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A system of coupled oscillators on an arbitrary graph is locally driven bythe tendency to mutual synchronization between nearby oscillators, but can andoften exhibit nonlinear behavior on the whole graph. Understanding suchnonlinear behavior has been a key challenge in predicting whether alloscillators in such a system will eventually synchronize. In this paper, wedemonstrate that, surprisingly, such nonlinear behavior of coupled oscillatorscan be effectively linearized in certain latent dynamic spaces. The key insightis that there is a small number of `latent dynamics filters', each with aspecific association with synchronizing and non-synchronizing dynamics onsubgraphs so that any observed dynamics on subgraphs can be approximated by asuitable linear combination of such elementary dynamic patterns. Taking anensemble of subgraph-level predictions provides an interpretable predictor forwhether the system on the whole graph reaches global synchronization. Wepropose algorithms based on supervised matrix factorization to learn suchlatent dynamics filters. We demonstrate that our method performs competitivelyin synchronization prediction tasks against baselines and black-boxclassification algorithms, despite its simple and interpretable architecture.

A latent linear model for nonlinear coupled oscillators on graphs