KAN 2.0: Kolmogorov-Arnold Networks Meet Science
This work addresses the challenge of bridging AI and science for researchers in scientific domains, though it appears incremental by extending KANs with new functionalities.
The paper tackles the incompatibility between AI's connectionism and science's symbolism by proposing a framework that integrates Kolmogorov-Arnold Networks (KANs) with scientific discovery, enabling tasks like feature identification and symbolic formula extraction, and demonstrates its capability to discover physical laws such as conserved quantities and symmetries.
A major challenge of AI + Science lies in their 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 the pykan package: (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) to 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.