Learning to predict synchronization of coupled oscillators on heterogeneous graphs

Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some short period. Can we predict whether the system will eventually synchronize? Even with known underlying graph structure, this is an important but analytically intractable question in general. In this work, we take a novel approach that we call ``learning to predict synchronization'' (L2PSync), by viewing it as a classification problem for sets of initial dynamics into two classes: `synchronizing' or `non-synchronizing'. While a baseline predictor using concentration principle misses a large proportion of synchronizing examples, standard binary classification algorithms trained on large enough datasets of initial dynamics can successfully predict the unseen future of a system on highly heterogeneous sets of unknown graphs with surprising accuracy. In addition, we find that the full graph information gives only marginal improvements over what we can achieve by only using the initial dynamics. We demonstrate our method on three models of continuous and discrete coupled oscillators -- The Kuramoto model, the Firefly Cellular Automata, and the Greenberg-Hastings model. Finally, we show our method applied on larger systems is robust under using initial dynamics partially observed only on some small subgraphs.