{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T18:21:12Z","timestamp":1787077272043,"version":"3.56.0"},"reference-count":55,"publisher":"American Physical Society (APS)","issue":"4","license":[{"start":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T00:00:00Z","timestamp":1765929600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["PHY-2019786"],"award-info":[{"award-number":["PHY-2019786"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. X"],"accepted":{"date-parts":[[2025,9,30]]},"abstract":"<jats:p>A major challenge of AI plus science lies in its inherent incompatibility: Today\u2019s 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\u2019 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 : (1)\u00a0MultKAN, KANs with multiplication nodes, (2)\u00a0kanpiler, a KAN compiler that compiles symbolic formulas into KANs; (3)\u00a0tree converter, convert KANs (or any neural networks) into tree graphs. Based on these tools, we demonstrate KANs\u2019 capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.<\/jats:p>","DOI":"10.1103\/4t7t-v19l","type":"journal-article","created":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T15:47:21Z","timestamp":1759247241000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":237,"title":["Kolmogorov-Arnold Networks Meet Science"],"prefix":"10.1103","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3581-7494","authenticated-orcid":true,"given":"Ziming","family":"Liu","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04pvzz946","id-type":"ROR","asserted-by":"publisher"}],"name":"The NSF Institute for Artificial Intelligence and Fundamental Interactions"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7670-7190","authenticated-orcid":true,"given":"Max","family":"Tegmark","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04pvzz946","id-type":"ROR","asserted-by":"publisher"}],"name":"The NSF Institute for Artificial Intelligence and Fundamental Interactions"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5698-9503","authenticated-orcid":true,"given":"Pingchuan","family":"Ma","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/042nb2s44","id-type":"ROR","asserted-by":"publisher"}],"name":"Massachusetts Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0212-5643","authenticated-orcid":true,"given":"Wojciech","family":"Matusik","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/042nb2s44","id-type":"ROR","asserted-by":"publisher"}],"name":"Massachusetts Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7305-5422","authenticated-orcid":true,"given":"Yixuan","family":"Wang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05dxps055","id-type":"ROR","asserted-by":"publisher"}],"name":"California Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,12,17]]},"reference":[{"key":"4t7t-v19lCc1R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-021-03819-2","type":"journal-article"},{"key":"4t7t-v19lCc2R1","first-page":"21573","type":"journal-article","volume":"36","author":"K. 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However, if different k values are used within the same layer, it can be challenging to parallelize these multiplications.","type":"other"},{"key":"4t7t-v19lCc10R1","unstructured":"For subnodes belonging to the multiplication node, the subnodes inherit their scores from the multiplication node.","type":"other"},{"key":"4t7t-v19lCc11R1","unstructured":"Other choices can be made based on the perceived importance of each output dimension, though this is less critical when outputs are typically one dimensional.","type":"other"},{"key":"4t7t-v19lCc12R1","doi-asserted-by":"publisher","DOI":"10.3390\/e26010041","type":"journal-article"},{"key":"4t7t-v19lCc14R1","first-page":"4860","type":"journal-article","volume":"33","author":"S.-M. Udrescu","year":"2020","journal-title":"Adv. Neural Inf. Process. 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All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92025 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"041051"}}