Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems
<|reference_start|>Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems: 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 method for KANs that allows for several small KANs to be trained in parallel to give accurate solutions for multiscale problems. We show that finite basis KANs (FBKANs) can provide accurate results with noisy data and for physics-informed training.<|reference_end|>
@article{howard2024finite,
    title={Finite basis Kolmogorov-Arnold networks: domain decomposition for
  data-driven and physics-informed problems},
    author={Amanda A. Howard, Bruno Jacob, Sarah H. Murphy, Alexander Heinlein,
  Panos Stinis},
    journal={arXiv preprint arXiv:2406.19662},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.19662},
    primaryClass={cs.LG physics.comp-ph}
}