State space

Quantum mechanics

Algorithm

Normalization (sociology)

Chaotic

Biology

Statistics

Multivariate statistics

Time series

Lorenz system

Phase space

Computer science

Anthropology

Paleontology

Thermodynamics

Physics

Pattern recognition (psychology)

Mathematics

Dynamical system (definition)

Sociology

Artificial intelligence

Series (stratigraphy)

Logistic map

Dynamical systems theory

Artificial neural network

Machine learning

Univariate

Physica D Nonlinear Phenomena

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.

Classification of chaotic time series with deep learning