Adaptive Ensemble Kalman Inversion with Statistical Linearization

Adaptive Ensemble Kalman Inversion with Statistical Linearization

Year:    2023

Author:    Yanyan Wang, Qian Li, Liang Yan

Communications in Computational Physics, Vol. 33 (2023), Iss. 5 : pp. 1357–1380

Abstract

The ensemble Kalman inversion (EKI), inspired by the well-known ensemble Kalman filter, is a derivative-free and parallelizable method for solving inverse problems. The method is appealing for applications in a variety of fields due to its low computational cost and simple implementation. In this paper, we propose an adaptive ensemble Kalman inversion with statistical linearization (AEKI-SL) method for solving inverse problems from a hierarchical Bayesian perspective. Specifically, by adaptively updating the unknown with an EKI and updating the hyper-parameter in the prior model, the method can improve the accuracy of the solutions to the inverse problem. To avoid semi-convergence, we employ Morozov’s discrepancy principle as a stopping criterion. Furthermore, we extend the method to simultaneous estimation of noise levels in order to reduce the randomness of artificially ensemble noise levels. The convergence of the hyper-parameter in prior model is investigated theoretically. Numerical experiments show that our proposed methods outperform the traditional EKI and EKI with statistical linearization (EKI-SL) methods.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2023-0012

Communications in Computational Physics, Vol. 33 (2023), Iss. 5 : pp. 1357–1380

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Ensemble Kalman inversion statistical linearization adaptive Bayesian inverse problem.

Author Details

Yanyan Wang

Qian Li

Liang Yan