Well posedness and convergence analysis of the ensemble Kalman inversion

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Bloemker D, Schillings C, Wacker PK, Weissmann S
Zeitschrift: Inverse Problems
Jahr der Veröffentlichung: 2019
Band: 35
Heftnummer: 8
ISSN: 0266-5611


Abstract

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.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Wacker, Philipp Konstantin Dr.
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)


Einrichtungen weiterer Autorinnen und Autoren

Universität Augsburg
Universität Mannheim


Zitierweisen

APA:
Bloemker, D., Schillings, C., Wacker, P.K., & Weissmann, S. (2019). Well posedness and convergence analysis of the ensemble Kalman inversion. Inverse Problems, 35(8). https://dx.doi.org/10.1088/1361-6420/ab149c

MLA:
Bloemker, Dirk, et al. "Well posedness and convergence analysis of the ensemble Kalman inversion." Inverse Problems 35.8 (2019).

BibTeX: 

Zuletzt aktualisiert 2019-16-08 um 16:53