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<p>Predicting the triaxial compressive strength (<i>σ</i><sub><i>t</i></sub>) 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 (<i>σ</i><sub><i>cd</i></sub>)—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<sup>2</sup> of 0.982 ± 0.003 and a low RMSE of 16.84 ± 2.04&#xa0;MPa. An ablation study further demonstrated the model’s exceptional robustness, showing strong performance (R<sup>2</sup> = 0.962 ± 0.011) even when the highly correlated <i>σ</i><sub><i>cd</i></sub>&#xa0;feature was excluded.&#xa0;The hybrid model demonstrated exceptional robustness, maintaining strong performance (R<sup>2</sup> = 0.962 ± 0.011) even when <i>σ</i><sub><i>cd</i></sub> 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.&#xa0;The PhysicsXGB model thus offers a validated, robust, and explainable framework for predicting the complex strength behavior of heat-treated rock.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月16日

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  • Stephen Akosah,
  • Ivan Gratchev,
  • Courage Kwasi Dzaklo

摘要

Predicting the triaxial compressive strength (σt) 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 (σcd)—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 R2 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 (R2 = 0.962 ± 0.011) even when the highly correlated σcd feature was excluded. The hybrid model demonstrated exceptional robustness, maintaining strong performance (R2 = 0.962 ± 0.011) even when σcd 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.