A Survey on Physics-Informed Neural Networks for Shallow Water Problems

Abstract:

This study explores the capabilities of physics-informed neural networks for shallow water problems. Obtaining reliable hydrodynamic measurements can be costly and time consuming, therefore, measurements are rarely available and numerical models are used to simulate hydrodynamic conditions in the spatial and temporal domain. Advances in computational modeling have significantly improved the accuracy of numerical methods. Although at the expense of considerable computational costs, these methods have allowed engineers to generate vast amounts of accurate physics-based data that can be leveraged using machine learning methods like physics-informed neural networks. By adding physical constraints to the solution space, we can train neural networks on a small amount of physically accurate data and extrapolate to other domains. Once these neural networks are trained, they can be orders of magnitude faster than a numerical model.