Machine learning for detection of equivariant finite symmetry groups in dynamical systems
In this work, we introduce the equivariance seeker model (ESM), a data-driven method for discovering the underlying finite equivariant symmetry group of an arbitrary function. ESM achieves this by optimizing a loss function that balances equivariance preservation with the penalization of redundant s...
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IOP Publishing
2025-01-01
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| Series: | Machine Learning: Science and Technology |
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| Online Access: | https://doi.org/10.1088/2632-2153/ade04d |
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| author | Pablo Calvo-Barlés Sergio G Rodrigo Luis Martín-Moreno |
| author_facet | Pablo Calvo-Barlés Sergio G Rodrigo Luis Martín-Moreno |
| author_sort | Pablo Calvo-Barlés |
| collection | DOAJ |
| description | In this work, we introduce the equivariance seeker model (ESM), a data-driven method for discovering the underlying finite equivariant symmetry group of an arbitrary function. ESM achieves this by optimizing a loss function that balances equivariance preservation with the penalization of redundant solutions, ensuring the complete and accurate identification of all symmetry transformations. We apply this framework specifically to dynamical systems, identifying their symmetry groups directly from observed trajectory data. To demonstrate its versatility, we test ESM on multiple systems in two distinct scenarios: (i) when the governing equations are known theoretically and (ii) when they are unknown, and the equivariance finding relies solely on observed data. The latter case highlights ESM’s fully data-driven capability, as it requires no prior knowledge of the system’s equations to operate. |
| format | Article |
| id | doaj-art-e27c83db3ee44823853581905aebcf4d |
| institution | OA Journals |
| issn | 2632-2153 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj-art-e27c83db3ee44823853581905aebcf4d2025-08-20T02:33:16ZengIOP PublishingMachine Learning: Science and Technology2632-21532025-01-016202505810.1088/2632-2153/ade04dMachine learning for detection of equivariant finite symmetry groups in dynamical systemsPablo Calvo-Barlés0https://orcid.org/0000-0002-8371-9840Sergio G Rodrigo1https://orcid.org/0000-0001-6575-168XLuis Martín-Moreno2https://orcid.org/0000-0001-9273-8165Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza , 50009 Zaragoza, Spain; Departamento de Física de la Materia Condensada, Universidad de Zaragoza , 50009 Zaragoza, SpainInstituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza , 50009 Zaragoza, Spain; Departamento de Física Aplicada, Universidad de Zaragoza , 50009 Zaragoza, SpainInstituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza , 50009 Zaragoza, Spain; Departamento de Física de la Materia Condensada, Universidad de Zaragoza , 50009 Zaragoza, SpainIn this work, we introduce the equivariance seeker model (ESM), a data-driven method for discovering the underlying finite equivariant symmetry group of an arbitrary function. ESM achieves this by optimizing a loss function that balances equivariance preservation with the penalization of redundant solutions, ensuring the complete and accurate identification of all symmetry transformations. We apply this framework specifically to dynamical systems, identifying their symmetry groups directly from observed trajectory data. To demonstrate its versatility, we test ESM on multiple systems in two distinct scenarios: (i) when the governing equations are known theoretically and (ii) when they are unknown, and the equivariance finding relies solely on observed data. The latter case highlights ESM’s fully data-driven capability, as it requires no prior knowledge of the system’s equations to operate.https://doi.org/10.1088/2632-2153/ade04dsymmetry detectionmachine learningdynamical systemsequivariance |
| spellingShingle | Pablo Calvo-Barlés Sergio G Rodrigo Luis Martín-Moreno Machine learning for detection of equivariant finite symmetry groups in dynamical systems Machine Learning: Science and Technology symmetry detection machine learning dynamical systems equivariance |
| title | Machine learning for detection of equivariant finite symmetry groups in dynamical systems |
| title_full | Machine learning for detection of equivariant finite symmetry groups in dynamical systems |
| title_fullStr | Machine learning for detection of equivariant finite symmetry groups in dynamical systems |
| title_full_unstemmed | Machine learning for detection of equivariant finite symmetry groups in dynamical systems |
| title_short | Machine learning for detection of equivariant finite symmetry groups in dynamical systems |
| title_sort | machine learning for detection of equivariant finite symmetry groups in dynamical systems |
| topic | symmetry detection machine learning dynamical systems equivariance |
| url | https://doi.org/10.1088/2632-2153/ade04d |
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