Adaptive Ensemble Kalman Inversion with Statistical Linearization (Communications in Computational Physics, 2023)
The ensemble Kalman inversion (EKI), inspired by the well-known ensemble Kalman filter, is a derivative-free and parallelizable method for solving inverseproblems. The method is appealing for applications in a variety of fields due to itslow computational cost and simple implementation. In this paper, we propose anadaptive ensemble Kalman inversion with statistical linearization (AEKI-SL) methodfor solving inverse problems from a hierarchical Bayesian perspective. Specifically, byadaptively updating the unknown with an EKI and updating the hyper-parameter inthe prior model, the method can improve the accuracy of the solutions to the inverseproblem. To avoid semi-convergence, we employ Morozov’s discrepancy principle asa stopping criterion. Furthermore, we extend the method to simultaneous estimationof 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 traditionalEKI and EKI with statistical linearization (EKI-SL) methods.