Physics-Informed Neural Network for 2D Steady Seepage

This paper shows how a physics-informed neural network (PINN) can solve a two-dimensional steady-state seepage problem beneath an impermeable sheet-pile wall. By directly embedding the governing equation (Laplace’s equation) and boundary conditions into the training loss function, the PINN learns to minimize the residuals at randomly sampled interior and boundary points. The resulting solution closely matches approximate methods and captures physically consistent head contours and velocity fields, with only minor discrepancies in strictly enforcing boundary head values. Although training demands more computation than standard numerical approaches, PINNs avoid mesh generation and can readily incorporate measurement data, making them a promising alternative for complex or data-intensive geotechnical problems.