elucidate feature- T c correlations and mitigate the black-box nature of conventional machine learning. Furthermore, the Sure Independence Screening and Sparsifying Operator method extracts explicit mathematical formulas correlating with experimental T c values ( R 2 > 0.90). This work not only advances the rational design of lead-based piezoelectric ceramics for temperature-specific applications but also establishes a paradigm for machine learning in other functional material systems. • A high-performance ML model ( R 2 > 0.98) was developed to predict the T C of lead-based piezoelectric ceramics. • Models were optimized through feature engineering and Bayesian optimization. • Interpretability of the model was systematically clarified based on SHAP and partial dependence analysis. • Visual formulas with a high correlation to experimental data were constructed via SISSO method.