Research on the applicability of Physics-Informed Neural Networks to two-dimensional shallow water equation

Abstract

Physical-Informed Neural Networks (PINNs), which directly approximate the partial differential terms of simultaneous partial differential equations, can achieve higher reproducibility than conventional solution methods that use differences. Furthermore, the solution can be obtained much faster. In this study, we investigated the possibility of applying a two-dimensional shallow water equation for calculating the external water inundation of a flood to actual topographical conditions. Since PINNs approximate the partial differential term as a continuous function, they are generally not good at dealing with complex topography with discontinuous shapes. In this research, the water level distribution of complex topography was reproduced by introducing Positional Encoding to improve expressiveness and mitigating discontinuous topography by adding spatial dimension. Furthermore, the calculation time, which used to take about two days, was shortened to a few minutes.