We adopt long short-term memory (LSTM) networks to model and characterize chaotic systems rather than conventional dynamical equations. We find that a well-trained LSTM system can synchronize with its learned chaotic system via transmitting a common signal. In the same fashion, we show that when learning an identical chaotic system, the trained LSTM systems can also be synchronized. Remarkably, we find that a cascading synchronization will be achieved among chaotic systems and their trained LSTM systems in the same manner. We further validate that this synchronization behavior is robust even the transmitting signal is contaminated with relatively a high level of white noise. Our work reveals that synchronization is a common behavior linking chaotic systems and their learned LSTM networks.

中文翻译：

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通过共享单个变量实现混沌系统和长期短期记忆网络的同步

我们采用长短期记忆 (LSTM) 网络来建模和表征混沌系统，而不是传统的动力学方程。我们发现一个训练有素的 LSTM 系统可以通过传输一个公共信号与其学习的混沌系统同步。以同样的方式，我们展示了在学习相同的混沌系统时，训练的 LSTM 系统也可以同步。值得注意的是，我们发现在混沌系统及其训练的 LSTM 系统之间将以相同的方式实现级联同步。我们进一步验证即使传输信号被相对较高水平的白噪声污染，这种同步行为也是稳健的。我们的工作表明，同步是连接混沌系统及其学习 LSTM 网络的常见行为。