Deterministic Mean-Field Ensemble Kalman Filtering

Handle URI:
http://hdl.handle.net/10754/608649
Title:
Deterministic Mean-Field Ensemble Kalman Filtering
Authors:
Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
KAUST Department:
SRI Uncertainty Quantification Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Deterministic Mean-Field Ensemble Kalman Filtering 2016, 38 (3):A1251 SIAM Journal on Scientific Computing
Publisher:
Society for Industrial &amp; Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
3-May-2016
DOI:
10.1137/140984415
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This work was supported by the King Abdullah University of Science and Technology (KAUST) SRI-UQ Center.
Additional Links:
http://epubs.siam.org/doi/10.1137/140984415
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLaw, Kody J. H.en
dc.contributor.authorTembine, Hamidouen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2016-05-09T08:16:21Zen
dc.date.available2016-05-09T08:16:21Zen
dc.date.issued2016-05-03en
dc.identifier.citationDeterministic Mean-Field Ensemble Kalman Filtering 2016, 38 (3):A1251 SIAM Journal on Scientific Computingen
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/140984415en
dc.identifier.urihttp://hdl.handle.net/10754/608649en
dc.description.abstractThe proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.en
dc.description.sponsorshipThis work was supported by the King Abdullah University of Science and Technology (KAUST) SRI-UQ Center.en
dc.language.isoenen
dc.publisherSociety for Industrial &amp; Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/140984415en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjectfilteringen
dc.subjectFokker--Plancken
dc.subjectEnKFen
dc.titleDeterministic Mean-Field Ensemble Kalman Filteringen
dc.typeArticleen
dc.contributor.departmentSRI Uncertainty Quantification Centeren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionComputer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831en
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorLaw, Kody J. H.en
kaust.authorTembine, Hamidouen
kaust.authorTempone, Raulen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.