Full Lyapunov exponents spectrum with Deep Learning from single-variable time series

Mayora-Cebollero, Carmen (Universidad de Zaragoza) ; Mayora-Cebollero, Ana (Universidad de Zaragoza) ; Lozano, Álvaro (Universidad de Zaragoza) ; Barrio, Roberto (Universidad de Zaragoza)

Resumen: In this article we study if a Deep Learning technique can be used to obtain an approximate value of the Lyapunov exponents of a dynamical system. Moreover, we want to know if Machine Learning techniques are able, once trained, to provide the full Lyapunov exponents spectrum with just single-variable time series. We train a Convolutional Neural Network and use the resulting network to approximate the full spectrum using the time series of just one variable from the studied systems (Lorenz system and coupled Lorenz system). The results are quite surprising since all the values are well approximated with only partial data. This strategy allows to speed up the complete analysis of the systems and also to study the hyperchaotic dynamics in the coupled Lorenz system.

Idioma: Inglés

DOI: 10.1016/j.physd.2024.134510

Año: 2024

Publicado en: PHYSICA D-NONLINEAR PHENOMENA 472 (2024), 134510 [17 pp.]
ISSN: 0167-2789

Factor impacto JCR: 2.9 (2024)

Categ. JCR: MATHEMATICS, APPLIED rank: 22 / 343 = 0.064 (2024) - Q1 - T1
Categ. JCR: PHYSICS, FLUIDS & PLASMAS rank: 9 / 41 = 0.22 (2024) - Q1 - T1
Categ. JCR: PHYSICS, MATHEMATICAL rank: 8 / 61 = 0.131 (2024) - Q1 - T1
Categ. JCR: PHYSICS, MULTIDISCIPLINARY rank: 35 / 114 = 0.307 (2024) - Q2 - T1

Factor impacto SCIMAGO: 0.94 - Applied Mathematics (Q1) - Condensed Matter Physics (Q1) - Mathematical Physics (Q1) - Statistical and Nonlinear Physics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/AEI/PID2021-122961NB-I00
Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-23R
Financiación: info:eu-repo/grantAgreement/ES/DGA/E24-23R
Financiación: info:eu-repo/grantAgreement/ES/DGA/LMP94_21

Tipo y forma: Article (Published version)

Área (Departamento): Área Geometría y Topología (Dpto. Matemáticas)
Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)