Residual-Guided CatBoost for Dual-Property Prediction in Solid-Solution UHTCs

Designing solid-solution ultra-high-temperature ceramics (UHTCs) is challenging due to the need to balance multiple performance metrics, particularly hardness and fracture toughness. Here, we develop a residual-guided data-consistency screening strategy coupled with a machine-learning-enabled dual-property regression framework to predict both properties from literature-derived experimental datasets. Seven physically grounded descriptors are employed to represent processing, microstructure, and bonding effects, including homologous temperature, relative density, average grain size, configurational mixing entropy, atomic size mismatch, average cation radius, and average Pauling electronegativity. Using property-specific CatBoost regressors under a unified modeling workflow, the framework achieved coefficients of determination of 0.907 for hardness and 0.905 for fracture toughness. The corresponding MAE/RMSE values were 0.420/0.531 GPa for hardness and 0.339/0.425 MPa·m^1/2 for fracture toughness, indicating stable predictive performance for both responses. Residual-guided screening was used to improve data consistency and support model generalization. Benchmark experiments on two ZrB₂-based solid-solution ceramics show that the model accurately reproduces hardness and captures the relative trend in fracture toughness. The proposed framework is readily extensible to larger composition spaces and additional coupled properties, providing a data-efficient route to accelerate multi-objective design of solid-solution UHTCs.