Analysis of chaotic dynamical systems with autoencoders

We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space dimension of each system and thus determines the minimal number...

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Published in:arXiv.org
Main Authors: Almazova, N, Barmparis, G D, Tsironis, G P
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 22.09.2021
Subjects:
Dynamical systems
Liapunov exponents
Neural networks
Time series
ISSN:2331-8422
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Abstract We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space dimension of each system and thus determines the minimal number of nodes necessary to capture the essential information contained in the chaotic time series. The constructed chaotic autoencoders generate similar maximal Lyapunov exponents as the original chaotic systems and thus encompass their essential dynamical information.
AbstractList We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space dimension of each system and thus determines the minimal number of nodes necessary to capture the essential information contained in the chaotic time series. The constructed chaotic autoencoders generate similar maximal Lyapunov exponents as the original chaotic systems and thus encompass their essential dynamical information.
Author Barmparis, G D
Tsironis, G P
Almazova, N
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Liapunov exponents
Neural networks
Time series
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