{
  "abstract": "PDECheck audits learned PDE simulators through callable propagators or saved predictions. It evaluates relative $L^2$ error, temporal composition, finite-difference generators, and equation-specific physical residuals, retaining horizons and missing prerequisites. Analytic and manufactured defects verify the kernels. A heat-equation sweep quantifies generator sensitivity to timestep, frequency, grid, and precision. A three-equation, five-seed FNO study compares supervised, PINO-style, and composition-regularized training. An accuracy-matched advection comparison has state errors below 0.3% and a semigroup-error ratio of 1.48 (95% interval 1.34-1.62). The composition penalty lowers semigroup error but increases composed-state and longer-rollout prediction error. A time-reparameterization check produces identical low-error endpoints with different compositions. Applications to five external equation families exercise the readers and physical contracts on coarse grids. The release includes reproducibility artifacts and measured CPU/CUDA costs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.18200",
  "author_total": 1,
  "authors": [
    {
      "name": "Lennon J. Shikhman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a3sz8b75zhm1v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.18200",
  "fulltext_url": null,
  "id": "a3sz8b75zhm1v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.18200",
  "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.MS"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7165019178",
  "pdf_url": "https://arxiv.org/pdf/2606.18200",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a3sz8b75zhm1v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2606.18200",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.18200"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "PDECheck: A Diagnostic Software Suite for Auditing Learned PDE Simulators",
  "title_text": "PDECheck: A Diagnostic Software Suite for Auditing Learned PDE Simulators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/a3sz8b75zhm1v",
  "venue": "arXiv",
  "versions": []
}