Analysis of chaotic dynamical systems with autoencoders
This work addresses the problem of efficiently modeling chaotic systems for researchers in dynamical systems or machine learning, but it appears incremental as it applies an existing method (autoencoders) to a specific domain.
The paper tackled analyzing chaotic dynamical systems by using autoencoders to determine the latent space dimension and minimal nodes needed to capture essential information from chaotic time series, resulting in autoencoders that generate similar maximal Lyapunov exponents as the original systems.
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.