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控制理论和非线性滤波讨论班
Importance Sampling for Rare Event Tracking within the Ensemble Kalman Filtering Framework
Importance Sampling for Rare Event Tracking within the Ensemble Kalman Filtering Framework
组织者
演讲者
孙泽钜
时间
2024年03月27日 14:30 至 15:00
地点
理科楼A-304
摘要
We will review and discuss the paper entitled ‘Importance Sampling for Rare Event Tracking within the Ensemble Kalman Filtering Framework’ by N. B. Rached et al. The abstract of this paper is as follows: ‘In this work we employ importance sampling (IS) techniques to track a small over-threshold probability of a running maximum associated with the solution of a stochastic differential equation (SDE) within the framework of ensemble Kalman filtering (EnKF). Between two observation times of the EnKF, we propose to use IS with respect to the initial condition of the SDE, IS with respect to the Wiener process via a stochastic optimal control formulation, and combined IS with respect to both initial condition and Wiener process. Both IS strategies require the approximation of the solution of Kolmogorov Backward equation (KBE) with boundary conditions. In multidimensional settings, we employ a Markovian projection dimension reduction technique to obtain an approximation of the solution of the KBE by just solving a one dimensional PDE. The proposed ideas are tested on two illustrative examples: Double Well SDE and Langevin dynamics, and showcase a significant variance reduction compared to the standard Monte Carlo method and another sampling-based IS technique, namely, multilevel cross entropy.