An Optimal Control Method to Compute the Most Likely Transition Path for Stochastic Dynamical Systems with Jumps
This work addresses a challenge in modeling rare events with jumps in complex systems, which is incremental as it applies a neural network to an existing optimal control formulation for a specific domain.
The authors tackled the problem of computing the most likely transition paths for stochastic dynamical systems with jumps under non-Gaussian Lévy noise, by formulating it as an optimal control problem and developing a neural network method to solve it, with experiments conducted for both Gaussian and non-Gaussian cases.
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.