{
  "abstract": "Physics-informed learning is increasingly used for partial differential equation (PDE)-governed inverse problems, but its reliability remains difficult to certify. This paper develops a no-harm certification-and-selection framework for physics-informed inverse learning. A learned reconstruction is accepted only when its residual-calibrated radius is no worse than the baseline radius, namely when $$R_{\\mathrm{learn}}\\le R_{\\mathrm{base}}+\\varepsilon_{\\mathrm{safe}};$$otherwise, the method returns the baseline. The certificate combines data, physics, boundary or initial-condition, and optimization residuals. Under a conditional stability estimate, these residuals yield an a posteriori reconstruction-error bound and a deterministic uncertainty radius. A high-probability certificate is also derived for physics residuals estimated from independent random collocation points. Numerical tests on Poisson source recovery, inverse heat reconstruction, limited-angle tomography, elliptic coefficient identification, and stochastic residual validation show that the selector accepts certified improvements, rejects shifted, hallucinated, or unfinished candidates, and becomes conservative in strongly ill-posed regimes. The framework is therefore a certification-and-selection layer, not another reconstruction architecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.07153",
  "author_total": 1,
  "authors": [
    {
      "name": "Ronald Katende"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fdj36tqm6523b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.07153",
  "fulltext_url": null,
  "id": "fdj36tqm6523b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.07153",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7163882517",
  "pdf_url": "https://arxiv.org/pdf/2606.07153",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fdj36tqm6523b.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2606.07153",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.07153"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "No-Harm Physics-Informed Inverse Learning with Residual-Calibrated Uncertainty",
  "title_text": "No-Harm Physics-Informed Inverse Learning with Residual-Calibrated Uncertainty",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/fdj36tqm6523b",
  "venue": "arXiv",
  "versions": []
}