  Suppose we are given a system of coupled oscillators on an arbitrary graph
along with the trajectory of the system during some period. Can we predict
whether the system will eventually synchronize? This is an important but
analytically intractable question especially when the structure of the
underlying graph is highly varied. In this work, we take an entirely different
approach that we call "learning to predict synchronization" (L2PSync), by
viewing it as a classification problem for sets of graphs paired with initial
dynamics into two classes: `synchronizing' or `non-synchronizing'. Our
conclusion is that, once trained on large enough datasets of synchronizing and
non-synchronizing dynamics on heterogeneous sets of graphs, a number of binary
classification algorithms can successfully predict the future of an unknown
system with surprising accuracy. We also propose an "ensemble prediction"
algorithm that scales up our method to large graphs by training on dynamics
observed from multiple random subgraphs. We find that in many instances, the
first few iterations of the dynamics are far more important than the static
features of the graphs. 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.
