Classification of chaotic time series with deep learning

PHYSICA D-NONLINEAR PHENOMENA

卷:403

Article

Boulle, Nicolas¹  Dallas, Vassilios¹  Nakatsukasa, Yuji¹  Samaddar, D.² 

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

[2] United Kingdom Atom Energy Author, Culham Ctr Fus Energy, Culham Sci Ctr, Abingdon OX14 3DB, Oxon, England

关键词: Dynamical systems;    Chaos;    Deep learning;    Time series;    Classification;   

DOI  :  10.1016/j.physd.2019.132261

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free