{
  "abstract": "Deep lid-driven cavities contain strong motion beneath the lid and much weaker recirculation at depth, so agreement in bulk velocity is an incomplete assessment of a computed flow. We examine data-free physics-informed neural networks (PINNs) for steady, two-dimensional incompressible flow in a cavity of depth-to-width ratio five at Reynolds numbers 100, 250, 500 and 1000. An established hard-constrained streamfunction formulation is combined with prescribed regional collocation, transferred initialization, and selected residual-scaling and envelope variants. Independent spectral/$hp$ calculations with the same Gaussian-regularized lid provide the reference fields. For a cavity of depth-to-width ratio $D/W=5$ at Reynolds numbers $\\mathrm{Re}=100$, 250, 500, and 1000, evaluation on a common $121\\times605$ grid gives interior relative velocity discrepancies of 5.130\\%--7.850\\%. Over the same cases, floor-region relative velocity discrepancies remain below 5\\%, with absolute RMS discrepancies ranging from $1.255\\times10^{-10}U$ to $2.332\\times10^{-9}U$, where $U$ is the lid-velocity scale. In a separate $161\\times801$ assessment at $\\Rey=1000$, the refined workflow lowers interior velocity discrepancy from 5.624\\% to 2.658\\% and gauge-aligned pressure RMS discrepancy from $2.793\\times10^{-3}$ to $1.167\\times10^{-3}ρU^2$. The improvements compare accumulated training workflows and do not isolate regional sampling. Configuration rankings depend on both region and observable. These finite-budget comparisons establish where the retained workflows agree with the reference and where rotational-field discrepancies remain substantial.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38814",
  "author_total": 2,
  "authors": [
    {
      "name": "Ehsan Roohi"
    },
    {
      "name": "Christopher J. McDevitt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/931cs97beja7c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38814",
  "fulltext_url": null,
  "id": "931cs97beja7c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38814",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38814",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/931cs97beja7c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.38814",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38814"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Regional accuracy of physics-informed neural networks (PINNs) for recirculation in a deep lid-driven cavity",
  "title_text": "Regional accuracy of physics-informed neural networks (PINNs) for recirculation in a deep lid-driven cavity",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/931cs97beja7c",
  "venue": "arXiv",
  "versions": []
}