Classification of chaotic time series with deep learning
This addresses the challenge of classifying chaotic behavior in time series for applications lacking precise models, though it appears incremental as it applies standard networks to known systems.
The paper tackles the problem of classifying chaotic versus non-chaotic univariate time series using deep learning, achieving high accuracy with a convolutional neural network that outperforms state-of-the-art methods.
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.