Discovering Artificial Viscosity Models for Discontinuous Galerkin Approximation of Conservation Laws using Physics-Informed Machine Learning

arXiv:2402.16517v1 Announce Type: cross
Abstract: Finite element-based high-order solvers of conservation laws offer large accuracy but face challenges near discontinuities due to the Gibbs phenomenon. Artificial viscosity is a popular and effective solution to this problem based on physical insight. In this work, we present a physics-informed machine learning algorithm to automate the discovery of artificial viscosity models in a non-supervised paradigm. The algorithm is inspired by reinforcement learning and trains a neural network acting cell-by-cell (the viscosity model) by …

abstract accuracy approximation artificial arxiv challenges conservation cs.lg cs.na element face gibbs insight laws machine machine learning math.na near physics physics-informed popular solution type work