Anticipating synchronization with machine learning

TL;DR

This paper introduces a data-driven machine learning framework using reservoir computing to predict synchronization transitions in dynamical systems, including complex first-order and hysteresis behaviors, without requiring system equations.

Contribution

It develops a novel parameter-aware machine learning approach that accurately predicts both continuous and abrupt synchronization transitions in unknown dynamical systems.

Findings

Successfully predicts synchronization onset in chaotic models.

Accurately captures first-order transition and hysteresis features.

Demonstrates effectiveness on small network systems with complex transitions.

Abstract

In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In experimental and real settings, the system equations are often unknown, raising the need to develop a prediction framework that is model free and fully data driven. We contemplate that this challenging problem can be addressed with machine learning. In particular, exploiting reservoir computing or echo state networks, we devise a "parameter-aware" scheme to train the neural machine using asynchronous time series, i.e., in the parameter regime prior to the onset of synchronization. A properly trained machine will possess the power to predict the synchronization transition in that, with a given amount of parameter drift, whether the system would remain asynchronous or exhibit synchronous dynamics can be accurately anticipated. We demonstrate the machine-learning based framework using representative chaotic models and small network systems that exhibit continuous (second-order) or abrupt (first-order) transitions. A remarkable feature is that, for a network system exhibiting an explosive (first-order) transition and a hysteresis loop in synchronization, the machine learning scheme is capable of accurately predicting these features, including the precise locations of the transition points associated with the forward and backward transition paths.