Machine Learning Based Mesh Movement for Non-Hydrostatic Tsunami Simulation

This study investigates the use of machine learning based mesh adaptivity, specifically mesh movement methods (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 and yield numerical solutions in close agreement with reference computations and measured data. Numerical results indicate that the UM2N surrogate based approach significantly accelerates conventional mesh movement techniques and has high robustness over long integration periods and under strongly nonlinear wave conditions.