  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.
