Evaluating generation of chaotic time series by convolutional generative adversarial networks
This work addresses the challenge of mimicking complex temporal signals for applications in time series analysis, but it is incremental as it builds on existing GAN methods.
The researchers tackled the problem of generating chaotic time series using convolutional generative adversarial networks, finding that the generated series reproduced chaotic properties like determinism and Lyapunov exponents well, but with large errors occurring at a low but non-negligible rate.
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.