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Peer-reviewedCC BYAdvances in Computational Mathematics

Finite basis Kolmogorov-Arnold networks: Domain decomposition for data-driven and physics-informed problems

  • Amanda A. Howard1
  • Bruno Jacob1
  • Sarah Helfert2,1
  • Alexander Heinlein3
  • Panos Stinis4,5,1
5 affiliations
  1. 1Pacific Northwest National Laboratory, Richland, WA, 99354, USA
  2. 2Department of Mathematics & Statistics, University of North Carolina Charlotte, Charlotte, NC, 28223, USA
  3. 3Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628 CD, South-Holland, The Netherlands
  4. 4Department of Applied Mathematics, University of Washington, Seattle, WA, 98195, USA
  5. 5Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA
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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.

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Cite

BibTeXRIS
BibTeX
@article{howard2026finite,
  title = {{Finite basis Kolmogorov-Arnold networks: Domain decomposition for data-driven and physics-informed problems}},
  author = {Amanda A. Howard and Bruno Jacob and Sarah Helfert and Alexander Heinlein and Panos Stinis},
  journal = {Advances in Computational Mathematics},
  year = {2026},
  month = nov,
  doi = {10.1007/s10444-026-10376-7},
  url = {https://doi.org/10.1007/s10444-026-10376-7},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Finite basis Kolmogorov-Arnold networks: Domain decomposition for data-driven and physics-informed problems
AU  - Amanda A. Howard
AU  - Bruno Jacob
AU  - Sarah Helfert
AU  - Alexander Heinlein
AU  - Panos Stinis
PY  - 2026
DA  - 2026/11/05
JO  - Advances in Computational Mathematics
DO  - 10.1007/s10444-026-10376-7
UR  - https://doi.org/10.1007/s10444-026-10376-7
AB  - 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.
SN  - 1019-7168
SN  - 1572-9044
ER  -