{
  "abstract": "Kolmogorov-Arnold networks (KANs) have attracted attention recently as an alternative to multilayer perceptrons (MLPs) for scientific machine learning. However, KANs can be expensive to train, even for relatively small networks. Inspired by finite basis physics-informed neural networks (FBPINNs), in this work, we develop a domain decomposition-based architecture for KANs that allows for several small KANs to be trained in parallel to give accurate solutions for multiscale problems. We denote this new approach as finite basis KANs (FBKANs) and show that it yields accurate results for noisy data as well as physics-informed training. We extend to multilevel FBKANs, which train KANs across multiple levels of subdomains simultaneously. We show that FBKANs outperform KANs for multiscale problems, even when the KANs are adapted with grid extension.",
  "abstract_shown": true,
  "affiliations": [
    "Pacific Northwest National Laboratory, Richland, WA, 99354, USA",
    "Department of Mathematics & Statistics, University of North Carolina Charlotte, Charlotte, NC, 28223, USA",
    "Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628 CD, South-Holland, The Netherlands",
    "Department of Applied Mathematics, University of Washington, Seattle, WA, 98195, USA",
    "Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Amanda A. Howard",
      "orcid": "0000-0002-6411-6198"
    },
    {
      "affs": [
        0
      ],
      "name": "Bruno Jacob",
      "orcid": "0009-0001-5361-3105"
    },
    {
      "affs": [
        1,
        0
      ],
      "name": "Sarah Helfert"
    },
    {
      "affs": [
        2
      ],
      "name": "Alexander Heinlein",
      "orcid": "0000-0003-1578-8104"
    },
    {
      "affs": [
        3,
        4,
        0
      ],
      "name": "Panos Stinis",
      "orcid": "0000-0002-9928-5637"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/08m3mejgwn2be.bib",
  "cited_by": 31,
  "doi": "10.1007/s10444-026-10376-7",
  "fulltext_url": null,
  "id": "08m3mejgwn2be",
  "issns": [
    "1019-7168",
    "1572-9044"
  ],
  "landing_url": "https://doi.org/10.1007/s10444-026-10376-7",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W4400222592",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": "Springer Science+Business Media",
  "ris": "https://research.draconitic.com/paper/08m3mejgwn2be.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T13:20:23Z",
      "native_id": "W4400222592",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s10444-026-10376-7"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3109|Model Reduction and Neural Networks",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Finite basis Kolmogorov-Arnold networks: Domain decomposition for data-driven and physics-informed problems",
  "title_text": "Finite basis Kolmogorov-Arnold networks: Domain decomposition for data-driven and physics-informed problems",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:44Z",
  "url": "https://research.draconitic.com/paper/08m3mejgwn2be",
  "venue": "Advances in Computational Mathematics",
  "versions": []
}