research-article

Multilevel ensemble Kalman filtering

Authors:

Kody J. H. Law,

Raul TemponeAuthors Info & Claims

SIAM Journal on Numerical Analysis, Volume 54, Issue 3

Pages 1813 - 1839

https://doi.org/10.1137/15M100955X

Published: 01 January 2016 Publication History

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.

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Multilevel ensemble Kalman filtering

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Multi-index ensemble Kalman filtering
Abstract
In this work we combine ideas from multi-index Monte Carlo and ensemble Kalman filtering (EnKF) to produce a highly efficient filtering method called multi-index EnKF (MIEnKF). MIEnKF is based on independent samples of four-coupled ...
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Ensemble Kalman filters (EnKF) based on a small ensemble tend to provide collapse of the ensemble over time. It is demonstrated that this collapse is caused by positive coupling of the ensemble members due to use of the estimated Kalman gain for the ...
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Published In

cover image SIAM Journal on Numerical Analysis

SIAM Journal on Numerical Analysis Volume 54, Issue 3

2016

632 pages

ISSN:0036-1429

DOI:10.1137/sjnaam.54.3

Issue’s Table of Contents

© 2016, Society for Industrial and Applied Mathematics.

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2016

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Cited By

Alsup THartland TPeherstorfer BPetra N(2024)Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice modelsAdvances in Computational Mathematics10.1007/s10444-024-10153-450:4Online publication date: 3-Jul-2024
https://dl.acm.org/doi/10.1007/s10444-024-10153-4
Jasra ALaw KWalton NYang S(2024)Multi-index Sequential Monte Carlo Ratio Estimators for Bayesian Inverse problemsFoundations of Computational Mathematics10.1007/s10208-023-09612-z24:4(1249-1304)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1007/s10208-023-09612-z
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https://dl.acm.org/doi/10.5555/3618408.3619415
Ruzayqat HChada NJasra A(2022)Multilevel estimation of normalization constants using ensemble Kalman–Bucy filtersStatistics and Computing10.1007/s11222-022-10094-232:3Online publication date: 1-Jun-2022
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Chada NHoel HJasra AZouraris G(2022)Improved Efficiency of Multilevel Monte Carlo for Stochastic PDE through Strong Pairwise CouplingJournal of Scientific Computing10.1007/s10915-022-02031-293:3Online publication date: 1-Dec-2022
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Zhang J(2021)Modern Monte Carlo methods for efficient uncertainty quantification and propagationWIREs Computational Statistics10.1002/wics.153913:5Online publication date: 5-Aug-2021
https://dl.acm.org/doi/10.1002/wics.1539

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