Shallow Water Equation

Shallow water equations (SWEs) model fluid flow in shallow bodies of water, crucial for applications like flood prediction and coastal engineering. Current research focuses on improving SWE solvers' accuracy and efficiency using machine learning (ML), particularly neural networks like U-Nets, convolutional autoencoders, and physics-informed neural networks (PINNs), often combined with techniques like flux limiting and spectral methods to address issues like spectral bias and long-term prediction stability. These advancements aim to enable faster, more accurate simulations and facilitate tasks such as bathymetry inversion (reconstructing underwater topography from surface wave data), ultimately enhancing our ability to model and predict complex water dynamics.