Analysis of chaotic dynamical systems with autoencoders

TL;DR

This paper uses autoencoders to analyze chaotic systems, identifying minimal latent dimensions needed to capture their dynamics and preserving key properties like Lyapunov exponents.

Contribution

It introduces a method to determine the minimal autoencoder size that retains essential chaotic system dynamics.

Findings

Autoencoders can accurately replicate Lyapunov exponents of chaotic systems.

The minimal latent space dimension corresponds to the system's intrinsic complexity.

Autoencoders effectively capture the essential information of chaotic time series.

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.