Application of physics-informed neural networks for solving water penetration problems in unsaturated soils
摘要
Modeling water flow in unsaturated soils is essential for understanding various hydrological and ecological phenomena. The dynamics of soil water are usually described by the Richards’ equation, which is a well-known physical law. However, solving the Richards’ equation is difficult due to its nonlinear nature. In this paper, we consider two cases of the Richards’ equation and apply Physics-Informed Neural Networks (PINNs) approach to model it. In the approach, neural networks structures are involved, which learn the behavior of complex physical systems by optimizing the network parameters towards minimizing the residuals of the partial differential equations (PDEs). The equations of the residuals emerge from the framework of the governing PDEs, which are integrated within it. The derivatives of the estimated physical quantities are computed via deep learning libraries based on automatic differentiation, thus mandating the neural network to comply with the governing physics. In this work, the results provided by the PINNs are validated with the ground truth solutions on different time stages, along with the results of the semi-analytical and numerical techniques on a few selected time intervals. The current work concludes that the PINNs results demonstrate good agreement with results from the ground truth and the semi-analytical technique.