KAN 2.0: Kolmogorov-Arnold Networks Meet Science

TL;DR

This paper introduces a framework combining Kolmogorov-Arnold Networks with scientific discovery, enabling the extraction of physical laws and symbolic formulas from neural networks, bridging AI and science.

Contribution

It presents a novel framework and tools for integrating KANs with scientific knowledge, facilitating discovery of physical laws and symbolic representations.

Findings

KANs can discover conserved quantities and symmetries.

New functionalities enable symbolic formula compilation and tree conversion.

Demonstrated capability to uncover physical laws from data.

Abstract

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.