skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Multilevel ensemble Kalman filtering

Abstract

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

Authors:
 [1];  [2];  [3]
  1. Univ. of Oslo (Norway)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  3. King Abdullah University of Science and Technology (KAUST), Thuwal (Saudi Arabia)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1302921
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
SIAM Journal on Numerical Analysis
Additional Journal Information:
Journal Volume: 54; Journal Issue: 3; Journal ID: ISSN 0036-1429
Publisher:
Society for Industrial and Applied Mathematics
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Monte Carlo; multilevel; ltering; Kalman lter; ensemble Kalman lter

Citation Formats

Hoel, Hakon, Law, Kody J. H., and Tempone, Raul. Multilevel ensemble Kalman filtering. United States: N. p., 2016. Web. doi:10.1137/15M100955X.
Hoel, Hakon, Law, Kody J. H., & Tempone, Raul. Multilevel ensemble Kalman filtering. United States. doi:10.1137/15M100955X.
Hoel, Hakon, Law, Kody J. H., and Tempone, Raul. Tue . "Multilevel ensemble Kalman filtering". United States. doi:10.1137/15M100955X. https://www.osti.gov/servlets/purl/1302921.
@article{osti_1302921,
title = {Multilevel ensemble Kalman filtering},
author = {Hoel, Hakon and Law, Kody J. H. and Tempone, Raul},
abstractNote = {This study 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. Finally, the resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.},
doi = {10.1137/15M100955X},
journal = {SIAM Journal on Numerical Analysis},
number = 3,
volume = 54,
place = {United States},
year = {Tue Jun 14 00:00:00 EDT 2016},
month = {Tue Jun 14 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

Save / Share: