{
  "abstract": "We investigate the use of Physics-Informed Neural Networks (PINNs) for the numerical solving of Fredholm integral equations of the first and second kind, proposing both single-network and double-network formulations. Rigorous error estimates are derived for both approaches, establishing theoretical convergence guarantees in terms of training residuals. Numerical experiments demonstrate convergence across a range of benchmark problems. A systematic comparison with the classical Nyström method reveals that, for well-posed, well-conditioned problems with clean data, the Nyström method remains the solver of choice. However, the PINN framework demonstrates a marked advantage in challenging settings: when the input data are corrupted by noise or the problem is ill-conditioned, PINNs exhibit significantly greater robustness. This inherent stability, attributed to the implicit regularization of neural network training, positions PINNs as a compelling alternative for the solution of Fredholm integral equations arising in ill-posed inverse problems and data-corrupted regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Mathieu Fabre"
    },
    {
      "name": "Laurence Grammont"
    },
    {
      "name": "Youcef Mammeri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cmze4ve72ydhh.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "cmze4ve72ydhh",
  "issns": [],
  "landing_url": "https://hal.science/hal-05799002v1",
  "language": "en",
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05799002/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cmze4ve72ydhh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:56Z",
      "native_id": "hal-05799002",
      "source": "hal",
      "url": "https://hal.science/hal-05799002v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Solving Fredholm Integral Equations with Physics-Informed Neural Networks: Single-and double-network approaches",
  "title_text": "Solving Fredholm Integral Equations with Physics-Informed Neural Networks: Single-and double-network approaches",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:56Z",
  "url": "https://research.draconitic.com/paper/cmze4ve72ydhh",
  "venue": "HAL",
  "versions": []
}