Tikhonov Regularization Within Ensemble Kalman Inversion
- Creators
- Chada, Neil K.
- Stuart, Andrew M.
- Tong, Xin T.
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.
Additional Information
© 2020 Society for Industrial and Applied Mathematics. Received by the editors February 6, 2019; accepted for publication (in revised form) January 30, 2020; published electronically April 22, 2020. The first author's research was supported by Singapore Ministry of Education Academic Research Funds Tier 2 grant MOE2016-T2-2-135. The second author's research was supported by Office of Naval Research grant 00014-17-1-2079 and National Science Foundation grant DMS-1818977. The third author's research was supported by Singapore Ministry of Education Tier 1 grant R-146-000-292-114. The authors are grateful to Vanessa Styles (University of Sussex) for providing a solver for the eikonal equation and Marco Iglesias (University of Nottingham) for providing a solver for the Darcy flow model, used, respectively, in [11, 20], and guidance on its use.Attached Files
Published - 19m1242331.pdf
Submitted - 1901.10382.pdf
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Additional details
- Eprint ID
- 97299
- Resolver ID
- CaltechAUTHORS:20190719-130631059
- MOE2016-T2-2-135
- Ministry of Education (Singapore)
- N00014-17-1-2079
- Office of Naval Research (ONR)
- DMS-1818977
- NSF
- R-146-000-292-114
- National University of Singapore
- Created
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2019-07-19Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field