Work

A diffusion-free multi-layer neural-network method for multidimensional nonlinear hyperbolic equations

Year: 2026

Type: preprint

Abstract: This paper is devoted to the non-diffusive computation of solutions to $N$-dimensional hyperbolic systems of conservation laws (HCL) and more specifically the accurate approximation of simple waves. We develop the LeafNet algorithm, which relies on: i) a reformulation of HCL as a coupled system involving smooth solutions, and ii) an accurate physics informed algorithms approximating smooth functions. An error estimate analysis and two-dimensional numerical experiments are proposed to illustrate the presented strategy.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.28971

Authors: Lorin, Emmanuel, Novruzi, Arian

Institutions: Centre de recherches mathématiques, Carleton University, Université de Montréal, University of Ottawa

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214382156

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