We design and analyse the performance of a multilevel ensemble Kalman filter method (MLEnKF) for filtering settings where the underlying state-space model is an infinite-dimensional spatio-temporal process. We consider underlying models that needs to be simulated by numerical methods, with discretization in both space and time. The multilevel Monte Carlo sampling strategy, achieving variance reduction through pairwise coupling of ensemble particles on neighboring resolutions, is used in the sample-moment step of MLEnKF to produce an efficent hierarchical filtering method for spatio-temporal models. Under sufficent regularity, MLEnKF is proven to be more efficient for weak approximations than EnKF, asymptotically in the large-ensemble and fine-numerical-resolution limit. Numerical examples support our theoretical findings.
|Original language||English (US)|
|State||Published - Feb 2 2018|
Bibliographical noteKAUST Repository Item: Exported on 2020-12-02
Acknowledged KAUST grant number(s): CRG4 Award Ref:2584
Acknowledgements: Research reported in this publication received support from the Alexander von Humboldt Foundation, KAUST CRG4 Award Ref:2584. HH acknowledges support by RWTH Aachen University and by Norges Forskningsråd, research Project 214495 LIQCRY. RT is a member of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering. KJHL was supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. KJHL was a staff scientist in the Computer Science and Mathematics Division at Oak Ridge National Laboratory (ORNL) while much of this research was done and was additionally supported by ORNL Laboratory Directed Research and Development Strategic Hire and Seed grants. We thank two referees for their comments which have greatly improved the article.