{
  "abstract": "We systematically investigate finite-difference (FD) derivative computation in Physics-Informed Neural Networks (PINNs) as an alternative to automatic differentiation (AD). On three benchmark PDEs we show that, with a properly calibrated step size, FD matches AD in accuracy on every problem while running faster across the full tested batch-size range and using substantially less GPU memory, and that a stochastic variant we propose outperforms AD on a stationary problem. We further show that for neural architectures with inter-sample dependencies (e.g. BatchNorm, self-attention) the standard PyTorch autograd idiom is silently incorrect; the correct per-sample alternative is computationally infeasible at PINN-relevant batch sizes, while FD provides a forward-only approximation that is empirically an order of magnitude closer to the true per-sample derivative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.11020",
  "author_total": 2,
  "authors": [
    {
      "name": "Maciej J. Mikulski"
    },
    {
      "name": "Tadeusz Uhl"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/10tx6pd32nfah.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.11020",
  "fulltext_url": null,
  "id": "10tx6pd32nfah",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.11020",
  "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.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
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    [
      "arxiv",
      "physics.comp-ph"
    ],
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      "openalex",
      "3109|Model Reduction and Neural Networks"
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  "openalex": "W7202277386",
  "pdf_url": "https://arxiv.org/pdf/2608.11020",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/10tx6pd32nfah.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:58Z",
      "native_id": "2608.11020",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.11020"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond",
  "title_text": "Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/10tx6pd32nfah",
  "venue": "arXiv",
  "versions": []
}