A system of coupled oscillators on an arbitrary graph is locally driven by
the tendency to mutual synchronization between nearby oscillators, but can and
often exhibit nonlinear behavior on the whole graph. Understanding such
nonlinear behavior has been a key challenge in predicting whether all
oscillators in such a system will eventually synchronize. In this paper, we
demonstrate that, surprisingly, such nonlinear behavior of coupled oscillators
can be effectively linearized in certain latent dynamic spaces. The key insight
is that there is a small number of `latent dynamics filters', each with a
specific association with synchronizing and non-synchronizing dynamics on
subgraphs so that any observed dynamics on subgraphs can be approximated by a
suitable linear combination of such elementary dynamic patterns. Taking an
ensemble of subgraph-level predictions provides an interpretable predictor for
whether the system on the whole graph reaches global synchronization. We
propose algorithms based on supervised matrix factorization to learn such
latent dynamics filters. We demonstrate that our method performs competitively
in synchronization prediction tasks against baselines and black-box
classification algorithms, despite its simple and interpretable architecture.

耦合振子在任意图上本地驱动其相互同步的趋势，但通常会在整个图上表现出非线性行为。本文中，我们展示了这种耦合振子的非线性行为可以在某些潜在动态空间中被有效线性化。我们提出了基于监督矩阵分解的算法来学习这些潜在动态过滤器。我们的方法在同步预测任务中表现出竞争力，尽管其结构简单且可解释。