Solving the Richards infiltration equation by coupling physics-informed neural networks with Hydrus-1D.

The movement and infiltration of groundwater play a crucial role in environmental engineering and water resource management. The Richards equation, a fundamental model describing water flow in unsaturated soils, encounters significant challenges in traditional numerical solutions due to its strong nonlinearity, complex boundary conditions, and computational inefficiency. To address these issues, this study proposes an improved physics-informed neural network (PINN) method based on data fusion. This approach is designed to handle the intricate boundary conditions and nonlinear water diffusion characteristics in groundwater seepage by integrating data with physical constraints, thereby forming a dual-driven solution framework that leverages both data and physics. The proposed improved algorithm integrates Hydrus data, leveraging a small portion of data to reduce the model's dependence on parameter initialization. Simultaneously, it enables the model to automatically adjust to variations in physical processes under different data conditions, thereby enhancing the accuracy and stability of the solution. Comparaison with experimental results demonstrates the strong generalization ability of this method, particularly in data-scarce regions, where physical constraints ensure the reliability of the model's solutions.