Sonlu Taban Kolmogorov-Arnold Ağları: Veriye Dayalı ve Fizik Bilgilendirilmiş Problemler İçin Alan Ayrıştırma

Özet (abstract)

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.

Yazarların özeti; kaynağından alınmıştır. Advances in Computational Mathematics, 2026 · DOI ↗