Continuous time limit of the stochastic ensemble Kalman inversion: strong convergence analysis
The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partially, noisily observed dynamical systems and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences, and its gradual adoption in many other areas of application,...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
December 16, 2022
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| In: |
SIAM journal on numerical analysis
Year: 2022, Volume: 60, Issue: 6, Pages: 3181-3215 |
| ISSN: | 1095-7170 |
| DOI: | 10.1137/21M1437561 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/21M1437561 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/21M1437561 
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| Author Notes: | Dirk Blömker, Claudia Schillings, Philipp Wacker, and Simon Weissmann |
| Summary: | The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partially, noisily observed dynamical systems and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences, and its gradual adoption in many other areas of application, analysis of the method is in its infancy. Furthermore, much of the existing analysis deals with the large ensemble limit, far from the regime in which the method is typically used. The goal of this paper is to analyze the method when applied to inverse problems with fixed ensemble size. A continuous time limit is derived and the long-time behavior of the resulting dynamical system is studied. Most of the rigorous analysis is confined to the linear forward problem, where we demonstrate that the continuous time limit of the EnKF corresponds to a set of gradient flows for the data misfit in each ensemble member, coupled through a common preconditioner which is the empirical covariance matrix of the ensemble. Numerical results demonstrate that the conclusions of the analysis extend beyond the linear inverse problem setting. Numerical experiments are also given which demonstrate the benefits of various extensions of the basic methodology. |
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| Item Description: | Gesehen am 20.04.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1095-7170 |
| DOI: | 10.1137/21M1437561 |