Integrating multiple physical processes with deep learning for the prediction of coupled water-vapor-heat water flux in unsaturated zone

Water flux in unsaturated zones play a crucial role in the hydrological cycle, and accurately predicting them is essential for effective water resource development and management. Traditional methods encounter significant challenges due to the complexity of infiltration, evaporation, and soil water retention processes. Purely data-driven models lack a physical basis and interpretability, while physically-based models are hindered by the complexities of parameterization and boundary conditions. To overcome these limitations, this study introduces an innovative hybrid modeling approach that integrates deep neural networks with the physical mechanism of coupled water-vapor-heat processes to predict unsaturated zone water flux. The governing equations for water and heat transport are concurrently utilized to guide the training of deep learning models, thereby enhancing their precision in characterizing complex hydrological processes and ensuring physical consistency. Numerical experiments were designed to cover various soil types, boundary conditions, and datasets characterized by sparsity and noise. The results demonstrate that the hybrid model outperforms purely data-driven and traditional deep learning methods in terms of accuracy and generalizability. Further validation of the framework was performed using field data, where predicted water flux and its dynamic patterns showed strong agreement with observed meteorological, hydrological, and soil data. This study effectively integrates the advantages of both data-driven and physics-driven approaches, offering an innovative solution for unsaturated zone water flux prediction. Furthermore, it explores the paradigm and potential of merging multi-physical processes with deep learning, advancing the application of hybrid modeling in unsaturated zone hydrology.