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Learning nonequilibrium control forces to characterize dynamical phase transitions.

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Summary
This summary is machine-generated.

This study introduces a machine learning algorithm to efficiently sample rare trajectories in complex systems. The new method scales well for large systems and remains effective near dynamical phase transitions.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Machine Learning

Background:

  • Studying nonequilibrium systems requires analyzing rare dynamical fluctuations.
  • Existing methods for sampling rare trajectories struggle with scalability, particularly near phase transitions.

Purpose of the Study:

  • To develop a scalable machine learning algorithm for sampling rare trajectories.
  • To estimate large deviation functions in systems with many interacting particles.

Main Methods:

  • Utilizing deep neural networks for flexible function representation.
  • Implementing importance sampling in trajectory space.
  • Applying stochastic optimal control theory with a many-body control force.

Main Results:

  • The proposed algorithm demonstrates scalability to systems with hundreds of interacting particles.
  • The method proves robust even at dynamical phase transitions.

Conclusions:

  • This machine learning approach offers a significant advancement in studying nonequilibrium pattern formation.
  • The algorithm provides a powerful tool for analyzing complex systems where rare events are critical.