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dc.contributor.authorChernov, Alexey
dc.contributor.authorHoel, Håkon
dc.contributor.authorLaw, Kody J.H.
dc.contributor.authorNobile, Fabio
dc.contributor.authorTempone, Raul
dc.date.accessioned2020-11-30T06:57:13Z
dc.date.available2019-01-10T13:32:00Z
dc.date.available2020-11-30T06:57:13Z
dc.date.issued2018-02-02
dc.date.submitted2018-02-21
dc.identifier.citationChernov, A., Hoel, H., Law, K. J. H., Nobile, F., & Tempone, R. (2020). Multilevel ensemble Kalman filtering for spatio-temporal processes. Numerische Mathematik. doi:10.1007/s00211-020-01159-3
dc.identifier.issn0945-3245
dc.identifier.issn0029-599X
dc.identifier.doi10.1007/s00211-020-01159-3
dc.identifier.urihttp://hdl.handle.net/10754/630792
dc.description.abstractWe design and analyse the performance of a multilevel ensemble Kalman filter method (MLEnKF) for filtering settings where the underlying state-space model is an infinite-dimensional spatio-temporal process. We consider underlying models that needs to be simulated by numerical methods, with discretization in both space and time. The multilevel Monte Carlo sampling strategy, achieving variance reduction through pairwise coupling of ensemble particles on neighboring resolutions, is used in the sample-moment step of MLEnKF to produce an efficent hierarchical filtering method for spatio-temporal models. Under sufficent regularity, MLEnKF is proven to be more efficient for weak approximations than EnKF, asymptotically in the large-ensemble and fine-numerical-resolution limit. Numerical examples support our theoretical findings.
dc.description.sponsorshipResearch reported in this publication received support from the Alexander von Humboldt Foundation, KAUST CRG4 Award Ref:2584. HH acknowledges support by RWTH Aachen University and by Norges Forskningsråd, research Project 214495 LIQCRY. RT is a member of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering. KJHL was supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. KJHL was a staff scientist in the Computer Science and Mathematics Division at Oak Ridge National Laboratory (ORNL) while much of this research was done and was additionally supported by ORNL Laboratory Directed Research and Development Strategic Hire and Seed grants. We thank two referees for their comments which have greatly improved the article.
dc.publisherSpringer Nature
dc.relation.urlhttp://link.springer.com/10.1007/s00211-020-01159-3
dc.rightsThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0
dc.subjectMonte Carlo, multilevel, filtering, Kalman filter, ensemble Kalman filter, partial differential equations (PDE).
dc.titleMultilevel ensemble Kalman filtering for spatio-temporal processes
dc.typeArticle
dc.contributor.departmentOffice of the VP
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentAcademic Affairs
dc.identifier.journalNumerische Mathematik
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionInstitute for Mathematics, Carl von Ossietzky University Oldenburg, Oldenburg, Germany
dc.contributor.institutionChair of Mathematics for Uncertainty Quantification, RWTH Aachen University, Aachen, Germany
dc.contributor.institutionDepartment of Mathematics, University of Manchester, Manchester, UK
dc.contributor.institutionInstitute of Mathematics, École polytechnique fédérale de Lausanne, Lausanne, Switzerland
dc.identifier.arxivid1710.07282
kaust.personTempone, Raul
kaust.grant.numberCRG4 Award Ref:2584
dc.date.accepted2020-10-22
dc.identifier.eid2-s2.0-85096488512
refterms.dateFOA2019-01-10T13:32:00Z
kaust.acknowledged.supportUnitSRI Center for Uncertainty Quantification in Computational Science and Engineering.


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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
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