Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems
This work addresses efficiency issues in scientific machine learning for researchers and practitioners dealing with multiscale problems, though it is incremental as it builds on existing finite basis methods.
The paper tackled the high training cost of Kolmogorov-Arnold networks (KANs) by developing a domain decomposition method that enables parallel training of multiple small KANs, achieving accurate solutions for multiscale problems with noisy data and in physics-informed settings.
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.