Multilevel ensemble Kalman filtering algorithms

Hakon Hoel, RWTH Aachen - 11:15

The ensemble Kalman filter (EnKF) is a Monte-Carlo-based sequential filtering
method that is often both robust and efficient, but its performance may suffer
in settings where the computational cost of accurate simulations of ensemble
members/particles is high. I will present recent results [1, 2, 3] on marrying the
multilevel Monte Carlo method with EnKF to obtain the multilevel ensemble
Kalman filter (MLEnKF). The new method can be applied in the following
filtering settings:
(I) finite-dimensional state space and discrete-time observations,
(II) infinite-dimensional state space and discrete-time, finite-dimensional ob-
Theoretical results and numerical evidence of the performance gain of MLEnKF
over EnKF will be presented.
[1] H. Hoel, K. Law, and R. Tempone, Multilevel ensemble Kalman filtering,
SIAM J. Numer. Anal. 54(3), 18131839, 2016.
[2] A. Chernov, H. Hoel, K. Law, F. Nobile, and R. Tempone, Multilevel ensem-
ble Kalman filtering for spatio-temporal processes, arXiv:1710.07282, 2017.
[3] H. Hoel, G. Shaimerdenova, and R. Tempone, Multilevel Ensemble Kalman
Filtering with local-level Kalman gains, arXiv:2002.00480, 2020.