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)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material.
Exportado de SIDERAL (2025-10-17-14:32:23)
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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)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material. Exportado de SIDERAL (2025-10-17-14:32:23)
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Record created 2025-02-10, last modified 2025-10-17