Learning nonequilibrium control forces to characterize dynamical phase transitions

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.

11 pages, 5 figures. v2: corrected version, close to published version

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• Landau theory for finite-time dynamical phase transitions
• Variational deep learning of equilibrium transition path ensembles
• Modeling of biomolecular machines in non-equilibrium steady states
• Biased ensembles of pulsating active matter
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Finding the effective dynamics to make rare events typical in chaotic maps
• Computing non-equilibrium trajectories by a deep learning approach
• Convergence of the Integral Fluctuation Theorem estimator for nonequilibrium Markov systems
• An introduction to large deviations with applications in physics
• Adaptive power method for estimating large deviations in Markov chains
• Physics-informed graph neural networks enhance scalability of variational nonequilibrium optimal control
• Variational time reversal for free energy estimation in nonequilibrium steady states
• Role of interactions in non-equilibrium transformations
• Understanding random-walk dynamical phase coexistence through waiting times
• Towards neural reinforcement learning for large deviations in nonequilibrium systems with memory
• Mechanical analysis of a dynamical phase transition for particles in a channel
• Global thermodynamic manifold for conservative control of stochastic systems