# Classification of chaotic time series with deep learning

## TL;DR

This paper demonstrates that convolutional neural networks can effectively classify chaotic versus non-chaotic univariate time series from various dynamical systems, generalizing well to complex systems.

## Contribution

It introduces a CNN-based approach that generalizes from simple to complex dynamical systems for chaos classification, outperforming existing neural network methods.

## Key findings

- CNN outperforms state-of-the-art neural networks in chaos classification
- The approach generalizes from low-dimensional to high-dimensional systems
- High accuracy achieved in classifying chaotic and non-chaotic time series

## Abstract

We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some of the most challenging real-life applications is to train different neural networks on a data set from a dynamical system with a basic or low-dimensional phase space and then use these networks to classify univariate time series of a dynamical system with more intricate or high-dimensional phase space. We illustrate this generalisation approach using the logistic map, the sine-circle map, the Lorenz system, and the Kuramoto--Sivashinsky equation. We observe that a convolutional neural network without batch normalization layers outperforms state-of-the-art neural networks for time series classification and is able to generalise and classify time series as chaotic or not with high accuracy.