Parameterizations for ensemble Kalman inversion
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...
| Main Authors: | , , , |
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| Format: | Article |
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IOP Publishing
2018
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| Online Access: | https://eprints.nottingham.ac.uk/51560/ |
| _version_ | 1848798523820081152 |
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| author | Chada, Neil Iglesias, Marco Lassi, Roininen Stuart, Andrew M. |
| author_facet | Chada, Neil Iglesias, Marco Lassi, Roininen Stuart, Andrew M. |
| author_sort | Chada, Neil |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:21:08Z |
| format | Article |
| id | nottingham-51560 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:21:08Z |
| publishDate | 2018 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-515602020-05-04T19:37:59Z https://eprints.nottingham.ac.uk/51560/ Parameterizations for ensemble Kalman inversion Chada, Neil Iglesias, Marco Lassi, Roininen Stuart, Andrew M. 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. IOP Publishing 2018-05-30 Article PeerReviewed Chada, Neil, Iglesias, Marco, Lassi, Roininen and Stuart, Andrew M. (2018) Parameterizations for ensemble Kalman inversion. Inverse Problems, 34 (5). 055009. ISSN 0266-5611 http://iopscience.iop.org/article/10.1088/1361-6420/aab6d9/meta doi:10.1088/1361-6420/aab6d9 doi:10.1088/1361-6420/aab6d9 |
| spellingShingle | Chada, Neil Iglesias, Marco Lassi, Roininen Stuart, Andrew M. Parameterizations for ensemble Kalman inversion |
| title | Parameterizations for ensemble Kalman inversion |
| title_full | Parameterizations for ensemble Kalman inversion |
| title_fullStr | Parameterizations for ensemble Kalman inversion |
| title_full_unstemmed | Parameterizations for ensemble Kalman inversion |
| title_short | Parameterizations for ensemble Kalman inversion |
| title_sort | parameterizations for ensemble kalman inversion |
| url | https://eprints.nottingham.ac.uk/51560/ https://eprints.nottingham.ac.uk/51560/ https://eprints.nottingham.ac.uk/51560/ |