LeafNet: A Diffusion-Free Multi-Layer Neural Network Method for Multidimensional Nonlinear Hyperbolic EquationsNew

This paper addresses the numerical solution of N-dimensional hyperbolic systems of conservation laws, focusing on accurate approximation of simple waves. The authors develop the LeafNet algorithm, which reformulates hyperbolic conservation laws as a coupled system involving smooth solutions and employs accurate physics-informed algorithms for function approximation. The work includes theoretical error estimates and two-dimensional numerical experiments to validate the approach.