Learning Free-Surface Flow with Physics-Informed Neural Networks

TL;DR

This paper explores the use of physics-informed neural networks (PINNs) to model free-surface flows governed by shallow-water equations, demonstrating competitive accuracy with traditional simulations in 1-D and 2-D scenarios.

Contribution

It introduces and evaluates different PINN formulations and optimization strategies for shallow-water equations, achieving efficient and accurate free-surface flow modeling.

Findings

PINNs can effectively model free-surface flows with low error.

Different residual formulations impact convergence and accuracy.

The method achieves an $L_2$ error of 8.9e-3 in complex bathymetry scenarios.

Abstract

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 $8.9e-3$.