Learning nonequilibrium control forces to characterize dynamical phase transitions

TL;DR

This paper introduces a machine learning-based method using deep neural networks and stochastic control to efficiently sample rare trajectories and analyze dynamical phase transitions in large nonequilibrium systems.

Contribution

It presents a scalable, robust algorithm that combines importance sampling, neural networks, and optimal control to study large systems near phase transitions.

Findings

Scales to hundreds of particles

Remains robust at phase transitions

Efficiently estimates large deviation functions

Abstract

Sampling the collective, dynamical fluctuations that lead to nonequilibrium pattern formation requires probing rare regions of trajectory space. Recent approaches to this problem based on importance sampling, cloning, and spectral approximations, have yielded significant insight into nonequilibrium systems, but tend to scale poorly with the size of the system, especially near dynamical phase transitions. Here we propose a machine learning algorithm that samples rare trajectories and estimates the associated large deviation functions using a many-body control force by leveraging the flexible function representation provided by deep neural networks, importance sampling in trajectory space, and stochastic optimal control theory. We show that this approach scales to hundreds of interacting particles and remains robust at dynamical phase transitions.