Machine learning for detection of equivariant finite symmetry groups in dynamical systems

Calvo-Barlés, Pablo ; Gutierrez Rodrigo, Sergio (Universidad de Zaragoza) ; Martín-Moreno, Luis

Resumen: 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.

Idioma: Inglés

DOI: 10.1088/2632-2153/ade04d

Año: 2025

Publicado en: Machine Learning: Science and Technology 6, 2 (2025), 025058 [20 pp.]
ISSN: 2632-2153

Financiación: info:eu-repo/grantAgreement/ES/DGA/Q-MAD
Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2023-148359NB-C21
Financiación: info:eu-repo/grantAgreement/ES/MICIU/CEX2023-001286-S

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Óptica (Dpto. Física Aplicada)