Learning Free-Surface Flow with Physics-Informed Neural Networks
This work addresses modeling free-surface flows for applications such as flood and tsunami prediction, but it is incremental as it builds on existing PINN methods.
The paper tackled simulating free-surface flows like flood waves using physics-informed neural networks (PINNs) applied to shallow-water equations, achieving a total relative L2 error of 8.9e-3 compared to direct numerical simulation.
The interface between data-driven learning methods and classical simulation poses an interesting field offering a multitude of new applications. In this work, we build on the notion of physics-informed neural networks (PINNs) and employ them in the area of shallow-water equation (SWE) models. These models play an important role in modeling and simulating free-surface flow scenarios such as in flood-wave propagation or tsunami waves. Different formulations of the PINN residual are compared to each other and multiple optimizations are being evaluated to speed up the convergence rate. We test these with different 1-D and 2-D experiments and finally demonstrate that regarding a SWE scenario with varying bathymetry, the method is able to produce competitive results in comparison to the direct numerical simulation with a total relative $L_2$ error of $8.9e-3$.