Department of Chemistry, Stanford University, Stanford, California 94305, USA.
J Chem Phys. 2022 Aug 21;157(7):074101. doi: 10.1063/5.0095593.
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 ansatz 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.
当物理系统远离平衡时，其动力学轨迹的统计分布可以提供其许多物理性质的信息。描述动力学可观测量（如电流或熵产生率）分布的性质已成为非平衡统计力学中的一个核心问题。对于一大类可观测量，在动力学是马尔可夫过程的情况下，当动力学是马尔可夫过程时，给定可观测量的分布满足大偏差原理，这意味着可以通过计算标度累积生成函数来描述长时间尺度上的波动。对于复杂的相互作用系统，解析（通常也不是数值）计算此函数并不可行，因此需要开发稳健的数值技术来进行此计算，以探究非平衡材料的性质。在这里，我们描述了一种将此任务重新表述为可以变分求解的最优控制问题的算法。我们使用针对所施加力的物理系统进行了定制的神经网络假设来求解最优控制力。我们证明了，在两个具有大量相互作用粒子的系统中，这种方法可以得到可转移且准确的解。
