Digital Twins of Networked Dynamical Systems: Machine Learning Prediction of Synchronization Transitions in Coupled Chaotic Oscillators

Abstract

Collective behaviors such as synchronization transitions are emergent properties of coupled oscillator systems, and how to reproduce them from data for large-scale systems remains an open problem. Here we propose a model-free coupled reservoir computing (CRC) architecture for constructing digital twins of coupled oscillator systems. The CRC decomposes the twin into three modules that mimic the nodal dynamics, the coupling function, and the coupling network, respectively, so that the modules can be reassembled for different coupled systems. Importantly, it is found that the trained CRC reproduces not only the collective states, including complete synchronization, phase synchronization, and chimera states, but also the synchronization transitions as the coupling strength varies, and the predicted collective behaviors are practically identical to those obtained by direct simulations of the original system. Moreover, the CRC is trained only on the time series of an isolated oscillator and of a pair of coupled oscillators, and the trained modules can be reused for different complex networks and for non-identical oscillators. Our findings establish the CRC architecture as a promising platform for digital twins of complex systems.