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Anticipating measure synchronization in coupled Hamiltonian systems with machine learning.

Han Zhang1, Huawei Fan2, Yao Du1

  • 1School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.

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Summary

This study introduces a model-free machine learning method to predict measure synchronization in coupled Hamiltonian systems. The approach accurately forecasts critical coupling parameters and system behavior near synchronization transitions.

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Area of Science:

  • Physics
  • Complex Systems
  • Machine Learning

Background:

  • Coupled Hamiltonian systems exhibit complex dynamics, including measure synchronization.
  • Predicting synchronization transitions in these systems is challenging due to their complexity.

Purpose of the Study:

  • To develop a model-free approach for anticipating measure synchronization in coupled Hamiltonian systems.
  • To leverage machine learning for predicting synchronization critical points and system dynamics.

Main Methods:

  • Utilized parameter-aware reservoir computing, a machine learning technique.
  • Trained a machine learning model on time series data from coupled Hamiltonian systems at various coupling parameters.

Main Results:

  • The trained model accurately predicted critical coupling parameters for measure synchronization.
  • The model successfully forecasted the variation of system order parameters around synchronization transitions.
  • Demonstrated effectiveness in systems with two coupled oscillators and three globally coupled oscillators.

Conclusions:

  • Model-free, data-driven analysis using machine learning is effective for studying measure synchronization.
  • This approach offers a powerful tool for analyzing large-size Hamiltonian systems and complex synchronization phenomena.