论文标题
一种最佳控制方法，用于计算带有跳跃的随机动力学系统最可能的过渡路径
An Optimal Control Method to Compute the Most Likely Transition Path for Stochastic Dynamical Systems with Jumps
论文作者
论文摘要
许多复杂的现实世界现象表现出突然，间歇性或跳跃行为，在非高斯莱维噪声下，它们更适合用随机微分方程来描述。在这些复杂现象中，亚稳态状态之间最可能的过渡路径很重要，因为这些罕见事件在某些情况下可能会产生很大的影响。基于大偏差原理，最可能的过渡路径可以视为在连接两个点的路径上的速率函数的最小化器。在非高斯lévy噪声下计算随机动力学系统最可能的过渡路径的挑战之一是，相关的速率函数无法通过路径明确表示。因此，我们提出一个最佳控制问题，以获得最佳状态作为最可能的过渡路径。然后，我们开发一种神经网络方法来解决此问题。对高斯和非高斯病例研究了几项实验。
Many complex real world phenomena exhibit abrupt, intermittent or jumping behaviors, which are more suitable to be described by stochastic differential equations under non-Gaussian Lévy noise. Among these complex phenomena, the most likely transition paths between metastable states are important since these rare events may have a high impact in certain scenarios. Based on the large deviation principle, the most likely transition path could be treated as the minimizer of the rate function upon paths that connect two points. One of the challenges to calculate the most likely transition path for stochastic dynamical systems under non-Gaussian Lévy noise is that the associated rate function can not be explicitly expressed by paths. For this reason, we formulate an optimal control problem to obtain the optimal state as the most likely transition path. We then develop a neural network method to solve this issue. Several experiments are investigated for both Gaussian and non-Gaussian cases.
