Machine Learning Based Mesh Movement for Non-Hydrostatic Tsunami Simulation

Abstract

This study investigates the use of machine learning based mesh movement method, specifically the Universal Mesh Movement Network (UM2N), with depth integrated non-hydrostatic shallow water models. Motivation for this comes from the need for models which balance efficiency and accuracy for use in probabilistic coastal hazard assessment. Implementations are built on the discontinuous Galerkin finite-element (DG-FE) based software, Thetis, which leverages the partial differential equation (PDE) framework Firedrake for automated code generation. Verification on benchmark test cases and validation against laboratory measurements of coastal hazards, focusing on tsunami propagation, run-up, and inundation is performed. In these tests, the UM2N-driven meshes help resolve key non-hydrostatic dynamics including wave refraction over a conical shoal, run-up with wetting-drying on a conical island, and tsunami inundation in the Monai Valley laboratory benchmark, and yield numerical solutions in close agreement with reference fine-mesh computations and measured data. Notably, in the Monai Valley case, UM2N achieves a ~91% reduction in wave-peak error at the nearshore gauge compared with ~74% for the conventional Monge--Amp\`ere (MA) mesh movement, both relative to the coarse fixed mesh. The UM2N surrogate based approach accelerates the conventional mesh movement step, achieving a ~32% reduction in total runtime and ~2 times speed-up in mesh movement step time over the MA solver on GPU, while offering a significant improvement in robustness over long integration periods and under strongly nonlinear wave conditions.