Parameterizations for ensemble Kalman inversion

Chada, Neil; Iglesias, Marco; Lassi, Roininen; Stuart, Andrew M.

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.

Citation

Chada, N., Iglesias, M., Lassi, R., & Stuart, A. M. (2018). Parameterizations for ensemble Kalman inversion. Inverse Problems, 34(5), https://doi.org/10.1088/1361-6420/aab6d9

• Journal Article Type: Article
• Acceptance Date: Mar 15, 2018
• Online Publication Date: Apr 13, 2018
• Publication Date: May 30, 2018
• Deposit Date: May 4, 2018
• Publicly Available Date: Apr 14, 2019
• Journal: Inverse Problems
• Print ISSN: 0266-5611
• Electronic ISSN: 0266-5611
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Issue: 5
• DOI: https://doi.org/10.1088/1361-6420/aab6d9
• Public URL: https://nottingham-repository.worktribe.com/output/934544
• Publisher URL: http://iopscience.iop.org/article/10.1088/1361-6420/aab6d9/meta
• Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6420/aab6d9.