Physics-Constrained Artificial Intelligence for Modeling Water–Heat Processes in Unsaturated Soil under Climate Change

Extreme climate change intensifies the spatiotemporal variability of soil moisture and temperature fields, thereby increasing the frequency and uncertainty of hydrogeological hazards such as floods, landslides, and droughts. These processes are governed by highly nonlinear water–heat coupling in unsaturated soil, where state variables and constitutive parameters are strongly interdependent. This complexity poses significant challenges for conventional physics-based numerical models due to difficulties in parameterization and uncertainty in boundary conditions, while purely data-driven models often lack physical consistency and interpretability. To address these limitations, this study proposes a hybrid modeling framework that integrates physical mechanisms with deep learning by embedding constitutive relationships and physical constraints derived from water–heat transport equations in unsaturated soil into a deep neural network. The proposed approach enables accurate prediction of the spatiotemporal evolution of soil moisture and temperature while preserving physical consistency. Numerical experiments were conducted for multiple soil types and boundary conditions, and the effects of data sparsity and noise on model performance were systematically evaluated. The results demonstrate that the hybrid model significantly outperforms purely data-driven approaches in terms of prediction accuracy and generalization capability, particularly in capturing localized moisture transport fronts and nonlinear dynamic behaviors. Further validation using bench-scale laboratory water–heat coupling experiments demonstrates that the proposed framework not only reconstructs key hydrothermal constitutive parameters but also successfully reproduces the temporal evolution of volumetric water content and temperature in unsaturated soil. Overall, this study provides a robust hybrid modeling strategy for simulating coupled water–vapor–heat processes in unsaturated soil. The proposed framework highlights the potential of physics-constrained deep learning for complex hydrological processes and supports its application in hydrogeological hazard analysis and risk assessment.