{
  "abstract": "Operator learning for parametric partial differential equations (PDEs) typically builds global models over prescribed domains, requiring cross-condition data or costly physics-constrained training. Here we show that the output Jacobian of a neural solution model trained at one condition defines a reusable response space for cross-condition solution variations. We introduce Linearized Subspace Transfer (LST) to exploit this space and recover target solutions by minimizing the target PDE-system residual over response-space coordinates. Because any single response space has finite coverage, Active Transfer Modeling (ATM) uses post-transfer residuals as coverage indicators to selectively acquire response spaces from additional single-condition models. Across six systems, single-condition response spaces supported cross-condition transfer, with enrichment improving accuracy when added spaces expanded representation capacity. Relative to evaluated physics-informed operator baselines, ATM reduced error and offline construction cost, with orders-of-magnitude accuracy gains in representative cases and millisecond-to-second target adaptation. These results establish neural solvers as reusable local parametric models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15432",
  "author_total": 2,
  "authors": [
    {
      "name": "Wenbo Cao"
    },
    {
      "name": "Weiwei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4twd993bh0jpg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15432",
  "fulltext_url": null,
  "id": "4twd993bh0jpg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15432",
  "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"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7213338009",
  "pdf_url": "https://arxiv.org/pdf/2609.15432",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4twd993bh0jpg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.15432",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15432"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Single-condition neural solvers encode transferable response spaces for parametric differential equations",
  "title_text": "Single-condition neural solvers encode transferable response spaces for parametric differential equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/4twd993bh0jpg",
  "venue": "arXiv",
  "versions": []
}