{
  "abstract": "Learning solution operators across broad parameter ranges can require substantial coverage of both input functions and physical parameters, particularly for purely data-driven parametric models. In addition, the resulting models may fail silently outside the training distribution. We introduce equation recast, which reformulates parametric operator learning as the learning of a single canonical operator. Parameter-induced operator variations are derived analytically from the governing equation and absorbed into effective sources, enabling zero-shot prediction across new parameter regimes. Across multi-parameter, nonlinear, and singular PDE settings, equation recast supports extrapolation, integrates sparse heterogeneous datasets in a shared canonical representation, and uses loss of convergence as an internal warning signal for failure of the recast iteration. In high-fidelity tokamak simulations for nuclear fusion, the framework unifies electron-temperature data across four device geometries through canonical-domain mapping within one jointly trained operator. Equation recast provides a route toward reusable neural PDE solvers combining equation-guided transfer, data efficiency, and monitorable inference.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02982",
  "author_total": 10,
  "authors": [
    {
      "name": "Qiyun Cheng"
    },
    {
      "name": "Valentin Duruisseaux"
    },
    {
      "name": "Cesar F. Clauser"
    },
    {
      "name": "Md Hossain Sahadath"
    },
    {
      "name": "Huihua Yang"
    },
    {
      "name": "Shaowu Pan"
    },
    {
      "name": "Nathaniel Ferraro"
    },
    {
      "name": "Anima Anandkumar"
    },
    {
      "name": "Wei Ji"
    },
    {
      "name": "Cristina Rea"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ak4tmwaz8raax.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02982",
  "fulltext_url": null,
  "id": "ak4tmwaz8raax",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02982",
  "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",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "physics.plasm-ph"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7208713059",
  "pdf_url": "https://arxiv.org/pdf/2609.02982",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ak4tmwaz8raax.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2609.02982",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02982"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.plasm-ph",
      "subfield": "plasma"
    }
  ],
  "title": "Equation Recast for Canonical Operator Learning Across Parametric PDEs",
  "title_text": "Equation Recast for Canonical Operator Learning Across Parametric PDEs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:31Z",
  "url": "https://research.draconitic.com/paper/ak4tmwaz8raax",
  "venue": "arXiv",
  "versions": []
}