{
  "abstract": "We introduce the Long-Short-Range Neural Network (LSR-Net), a novel neural operator architecture designed for data-driven forward evolution modeling, and extends it to the prediction of nonlinear fluid dynamics. LSR-Net learns the evolution operator of a dynamical system solely from pairs of initial and future state snapshots, which splits the learnable integral kernel into long-range (LR) and short-range (SR) components within stacked network blocks. While the SR component uses standard convolutions to capture local dynamics, the LR component employs a sum-of-exponentials (SOE) representation. This allows for the efficient computation of global interactions as a trainable Fourier multiplier, reducing computational complexity to $O(n \\log n)$ where $n$ is the number of pixels in an input snapshot and requiring only a few parameters per channel. LSR-Net is evaluated on three challenging 2D benchmarks: the coupled Burgers equation, the wave equation with a spatially varying coefficient, and the nonlinear shallow water equation {(SWE)}. Results demonstrate that LSR-Net significantly outperforms the baseline short-range network (SR-Net) as well as FNO and DeepONets in predictive accuracy, achieving substantially lower relative errors by effectively capturing both local fine-scale structures and crucial global pattern interactions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19039",
  "author_total": 4,
  "authors": [
    {
      "name": "Qian Hou"
    },
    {
      "name": "Sutrisno"
    },
    {
      "name": "Yuqing Li"
    },
    {
      "name": "Zecheng Gan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aggzdas4nvfdh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19039",
  "fulltext_url": null,
  "id": "aggzdas4nvfdh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19039",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19039",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aggzdas4nvfdh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.19039",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19039"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "LSR-Net: Learning the Forward Evolution Operator for Nonlinear Fluid Dynamics",
  "title_text": "LSR-Net: Learning the Forward Evolution Operator for Nonlinear Fluid Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/aggzdas4nvfdh",
  "venue": "arXiv",
  "versions": []
}