Physics-informed graph neural networks enhance scalability of variational nonequilibrium optimal control

TL;DR

This paper introduces a physics-informed graph neural network approach to efficiently compute large deviation functions in nonequilibrium systems by formulating the problem as an optimal control task solved variationally.

Contribution

It develops a novel neural network-based variational method to solve large deviation problems in complex nonequilibrium systems, improving scalability and transferability.

Findings

Accurately computes large deviation functions in interacting particle systems.

Demonstrates transferability of neural network solutions across different physical systems.

Provides a scalable algorithm for nonequilibrium statistical mechanics problems.

Abstract

When a physical system is driven away from equilibrium, the statistical distribution of its dynamical trajectories informs many of its physical properties. Characterizing the nature of the distribution of dynamical observables, such as a current or entropy production rate, has become a central problem in nonequilibrium statistical mechanics. Asymptotically, for a broad class of observables, the distribution of a given observable satisfies a large deviation principle when the dynamics is Markovian, meaning that fluctuations can be characterized in the long-time limit by computing a scaled cumulant generating function. Calculating this function is not tractable analytically (nor often numerically) for complex, interacting systems, so the development of robust numerical techniques to carry out this computation is needed to probe the properties of nonequilibrium materials. Here, we describe an algorithm that recasts this task as an optimal control problem that can be solved variationally. We solve for optimal control forces using neural network ans\"atze that are tailored to the physical systems to which the forces are applied. We demonstrate that this approach leads to transferable and accurate solutions in two systems featuring large numbers of interacting particles.