Multilevel ensemble Kalman filtering

Hoel, Hakon; Law, Kody J. H.; Tempone, Raul

doi:10.1137/15M100955X

Title: Multilevel ensemble Kalman filtering

Journal Article · Tue Jun 14 00:00:00 EDT 2016 · SIAM Journal on Numerical Analysis

DOI:https://doi.org/10.1137/15M100955X· OSTI ID:1302921

Hoel, Hakon ^[1]; Law, Kody J. H. ^[2]; Tempone, Raul ^[3]

Univ. of Oslo (Norway)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
King Abdullah University of Science and Technology (KAUST), Thuwal (Saudi Arabia)

This study embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. Finally, the resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1302921

Journal Information:: SIAM Journal on Numerical Analysis, Vol. 54, Issue 3; ISSN 0036-1429

Publisher:: Society for Industrial and Applied MathematicsCopyright Statement

Country of Publication:: United States

Language:: English

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Cited By (5)

Performance Analysis of Local Ensemble Kalman Filter Tong, Xin T. Journal of Nonlinear Science, Vol. 28, Issue 4 https://doi.org/10.1007/s00332-018-9453-2	journal	March 2018
Well posedness and convergence analysis of the ensemble Kalman inversion Blömker, Dirk; Schillings, Claudia; Wacker, Philipp Inverse Problems, Vol. 35, Issue 8 https://doi.org/10.1088/1361-6420/ab149c	journal	July 2019
Kalman Filtering Algorithm for Systems with Stochastic Nonlinearity Functions, Finite-Step Correlated Noises, and Missing Measurements He, Yonghui; Jiang, Jibin; Huang, Hischuan Discrete Dynamics in Nature and Society, Vol. 2018 https://doi.org/10.1155/2018/1516028	journal	January 2018
Assessment of multilevel ensemble-based data assimilation for reservoir history matching Fossum, Kristian; Mannseth, Trond; Stordal, Andreas S. Computational Geosciences, Vol. 24, Issue 1 https://doi.org/10.1007/s10596-019-09911-x	journal	December 2019
Assimilation of multiple linearly dependent data vectors Mannseth, Trond Computational Geosciences, Vol. 24, Issue 1 https://doi.org/10.1007/s10596-019-09924-6	journal	December 2019

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