KAN 2.0: Kolmogorov-Arnold Networks Meet Science

A major challenge of AI + Science lies in their inherent incompatibility:today’s AI is primarily based on connectionism, while science depends onsymbolism. To bridge the two worlds, we propose a framework to seamlesslysynergize Kolmogorov-Arnold Networks (KANs) and science. The frameworkhighlights KANs’ usage for three aspects of scientific discovery: identifyingrelevant features, revealing modular structures, and discovering symbolicformulas. The synergy is bidirectional: science to KAN (incorporatingscientific knowledge into KANs), and KAN to science (extracting scientificinsights from KANs). We highlight major new functionalities in the pykanpackage: (1) MultKAN: KANs with multiplication nodes. (2) kanpiler: a KANcompiler that compiles symbolic formulas into KANs. (3) tree converter: convertKANs (or any neural networks) to tree graphs. Based on these tools, wedemonstrate KANs’ capability to discover various types of physical laws,including conserved quantities, Lagrangians, symmetries, and constitutive laws.

Further reading#

• Access Paper in arXiv.org