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A diffusion-free multi-layer neural-network method for multidimensional nonlinear hyperbolic equations
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.
Related
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- Propagation Dynamics for Multidimensional Nonlocal Diffusion Equations: A General Freidlin-Gärtner Formula
- Long-time asymptotics of nonlinear Fokker-Planck equations with inhomogeneous diffusion and natural boundary conditions
- Characterization of intrinsic parabolic Harnack inequalities for doubly nonlinear equations of slow diffusion type
BibTeX
@misc{lorin2026diffusionfree,
title = {{A diffusion-free multi-layer neural-network method for multidimensional nonlinear hyperbolic equations}},
author = {Emmanuel Lorin and Arian Novruzi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28971},
eprint = {2609.28971},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28971},
}
RIS
TY - UNPB
TI - A diffusion-free multi-layer neural-network method for multidimensional nonlinear hyperbolic equations
AU - Emmanuel Lorin
AU - Arian Novruzi
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.28971
UR - https://arxiv.org/abs/2609.28971
AB - 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.
ER -