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:
-
- Univ. of Oslo (Norway)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- King Abdullah University of Science and Technology (KAUST), Thuwal (Saudi Arabia)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (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:
- 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. https://doi.org/10.1137/15M100955X
Hoel, Hakon, Law, Kody J. H., and Tempone, Raul. Tue .
"Multilevel ensemble Kalman filtering". United States. https://doi.org/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}
}
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Performance Analysis of Local Ensemble Kalman Filter
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Kalman Filtering Algorithm for Systems with Stochastic Nonlinearity Functions, Finite-Step Correlated Noises, and Missing Measurements
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Assessment of multilevel ensemble-based data assimilation for reservoir history matching
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