Multiphysics‐Informed Neural Networks for Coupled Soil Hydrothermal Modeling

Abstract Soil water and heat transport are two physical processes that are described by the Richardson–Richards equation and heat transport equation, respectively. Soil water and heat motion directly control transport or indirectly influence parameters. The physics‐informed neural network (PINN) is a new method that combines deep learning and physical laws that approximates and learns physical dynamics better than traditional data‐driven deep learning methods. In this study, we propose multiphysics‐informed neural networks for soil water‐heat systems, in which the soil moisture and temperature information complement each other well. With our framework, existing soil moisture neural networks are improved to reduce their dependency on the soil moisture measurement density. Furthermore, soil moisture data are employed to promote soil temperature dynamic learning and soil thermal conductivity estimation. Moreover, soil temperature data assist in recovering the nonlinearity of the soil hydraulic conductivity through hydrothermal coupling constraints, allowing better estimations of the soil water flux density. The gradient‐based annealing method is applied to adapt the loss function, which satisfactorily balances the water‐heat transport governing equation constraints on the neural networks. The robustness and generalizability of our framework are examined under diverse scenarios. This work demonstrates the mutual compensation of multisource data in coupled physical processes in a deep learning framework and highlights the significance of appropriate multiphysical constraints designed for nonlinear parameter recovery in PINNs.