Learning nonequilibrium control forces to characterize dynamical phase transitions

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.