Repository: Freie Universit├Ąt Berlin, Math Department

On the incorporation of box-constraints for ensemble Kalman inversion

Chada, Neil and Schillings, Claudia and Weissmann, Simon (2019) On the incorporation of box-constraints for ensemble Kalman inversion. Foundations of Data Science, 1 (4). pp. 433-456.

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Abstract

The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties in various areas of applications. In recent years, a complete analysis of the method has been developed for linear inverse problems adopting an optimization viewpoint. However, many applications require the incorporation of additional constraints on the parameters, e.g. arising due to physical constraints. We propose a new variant of the ensemble Kalman inversion to include box constraints on the unknown parameters motivated by the theory of projected preconditioned gradient flows. Based on the continuous time limit of the constrained ensemble Kalman inversion, we discuss a complete convergence analysis for linear forward problems. We adopt techniques from filtering, such as variance inflation, which are crucial in order to improve the performance and establish a correct descent. These benefits are highlighted through a number of numerical examples on various inverse problems based on partial differential equations.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group
ID Code:2987
Deposited By: Ulrike Eickers
Deposited On:26 May 2023 09:07
Last Modified:26 May 2023 09:07

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