A latent linear model for nonlinear coupled oscillators on graphs
Agam Goyal Zhaoxing Wu Richard P. Yim Binhao Chen Zihong Xu Hanbaek Lyu
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.