{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28971",
  "author_total": 2,
  "authors": [
    {
      "name": "Emmanuel Lorin"
    },
    {
      "name": "Arian Novruzi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9d1xxkv3gmr8m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28971",
  "fulltext_url": null,
  "id": "9d1xxkv3gmr8m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28971",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7214382156",
  "pdf_url": "https://arxiv.org/pdf/2609.28971",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9d1xxkv3gmr8m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28971",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28971"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A diffusion-free multi-layer neural-network method for multidimensional nonlinear hyperbolic equations",
  "title_text": "A diffusion-free multi-layer neural-network method for multidimensional nonlinear hyperbolic equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/9d1xxkv3gmr8m",
  "venue": "arXiv",
  "versions": []
}