Authors: Ziming Liu, Pingchuan Ma, Yixuan Wang, Wojciech Matusik, Max Tegmark
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.
Source: http://arxiv.org/abs/2408.10205v1
