Kolmogorov-Arnold Networks Meet Science

Abstract

A major challenge of AI plus science lies in its inherent incompatibility: Today’s AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold networks (KANs) and science. The framework highlights KANs’ usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in pykan: (1) MultKAN, KANs with multiplication nodes, (2) kanpiler, a KAN compiler that compiles symbolic formulas into KANs; (3) tree converter, convert KANs (or any neural networks) into tree graphs. Based on these tools, we demonstrate KANs’ capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.