{
  "abstract": "We introduce a variational physics-informed neural discretization for the nonlinear shallow-water equations with topography, in which a single global neural network represents the space-time trial state while the governing equations are enforced weakly in space through local cell moments and strongly in time at selected time nodes. Written in the free-surface variables (η, q), the output map preserves the non-negative water depth by construction, inherits the initial condition without a penalty term, and embeds wet and wet-dry lakes at rest in the same trial manifold. For shock-forming calculations, the conservative variational residual is supplemented with a one-sided mechanicalentropy loss, which penalizes only non-admissible positive energy production, and with a localized viscosity that concentrates dissipation near steep transitions. We establish two scheme-specific analytical results: an exact identity for the well-balanced defect generated by the positivity map, yielding distributional preservation for the positive part while quantifying the loss floor induced by a numerical film or a softplus map, and a two-regime consistency estimate for the nonlinear viscosity, which is O(h 2 ) in smooth regions, reaches the O(h) scale near an O(h) transition layer, and vanishes in distributions along refined sequences with uniformly bounded spatial variation. Wet-and dry-bed dam breaks, fully wet and partially dry equilibria, and one-and two-dimensional moving-shoreline solutions then assess these mechanisms numerically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Sacha Cardonna"
    },
    {
      "name": "Ali Haidar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/042n9wy393mc6.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "042n9wy393mc6",
  "issns": [],
  "landing_url": "https://hal.science/hal-05837658v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.info.info-ne"
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      "hal",
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05837658/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/042n9wy393mc6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05837658",
      "source": "hal",
      "url": "https://hal.science/hal-05837658v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-na",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A well-balanced shock-capturing variational physics-informed neural method for shallow-water flow with topography",
  "title_text": "A well-balanced shock-capturing variational physics-informed neural method for shallow-water flow with topography",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/042n9wy393mc6",
  "venue": "HAL",
  "versions": []
}