{
  "abstract": "Multi-fidelity learning uses low-fidelity information (coarse-scale PDE models) together with limited high-fidelity data (fine-scale solutions) to obtain high-accuracy PDE solutions. It is a data-driven approach to downscale reduced-order models to solve PDEs efficiently and accurately. Standard multi-fidelity learning focuses on one operator or PDE; given a new PDE, retraining using additional coarse-fine solution pairs may be required, which is costly. In this work, we propose an in-context multi-fidelity learning framework for learning multiple multi-fidelity operators with one shared model. The model is trained using paired low- and high-fidelity examples as demonstrations from multiple operators, together with a new coarse-scale solution query, to predict the corresponding fine-scale solution. Once trained, given a new PDE operator, a few (fewer than five) coarse-fine demonstration pairs, and a low-cost coarse query, the model predicts the corresponding fine-scale solution without fine-tuning. When the target operator appears in the training dataset but has a different prediction goal, such as predicting beyond the training time interval, no additional demonstrations are needed. Instead, the model uses training coarse-fine pairs from that PDE and information from other training operators. Testing then only requires generating a low-cost coarse-scale solution query, without fine-tuning. Notably, our smallest model contains only 255,364 trainable parameters, corresponding to approximately 456 parameters per training operator for 560 operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38179",
  "author_total": 4,
  "authors": [
    {
      "name": "Xinyuan Li"
    },
    {
      "name": "Matthew Zahr"
    },
    {
      "name": "Panos Stinis"
    },
    {
      "name": "Zecheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4n2cmzkn8rc6h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38179",
  "fulltext_url": null,
  "id": "4n2cmzkn8rc6h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38179",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38179",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4n2cmzkn8rc6h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38179",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38179"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "In-Context Learning for Multi-Fidelity Multiscale Model Closure and Cross-Operator Out-Of-Distribution Generalization",
  "title_text": "In-Context Learning for Multi-Fidelity Multiscale Model Closure and Cross-Operator Out-Of-Distribution Generalization",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4n2cmzkn8rc6h",
  "venue": "arXiv",
  "versions": []
}