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.

翻译：为理解卷积神经网络在生成模拟复杂时间信号的时间序列方面的能力与局限性，我们训练了一个由深度卷积网络构成的生成对抗网络，用于生成混沌时间序列，并采用非线性时间序列分析方法对生成的时间序列进行评估。确定性数值度量与李雅普诺夫指数（一种轨迹不稳定性度量）表明，生成的时间序列能较好地再现原始时间序列的混沌特性。然而，误差分布分析显示，虽然出现大误差的概率较低，但这一概率不可忽略。若假设误差分布服从指数分布，则此类大误差本不应出现。