Nonhydrostatic Transient Shallow Water Flow Modeling Using PINNs

Abstract

Fast and accurate river flow simulations are essential for designing efficient hydraulic structures and establishing reliable safety policies under climate change. Traditional numerical methods are frequently computationally expensive for simulating nonhydrostatic river flows, which is important under extreme flow scenarios. Neural networks offer a promising, though barely explored, solution for simulating these kinds of flows in rivers. In this paper, a physics-informed neural network (PINN) model is developed to solve the fully nonlinear Serre–Green–Naghdi (SGN) equations for shallow waters. The model uses a fully connected neural network architecture along with the ADAM optimizer for the training process. The loss function in the PINN integrates residuals from the governing equations, initial conditions, and boundary conditions. The effect of hyperparameters such as the number of collocation points, network layers and neurons, and grid type/density is explored and optimized. Validation involves experimental data of dam-break flow tests over horizontal and uneven beds and an analytical solution test, comparing results to finite volume numerical solutions and experimental data, resulting in excellent agreement. The use of experimental data for validation rather than for training of the PINN constitutes a key contribution of this study. The proposed PINN model is compared against previous PINN results for the SGN solution of steady flow over a Gaussian weir, showing excellent agreement while achieving a reduction in computational complexity as a single optimizer (i.e., ADAM) is used to solve the transient response, which is another novelty introduced herein. Given the simplicity and efficiency of this approach compared to traditional numerical schemes, the proposed PINN model represents a promising tool for enabling efficient flood management systems in rivers, such as flood warning systems, which rely on fast, numerous simulations.