Formation Energy Prediction and Feature Analysis of Lead-Free Double Perovskites Based on Deep Learning

Lead-free double perovskites (LFDPs) are emerging as promising low-toxicity and thermally stable candidates to replace lead-based perovskites in photovoltaic and optoelectronic devices. However, the rational design of high-stability LFDPs is severely constrained by the low efficiency of conventional experiments and density functional theory (DFT) calculations, as well as the limited accuracy and interpretability of existing machine learning models. To address these limitations, this study employed classic deep learning models to predict the DFT-calculated formation energy of the A₂BB'X₆ lead-free double perovskite material. Based on a dataset of 1027 DFT-calculated samples, four deep learning models, namely MLP, deep ensemble, PINN, and Transformer, were constructed to accurately predict the thermodynamic stability of LFDPs using formation energy as the core evaluation index. Combined with correlation analysis and SHapley Additive exPlanations (SHAP) interpretable learning, the optimal geometric stability window for LFDPs was identified, with a tolerance factor of 0.8~0.9 and an octahedral factor of 0.4~0.8. Comparative model validation demonstrates that the MLP model exhibits the best predictive performance, achieving a mean absolute error (MAE) of 0.0951 and a coefficient of determination (R²) of 0.9147 on the test set. SHAP analysis further reveals that the electronegativities of B1 and B2 cations are the dominant electronic factors governing the formation energy and phase stability of LFDPs, with a positive synergistic effect, while lattice size parameters (e.g., B2 ionic radius and B1 van der Waals radius) act as secondary influencing factors. This work constructs a high-precision, physically interpretable data-driven regression benchmark for formation energy, delivers multi-dimensional mechanistic interpretation of feature contributions, and acts as a reference for high-throughput material screening.