Learning Free-Surface Flow with Physics-Informed Neural Networks

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 $8.9e-3$.

References in corpus (8)

• Adam: A Method for Stochastic Optimization
• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
• Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
• Accelerating Eulerian Fluid Simulation With Convolutional Networks
• Understanding and mitigating gradient pathologies in physics-informed neural networks
• Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism
• PyClaw: Accessible, Extensible, Scalable Tools for Wave Propagation Problems