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.

翻译：在任意图上的耦合振子系统局部上受相邻振子相互同步趋势驱动，但整体上可能且经常呈现非线性行为。理解这类非线性行为一直是预测该系统所有振子最终是否同步的关键挑战。本文证明，令人惊讶的是，耦合振子的这类非线性行为可在某些隐动态空间中被有效线性化。核心洞见在于存在少量“隐动态滤波器”，每个滤波器与子图上同步或非同步动态具有特定关联，使得子图上的任何观测动态都可通过这些基本动态模式的适当线性组合来近似。基于子图级预测的集成，可为全图系统是否达到全局同步提供可解释的预测器。我们提出基于监督矩阵分解的算法来学习这类隐动态滤波器。实验表明，尽管架构简单且可解释，我们的方法在同步预测任务中的表现可与基线方法及黑箱分类算法相匹敌。