TY - JOUR
T1 - Adaptive Ensemble Kalman Inversion with Statistical Linearization
AU - Wang , Yanyan
AU - Li , Qian
AU - Yan , Liang
JO - Communications in Computational Physics
VL - 5
SP - 1357
EP - 1380
PY - 2023
DA - 2023/06
SN - 33
DO - http://doi.org/10.4208/cicp.OA-2023-0012
UR - https://global-sci.org/intro/article_detail/cicp/21764.html
KW - Ensemble Kalman inversion, statistical linearization, adaptive, Bayesian inverse problem.
AB - <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>