Classification of chaotic time series with deep learning

Author: 

Boullé, N
Dallas, V
Nakatsukasa, Y
Samaddar, D

Publication Date: 

1 February 2020

Journal: 

Physica D: Nonlinear Phenomena

Last Updated: 

2020-07-20T14:40:25.153+01:00

Volume: 

403

DOI: 

10.1016/j.physd.2019.132261

abstract: 

© 2019 Elsevier B.V. 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 normalisation 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.

Symplectic id: 

1046397

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article