# A latent linear model for nonlinear coupled oscillators on graphs

arXiv: https://arxiv.org/abs/2311.14910 · HTML: https://mlsanity.com/paper/2311.14910/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 65 references that are in the map.
- First posted on arXiv 25 Nov 2023.

## Builds on (most cited first, 17 of 17)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Long-term Recurrent Convolutional Networks for Visual Recognition and Description](https://mlsanity.com/paper/1411.4389/) (2014)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [Anticipating synchronization with machine learning](https://mlsanity.com/paper/2103.13358/) (2021)
- [Non-negative Matrix Factorization: Robust Extraction of Extended Structures](https://mlsanity.com/paper/1712.10317/) (2017)
- [Block majorization-minimization with diminishing radius for constrained nonsmooth nonconvex optimization](https://mlsanity.com/paper/2012.03503/) (2020)
- [Sampling random graph homomorphisms and applications to network data analysis](https://mlsanity.com/paper/1910.09483/) (2019)
- [Learning low-rank latent mesoscale structures in networks](https://mlsanity.com/paper/2102.06984/) (2021)
- [Evaluating the phase dynamics of coupled oscillators via time-variant topological features](https://mlsanity.com/paper/2005.03343/) (2020)
- [ALX: Large Scale Matrix Factorization on TPUs](https://mlsanity.com/paper/2112.02194/) (2021)
- [Exponentially Convergent Algorithms for Supervised Matrix Factorization](https://mlsanity.com/paper/2311.11182/) (2023)
- [Synchronization of finite-state pulse-coupled oscillators](https://mlsanity.com/paper/1407.1103/) (2014)
- [Global synchronization of pulse-coupled oscillators on trees](https://mlsanity.com/paper/1604.08381/) (2016)
- [Learning to predict synchronization of coupled oscillators on randomly generated graphs](https://mlsanity.com/paper/2012.14048/) (2020)
- [Supervised Dictionary Learning with Auxiliary Covariates](https://mlsanity.com/paper/2206.06774/) (2022)
- [Unraveling Low-Dimensional Network Dynamics: A Fusion of Sparse Identification and Proper Orthogonal Decomposition](https://mlsanity.com/paper/2308.10458/) (2023)

## Abstract (arXiv)

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.