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Learning to predict synchronization of coupled oscillators on randomly generated graphs.

Hardeep Bassi1, Richard P Yim2, Joshua Vendrow3

  • 1Department of Applied Mathematics, University of California, Merced, CA, 95343, USA.

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Summary
This summary is machine-generated.

Predicting coupled oscillator synchronization is challenging. This study uses machine learning on graph properties and initial dynamics, achieving high accuracy, even outperforming classical theory in difficult cases.

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Area of Science:

  • Complex Systems
  • Network Science
  • Dynamical Systems

Background:

  • Predicting synchronization in coupled oscillator systems is crucial but analytically intractable.
  • Existing methods struggle with unknown graph structures and complex dynamics.

Purpose of the Study:

  • To develop a machine learning approach for predicting synchronization in coupled oscillator systems.
  • To investigate the utility of graph statistics and initial system dynamics for synchronization prediction.

Main Methods:

  • Framing synchronization prediction as a classification problem.
  • Utilizing graph topology features (edge density, diameter) and initial system dynamics as input for machine learning models.
  • Testing on Kuramoto, Firefly Cellular Automata, and Greenberg-Hastings models.
  • Developing an ensemble prediction algorithm for scalability.

Main Results:

  • High prediction accuracy achieved using graph statistics when topologies differ significantly.
  • Significant accuracy improvement by incorporating initial dynamics when graph statistics are insufficient.
  • Nearly equivalent accuracy achieved using only initial dynamics in challenging cases.
  • Ensemble method successfully scales predictions to large graphs.

Conclusions:

  • Machine learning, particularly using initial dynamics, offers a powerful alternative for synchronization prediction in coupled oscillators.
  • Initial dynamics alone can be highly predictive, sometimes surpassing combined graph and dynamic features.
  • The ensemble approach enables practical application to large-scale complex systems.