Learning successive weak synchronization transitions and coupling directions by reservoir computing

Synchronization prediction from oscillatory time series is one of traditional topics in nonlinear dynamics. This becomes more challenging when coupled systems show a series of different synchronization transitions when the coupling strength is progressively increased. In this work, we generalize the control parameter-aware reservoir computing to predict transitions to phase synchronization which is a rather weak form of interactions between two processes requiring long-term phase dynamics prediction. We demonstrate that a reliable long prediction for the phase variables can be achieved by considering proper bias terms and one intermittent driving variable of the target system. In addition, the reservoir computing successfully predict different transitions from phase synchronization to lag synchronization. In even weaker coupling regimes with signatures of partial synchronization, the reservoir computing predicts the coupling directions which are promising for link predictions in networks.