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

Understand

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.