Synchronization of chaotic systems and their machine-learning models

Tongfeng Weng, Huijie Yang, Changgui Gu, Jie Zhang, Michael Small

Research output: Contribution to journalArticlepeer-review

75 Citations (Scopus)


Recent advances have demonstrated the effectiveness of a machine-learning approach known as "reservoir computing" for model-free prediction of chaotic systems. We find that a well-trained reservoir computer can synchronize with its learned chaotic systems by linking them with a common signal. A necessary condition for achieving this synchronization is the negative values of the sub-Lyapunov exponents. Remarkably, we show that by sending just a scalar signal, one can achieve synchronism in trained reservoir computers and a cascading synchronization among chaotic systems and their fitted reservoir computers. Moreover, we demonstrate that this synchronization is maintained even in the presence of a parameter mismatch. Our findings possibly provide a path for accurate production of all expected signals in unknown chaotic systems using just one observational measure.

Original languageEnglish
Article number042203
JournalPhysical Review E
Issue number4
Publication statusPublished - 5 Apr 2019


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