Machine Learning of Band Gaps and Thermodynamic Stability in A₂BB'X₆ (X = F, Cl, Br, I) Double Perovskites with Uncertainty-Aware Multi-Objective Screening

A₂BB'X₆ double perovskites offer broad compositional flexibility, requiring screening strategies that jointly consider electronic properties and thermodynamic stability. We developed a leakage-controlled machine learning workflow integrating canonical-formula grouping, robustness tests, descriptor-cost analysis, and prediction uncertainty. The dataset contains 1975 Materials Project entries represented by 398 descriptors. Extra Trees predicted band gaps with a held-out MAE of 0.2031 eV and R² of 0.9437, whereas histogram gradient boosting predicted energy above the hull with an MAE of 0.02122 eV atom^-1 and R² of 0.8601. The stability classifier achieved ROC-AUC, PR-AUC, and MCC values of 0.9603, 0.9632, and 0.8192, respectively. Removing 39 relaxed-structure descriptors increased hull-energy MAE by approximately 12.5%, supporting a two-stage workflow of composition-based triage followed by structure-informed refinement. Chemical-distribution-shift tests revealed substantial performance degradation and defined the applicability domain. Seventeen held-out compounds met the screening criteria, representing retrospective recovery rather than prospective discovery. Path-specific phonon calculations for one Tier-1 candidate and two representative Tier-2 fluorides showed no imaginary modes along L-Γ-X-W, but cannot establish full-zone dynamical stability. Their HSE06+SOC gaps of 2.148-2.919 eV exceeded the original 1.0-2.0 eV window, underscoring the need for multi-fidelity validation. Overall, the workflow provides a reproducible and well-defined strategy for prioritizing and validating double perovskites.