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Tikhonov Regularization Within Ensemble Kalman Inversion

Chada, Neil K. and Stuart, Andrew M. and Tong, Xin T. (2019) Tikhonov Regularization Within Ensemble Kalman Inversion. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190719-130631059

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Abstract

Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewed as a derivative-free optimization method. In its most basic form it regularizes ill-posed inverse problems through the subspace property: the solution found is in the linear span of the initial ensemble employed. In this work we demonstrate how further regularization can be imposed, incorporating prior information about the underlying unknown. In particular we study how to impose Tikhonov-like Sobolev penalties. As well as introducing this modified ensemble Kalman inversion methodology, we also study its continuous-time limit, proving ensemble collapse; in the language of multi-agent optimization this may be viewed as reaching consensus. We also conduct a suite of numerical experiments to highlight the benefits of Tikhonov regularization in the ensemble inversion context.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1901.10382arXivDiscussion Paper
ORCID:
AuthorORCID
Chada, Neil K.0000-0002-2180-0985
Additional Information:NKC acknowledges a Singapore Ministry of Education Academic Research Funds Tier 2 grant [MOE2016-T2-2-135]. The work of AMS was funded by US ONR grant N00014-17-1-2079 and the US AFOSR grant FA9550-17-1-0185. The research of XTT is supported by the National University of Singapore grant R-146-000-226-133. The authors are grateful to Vanessa Styles (University of Sussex) for providing a solver for the eikonal equation, and guidance on its use.
Funders:
Funding AgencyGrant Number
Ministry of Education (Singapore)MOE2016-T2-2-135
Office of Naval Research (ONR)N00014-17-1-2079
Air Force Office of Scientific Research (AFOSR)FA9550-17-1-0185
National University of SingaporeR-146-000-226-133
Subject Keywords:Ensemble Kalman inversion, Bayesian inverse problems, Tikhonov regularizartion, long-term behaviour
Classification Code:AMS subject classifications: 35Q93, 58E25, 65F22, 65M32
Record Number:CaltechAUTHORS:20190719-130631059
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190719-130631059
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97299
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:19 Jul 2019 20:21
Last Modified:19 Jul 2019 20:21

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