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Analysis of the ensemble Kalman filter for inverse problems

Schillings, Claudia and Stuart, Andrew M. (2017) Analysis of the ensemble Kalman filter for inverse problems. SIAM Journal on Numerical Analysis, 55 (3). pp. 1264-1290. ISSN 0036-1429. https://resolver.caltech.edu/CaltechAUTHORS:20161221-112013537

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Abstract

The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences, and its gradual adoption in many other areas of application, analysis of the method is in its infancy. Furthermore, much of the existing analysis deals with the large ensemble limit, far from the regime in which the method is typically used. The goal of this paper is to analyze the method when applied to inverse problems with fixed ensemble size. A continuous-time limit is derived and the long-time behavior of the resulting dynamical system is studied. Most of the rigorous analysis is confined to the linear forward problem, where we demonstrate that the continuous time limit of the EnKF corresponds to a set of gradient flows for the data misfit in each ensemble member, coupled through a common pre-conditioner which is the empirical covariance matrix of the ensemble. Numerical results demonstrate that the conclusions of the analysis extend beyond the linear inverse problem setting. Numerical experiments are also given which demonstrate the benefits of various extensions of the basic methodology.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1137/16M105959XDOIArticle
http://epubs.siam.org/doi/abs/10.1137/16M105959XPublisherArticle
https://arxiv.org/abs/1602.02020arXivDiscussion Paper
Additional Information:© 2017, Society for Industrial and Applied Mathematics. Received by the editors February 2, 2016; accepted for publication (in revised form) November 18, 2016; published electronically May 25, 2017. This work was supported by EPSRC Programme grant EQUIP. The work of the second author was also supported by DARPA and ONR. Both authors are grateful to Dean Oliver for helpful advice.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EQUIP
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Subject Keywords:Bayesian Inverse Problems, Ensemble Kalman Filter, Optimization
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ131
Issue or Number:3
Classification Code:AMS subject classifications. 65N21, 62F15, 65N75
Record Number:CaltechAUTHORS:20161221-112013537
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161221-112013537
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73076
Collection:CaltechAUTHORS
Deposited By: Linda Taddeo
Deposited On:21 Dec 2016 19:29
Last Modified:03 Oct 2019 16:24

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