Adaptive Ensemble Kalman Inversion with Statistical Linearization  

作　　者：Yanyan Wang Qian Li Liang Yan 

机构地区：[1]School of Mathematics,Southeast University,Nanjing 210096,China [2]Nanjing Center for Applied Mathematics,Nanjing 211135,China

出　　处：《Communications in Computational Physics》2023年第5期1357-1380,共24页计算物理通讯（英文）

基　　金：This work is supported by NSF of China(No.12171085).

摘　　要：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.

关 键 词：Ensemble Kalman inversion statistical linearization ADAPTIVE Bayesian inverse problem 

分 类 号：O17[理学—数学]