Multilevel ensemble Kalman filtering

Handle URI:
http://hdl.handle.net/10754/624861
Title:
Multilevel ensemble Kalman filtering
Authors:
Hoel, Haakon; Chernov, Alexey; Law, Kody; Nobile, Fabio; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
The ensemble Kalman filter (EnKF) is a sequential filtering method that uses an ensemble of particle paths to estimate the means and covariances required by the Kalman filter by the use of sample moments, i.e., the Monte Carlo method. EnKF is often both robust and efficient, but its performance may suffer in settings where the computational cost of accurate simulations of particles is high. The multilevel Monte Carlo method (MLMC) is an extension of classical Monte Carlo methods which by sampling stochastic realizations on a hierarchy of resolutions may reduce the computational cost of moment approximations by orders of magnitude. In this work we have combined the ideas of MLMC and EnKF to construct the multilevel ensemble Kalman filter (MLEnKF) for the setting of finite dimensional state and observation spaces. The main ideas of this method is to compute particle paths on a hierarchy of resolutions and to apply multilevel estimators on the ensemble hierarchy of particles to compute Kalman filter means and covariances. Theoretical results and a numerical study of the performance gains of MLEnKF over EnKF will be presented. Some ideas on the extension of MLEnKF to settings with infinite dimensional state spaces will also be presented.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
Issue Date:
8-Jan-2016
Type:
Presentation
Appears in Collections:
Applied Mathematics and Computational Science Program; Presentations; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)

Full metadata record

DC FieldValue Language
dc.contributor.authorHoel, Haakonen
dc.contributor.authorChernov, Alexeyen
dc.contributor.authorLaw, Kodyen
dc.contributor.authorNobile, Fabioen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2017-06-08T06:32:30Z-
dc.date.available2017-06-08T06:32:30Z-
dc.date.issued2016-01-08-
dc.identifier.urihttp://hdl.handle.net/10754/624861-
dc.description.abstractThe ensemble Kalman filter (EnKF) is a sequential filtering method that uses an ensemble of particle paths to estimate the means and covariances required by the Kalman filter by the use of sample moments, i.e., the Monte Carlo method. EnKF is often both robust and efficient, but its performance may suffer in settings where the computational cost of accurate simulations of particles is high. The multilevel Monte Carlo method (MLMC) is an extension of classical Monte Carlo methods which by sampling stochastic realizations on a hierarchy of resolutions may reduce the computational cost of moment approximations by orders of magnitude. In this work we have combined the ideas of MLMC and EnKF to construct the multilevel ensemble Kalman filter (MLEnKF) for the setting of finite dimensional state and observation spaces. The main ideas of this method is to compute particle paths on a hierarchy of resolutions and to apply multilevel estimators on the ensemble hierarchy of particles to compute Kalman filter means and covariances. Theoretical results and a numerical study of the performance gains of MLEnKF over EnKF will be presented. Some ideas on the extension of MLEnKF to settings with infinite dimensional state spaces will also be presented.en
dc.titleMultilevel ensemble Kalman filteringen
dc.typePresentationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 5-10, 2016en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)en
dc.conference.locationKAUSTen
dc.contributor.institutionUniversity of Osloen
dc.contributor.institutionÉcole Polytechnique Fédérale de Lausanneen
dc.contributor.institutionOak Ridge National Laboratoryen
kaust.authorTempone, Raulen
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