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Parameterizations for ensemble Kalman inversion

Chada, Neil K. and Iglesias, Marco A. and Roininen, Lassi and Stuart, Andrew M. (2018) Parameterizations for ensemble Kalman inversion. Inverse Problems, 34 (5). Art. No. 055009. ISSN 0266-5611. https://resolver.caltech.edu/CaltechAUTHORS:20180413-092058450

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Abstract

The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which lie in the linear span of the initial ensemble. Choice of the parameterization of the unknown field is thus a key component of the success of the method. We demonstrate how both geometric ideas and hierarchical ideas can be used to design effective parameterizations for a number of applied inverse problems arising in electrical impedance tomography, groundwater flow and source inversion. In particular we show how geometric ideas, including the level set method, can be used to reconstruct piecewise continuous fields, and we show how hierarchical methods can be used to learn key parameters in continuous fields, such as length-scales, resulting in improved reconstructions. Geometric and hierarchical ideas are combined in the level set method to find piecewise constant reconstructions with interfaces of unknown topology.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1088/1361-6420/aab6d9DOIArticle
http://iopscience.iop.org/article/10.1088/1361-6420/aab6d9/metaPublisherArticle
https://arxiv.org/abs/1709.01781arXivDiscussion Paper
ORCID:
AuthorORCID
Chada, Neil K.0000-0002-2180-0985
Iglesias, Marco A.0000-0002-8952-717X
Additional Information:© 2018 IOP Publishing Ltd. Received 6 September 2017; Accepted 15 March 2018; Accepted Manuscript online 15 March 2018; Published 13 April 2018. The authors are grateful to M. M. Dunlop, O. Papaspiliopoulos and G. O. Roberts for helpful discussions about centering and non-centering parameterizations. The research of AMS was partially supported by the EPSRC programme grant EQUIP and by AFOSR Grant FA9550-17-1-0185. LR was supported by the EPSRC programme grant EQUIP. NKC was partially supported by the EPSRC MASDOC Graduate Training Program and by Premier Oil.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EQUIP
Air Force Office of Scientific Research (AFOSR)FA9550-17-1-0185
Premier OilUNSPECIFIED
Subject Keywords:Ensemble Kalman inversion, hierarchical inversion, centered and non-centered parameterizations, discontinuous reconstructions, level set methods
Issue or Number:5
Classification Code:PACS numbers: 62M20, 49N45, G5L09
Record Number:CaltechAUTHORS:20180413-092058450
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180413-092058450
Official Citation:Neil K Chada et al 2018 Inverse Problems 34 055009
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85818
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Apr 2018 17:22
Last Modified:03 Oct 2019 19:36

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