A new physics-informed XGBoost model for predicting the triaxial compressive strength of heat-treated rocks

Abstract Predicting the triaxial compressive strength ( σ t ) of heat-treated rocks is critical for geotechnical engineering but remains challenging, as conventional machine learning (ML) models often lack physical interpretability and robustness across diverse thermal–mechanical regimes. This study introduces a novel PhysicsXGB model that integrates a simplified semi-empirical strength formulation with an eXtreme Gradient Boost (XGBoost) component. The physics-based component provides a prediction using key features—density, elastic modulus, temperature, and crack damage stress ( σ cd )—while the XGBoost component learns complex residuals, thereby enhancing accuracy while preserving interpretability. Evaluated on a compiled dataset of the heated rock under varying confining pressures via fivefold cross-validation, the PhysicsXGB model significantly outperformed standalone ML models and a pure semi-empirical baseline. It achieved the highest predictive accuracy, with a mean R 2 of 0.982 ± 0.003 and a low RMSE of 16.84 ± 2.04 MPa. An ablation study further demonstrated the model’s exceptional robustness, showing strong performance (R 2 = 0.962 ± 0.011) even when the highly correlated σ cd feature was excluded. The hybrid model demonstrated exceptional robustness, maintaining strong performance (R 2 = 0.962 ± 0.011) even when σ cd was excluded. This confirms the model’s ability to effectively generalize predictions without relying on a single dominant input. SHAP analysis verified the physical consistency of the learned relationships, providing clear insights into feature contributions across different thermal–mechanical states. The PhysicsXGB model thus offers a validated, robust, and explainable framework for predicting the complex strength behavior of heat-treated rock.