@Article{CiCP-33-1357,
author = {Wang , YanyanLi , Qian and Yan , Liang},
title = {Adaptive Ensemble Kalman Inversion with Statistical Linearization},
journal = {Communications in Computational Physics},
year = {2023},
volume = {33},
number = {5},
pages = {1357--1380},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0012},
url = {http://global-sci.org/intro/article_detail/cicp/21764.html}
}