The quasipotential is a natural generalization of the concept of energy functions to non-equilibrium systems. In the analysis of rare events in stochastic dynamics, it plays a central role in characterizing the statistics of transition events and the likely transition paths. However, computing the quasipotential is challenging, especially in high dimensional dynamical systems where a global landscape is sought. Traditional methods based on the dynamic programming principle or path space minimization tend to suffer from the curse of dimensionality. In this paper, we propose a simple and efficient machine learning method to resolve this problem. The key idea is to learn an orthogonal decomposition of the vector field that drives the dynamics, from which one can identify the quasipotential. We demonstrate on various example systems that our method can effectively compute quasipotential landscapes without requiring spatial discretization or solving path-space optimization problems. Moreover, the method is purely data driven in the sense that only observed trajectories of the dynamics are required for the computation of the quasipotential. These properties make it a promising method to enable the general application of quasipotential analysis to dynamical systems away from equilibrium.

翻译：准潜力是自然地将能源功能的概念概括为非平衡系统。 在分析随机动态的稀有事件时,它在描述过渡事件和可能的过渡路径的统计方面发挥着核心作用。然而,计算准潜力具有挑战性,特别是在寻求全球景观的高维动态系统中。基于动态编程原则或路径的空间最小化的传统方法往往受到维度诅咒的影响。在本文中,我们提出了一个简单有效的机器学习方法来解决这个问题。关键思想是学习驱动动态的矢量场的正方形分解,从中可以识别准潜能。我们在各种示例系统中展示,我们的方法可以有效地构造准潜在景观,而不需要空间分解或解决路径空间优化问题。此外,这种方法纯粹是数据驱动的,因为计算准潜能时只需要观察到动态的轨迹。这些特性使得能够将准潜能分析普遍应用到远离平衡的动态系统。