Complex network perspective on modelling chaotic systems via machine learning* *Project supported by the National Natural Science Foundation of China (Grant No. 11805128), the Fund from Xihu Scholar award from Hangzhou City, and the Hangzhou Normal University Starting Fund (Grant No. 4135C50220204098)

Abstract

Recent advances have demonstrated that a machine learning technique known as “reservoir computing” is a significantly effective method for modelling chaotic systems. Going beyond short-term prediction, we show that long-term behaviors of an observed chaotic system are also preserved in the trained reservoir system by virtue of network measurements. Specifically, we find that a broad range of network statistics induced from the trained reservoir system is nearly identical with that of a learned chaotic system of interest. Moreover, we show that network measurements of the trained reservoir system are sensitive to distinct dynamics and can in turn detect the dynamical transitions in complex systems. Our findings further support that rather than dynamical equations, reservoir computing approach in fact provides an alternative way for modelling chaotic systems.