Repository: Freie Universität Berlin, Math Department

Well posedness and convergence analysis of the ensemble Kalman inversion

Blömker, Dirk and Schillings, Claudia and Wacker, Philipp and Weissmann, Simon (2019) Well posedness and convergence analysis of the ensemble Kalman inversion. Inverse Problems, 35 . pp. 1-33.

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The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various areas of application. We present a complete analysis of the ensemble Kalman inversion with perturbed observations for a fixed ensemble size when applied to linear inverse problems. The well-posedness and convergence results are based on the continuous time scaling limits of the method. The resulting coupled system of stochastic differential equations allows one to derive estimates on the long-time behaviour and provides insights into the convergence properties of the ensemble Kalman inversion. We view the method as a derivative free optimization method for the least-squares misfit functional, which opens up the perspective to use the method in various areas of applications such as imaging, groundwater flow problems, biological problems as well as in the context of the training of neural networks.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2689
Deposited By: Monika Drueck
Deposited On:25 Jan 2022 15:36
Last Modified:25 Jan 2022 15:36

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