Multilevel ensemble Kalman filtering

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

doi:10.1137/15M100955X

Multilevel ensemble Kalman filtering

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

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

Abstract

This work 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. The resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.

Original language	English (US)
Pages (from-to)	1813-1839
Number of pages	27
Journal	SIAM Journal on Numerical Analysis
Volume	54
Issue number	3
DOIs	https://doi.org/10.1137/15M100955X
State	Published - Jun 14 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This research was supported by King Abdullah
University of Science and Technology (KAUST). The authors were members of the SRI Center for
Uncertainty Quantification at KAUST for much of the research reported.

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https://repository.kaust.edu.sa/bitstream/10754/617315/1/15m100955x.pdf

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title = "Multilevel ensemble Kalman filtering",

abstract = "This work 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. The resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.",

author = "Hakon Hoel and Law, {Kody J. H.} and Raul Tempone",

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AU - Law, Kody J. H.

AU - Tempone, Raul

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This research was supported by King Abdullah University of Science and Technology (KAUST). The authors were members of the SRI Center for Uncertainty Quantification at KAUST for much of the research reported.

PY - 2016/6/14

Y1 - 2016/6/14

N2 - This work 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. The resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.

AB - This work 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. 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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EP - 1839

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 3

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Multilevel ensemble Kalman filtering

Abstract

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