{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T20:52:03Z","timestamp":1759179123579,"version":"3.37.3"},"reference-count":27,"publisher":"IOP Publishing","issue":"1","license":[{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Universiteit van Amsterdam"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2024,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Symmetry detection, the task of discovering the underlying symmetries of a given dataset, has been gaining popularity in the machine learning community, particularly in science and engineering applications. Most previous works focus on detecting \u2018canonical\u2019 symmetries such as translation, scaling, and rotation, and cast the task as a modeling problem involving complex inductive biases and architecture design of neural networks. We challenge these assumptions and propose that instead of constructing biases, we can learn to detect symmetries from raw data without prior knowledge. The approach presented in this paper provides a flexible way to scale up the detection procedure to non-canonical symmetries, and has the potential to detect both known and unknown symmetries alike. Concretely, we focus on predicting the generators of Lie point symmetries of partial differential equations, more specifically, evolutionary equations for ease of data generation. Our results demonstrate that well-established neural network architectures are capable of recognizing symmetry generators, even in unseen dynamical systems. These findings have the potential to make non-canonical symmetries more accessible to applications, including model selection, sparse identification, and data interpretability.<\/jats:p>","DOI":"10.1088\/2632-2153\/ad2629","type":"journal-article","created":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T22:22:54Z","timestamp":1707171774000},"page":"015037","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Data-driven Lie point symmetry detection for continuous dynamical systems"],"prefix":"10.1088","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-0964-8918","authenticated-orcid":true,"given":"Alex","family":"Gabel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0299-0074","authenticated-orcid":false,"given":"Rick","family":"Quax","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8947-1332","authenticated-orcid":false,"given":"Efstratios","family":"Gavves","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2024,3,1]]},"reference":[{"key":"mlstad2629bib1","article-title":"Learning Lie groups for invariant visual perception","volume":"vol 11","author":"Rao","year":"1998"},{"article-title":"An unsupervised algorithm for learning Lie group transformations","year":"2010","author":"Sohl-Dickstein","key":"mlstad2629bib2"},{"article-title":"Learning the irreducible representations of commutative Lie groups","year":"2014","author":"Cohen","key":"mlstad2629bib3"},{"article-title":"Automatic symmetry discovery with Lie algebra convolutional network","year":"2021","author":"Dehmamy","key":"mlstad2629bib4"},{"article-title":"Detecting symmetries with neural networks","year":"2020","author":"Krippendorf","key":"mlstad2629bib5"},{"author":"Liu","key":"mlstad2629bib6","article-title":"Machine-learning hidden symmetries CoRR"},{"article-title":"Relaxing equivariance constraints with non-stationary continuous filters","year":"2022","author":"van der Ouderaa","key":"mlstad2629bib7"},{"key":"mlstad2629bib8","doi-asserted-by":"publisher","first-page":"3932","DOI":"10.1073\/pnas.1517384113","article-title":"Discovering governing equations from data by sparse identification of nonlinear dynamical systems","volume":"113","author":"Brunton","year":"2016"},{"article-title":"Physical symmetries embedded in neural networks","year":"2019","author":"Mattheakis","key":"mlstad2629bib9"},{"article-title":"Group equivariant convolutional networks","year":"2016","author":"Cohen","key":"mlstad2629bib10"},{"article-title":"A practical method for constructing equivariant multilayer perceptrons for arbitrary matrix groups","year":"2021","author":"Finzi","key":"mlstad2629bib11"},{"key":"mlstad2629bib12","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"Raissi","year":"2019","journal-title":"J. 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