Anticipating synchronization with machine learning

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.

arXiv comment13 pages; 12 figures

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• Early warning signals for critical transitions in complex systems
• Catch-22s of reservoir computing
• Criticality in Reservoir Computer of Coupled Phase Oscillators
• Reduced-order adaptive synchronization in a chaotic neural network with parameter mismatch: A dynamical system vs. machine learning approach
• Role of assortativity in predicting burst synchronization using echo state network
• Early detection of synchrony in coupled oscillator model
• Predicting the Onset of Quantum Synchronization Using Machine Learning
• Estimating the master stability function from the time series of one oscillator via reservoir computing
• How more data can hurt: Instability and regularization in next-generation reservoir computing
• Thermodynamic limit in learning period three
• Fold Bifurcation Identification through Scientific Machine Learning