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.

使用卷积神经网络和生成式对抗网络，我们生成了混沌时间序列，并使用非线性时间序列分析方法计算得出，该生成模型可以较好地重现原始时间序列的混沌特性，但存在学习误差。

卷积生成对抗网络生成混沌时间序列的评估

Evaluating generation of chaotic time series by convolutional generative  adversarial networks

In this work we study of the dynamics of large size random neural networks.
Different methods have been developed to analyse their behavior, most of them
rely on heuristic methods based on Gaussian assumptions regarding the
fluctuations in the limit of infinite sizes. These approaches, however, do not
justify the underlying assumptions systematically. Furthermore, they are
incapable of deriving in general the stability of the derived mean field
equations, and they are not amenable to analysis of finite size corrections.
Here we present a systematic method based on Path Integrals which overcomes
these limitations. We apply the method to a large non-linear rate based neural
network with random asymmetric connectivity matrix. We derive the Dynamic Mean
Field (DMF) equations for the system, and derive the Lyapunov exponent of the
system. Although the main results are well known, here for the first time, we
calculate the spectrum of fluctuations around the mean field equations from
which we derive the general stability conditions for the DMF states. The
methods presented here, can be applied to neural networks with more complex
dynamics and architectures. In addition, the theory can be used to compute
systematic finite size corrections to the mean field equations.

通过使用路径积分的系统方法，我们研究了大尺寸随机神经网络的动态，除了推导动态均场方程，计算系统的李雅普诺夫指数，还首次计算了均值场方程波动谱，并从中推导出参数的稳定性条件及系统的有限尺度修正。