Importance sampling for rare event tracking within the ensemble Kalman filtering framework
<|reference_start|>Importance sampling for rare event tracking within the ensemble Kalman filtering framework: 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 three illustrative examples: Double Well SDE, Langevin dynamics and noisy Charney-deVore model, and showcase a significant variance reduction compared to the standard Monte Carlo method and another sampling-based IS technique, namely, multilevel cross entropy.<|reference_end|>
@article{rached2024importance,
    title={Importance sampling for rare event tracking within the ensemble Kalman
  filtering framework},
    author={Nadhir Ben Rached, Erik von Schwerin, Gaukhar Shaimerdenova and Raul
  Tempone},
    journal={arXiv preprint arXiv:2403.12793},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.12793},
    primaryClass={math.NA cs.NA math.DS math.OC math.PR}
}