Learning to predict synchronization of coupled oscillators on randomly generated graphs

TL;DR

This paper introduces a machine learning approach to predict synchronization in coupled oscillators on random graphs, outperforming classical methods by leveraging initial dynamics and graph statistics, and scaling to large networks.

Contribution

It proposes a novel classification-based method using graph statistics and initial dynamics to predict synchronization, with improved accuracy over traditional theories and scalable ensemble algorithms.

Findings

High accuracy with graph statistics when topologies differ significantly.

Significant accuracy gains using initial dynamics alone in similar graph settings.

Effective ensemble prediction method for large graphs.

Abstract

Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph structure, this is an important yet analytically intractable question in general. In this work, we take an alternative approach to the synchronization prediction problem by viewing it as a classification problem based on the fact that any given system will eventually synchronize or converge to a non-synchronizing limit cycle. By only using some basic statistics of the underlying graphs such as edge density and diameter, our method can achieve perfect accuracy when there is a significant difference in the topology of the underlying graphs between the synchronizing and the non-synchronizing examples. However, in the problem setting where these graph statistics cannot distinguish the two classes very well (e.g., when the graphs are generated from the same random graph model), we find that pairing a few iterations of the initial dynamics along with the graph statistics as the input to our classification algorithms can lead to significant improvement in accuracy; far exceeding what is known by the classical oscillator theory. More surprisingly, we find that in almost all such settings, dropping out the basic graph statistics and training our algorithms with only initial dynamics achieves nearly the same accuracy. We demonstrate our method on three models of continuous and discrete coupled oscillators -- the Kuramoto model, Firefly Cellular Automata, and Greenberg-Hastings model. Finally, we also propose an "ensemble prediction" algorithm that successfully scales our method to large graphs by training on dynamics observed from multiple random subgraphs.