Evaluating generation of chaotic time series by convolutional generative adversarial networks

TL;DR

This paper investigates the capability of convolutional GANs to generate chaotic time series, demonstrating they can replicate key chaotic properties but also produce some significant errors.

Contribution

It introduces a method to evaluate chaotic time series generation by CNN-based GANs and assesses their effectiveness in capturing complex temporal dynamics.

Findings

Generated series reproduce chaotic properties like determinism and Lyapunov exponent.

Errors occur at a low but notable rate, not fitting an exponential distribution.

GANs can mimic complex chaotic signals but have limitations in error distribution.

Abstract

To understand the ability and limitations of convolutional neural networks to generate time series that mimic complex temporal signals, we trained a generative adversarial network consisting of deep convolutional networks to generate chaotic time series and used nonlinear time series analysis to evaluate the generated time series. A numerical measure of determinism and the Lyapunov exponent, a measure of trajectory instability, showed that the generated time series well reproduce the chaotic properties of the original time series. However, error distribution analyses showed that large errors appeared at a low but non-negligible rate. Such errors would not be expected if the distribution were assumed to be exponential.