Computer Science > Machine Learning
arXiv:2408.10205 (cs)
[Submitted on 19 Aug 2024]
Title:KAN 2.0: Kolmogorov-Arnold Networks Meet Science
View a PDF of the paper titled KAN 2.0: Kolmogorov-Arnold Networks Meet Science, by Ziming Liu and 4 other authors
View PDFHTML (experimental)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.
| Comments: | 27 pages, 14 figures |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computational Physics (physics.comp-ph); Data Analysis, Statistics and Probability (physics.data-an) |
| Cite as: | arXiv:2408.10205 [cs.LG] |
| (orarXiv:2408.10205v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2408.10205 arXiv-issued DOI via DataCite |
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View a PDF of the paper titled KAN 2.0: Kolmogorov-Arnold Networks Meet Science, by Ziming Liu and 4 other authors
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