Tikhonov regularization for ensemble Kalman inversion
The ensemble Kalman filter (EnKF) is a powerful but simple algorithm aimed at merging models with observational data. Since its formulation in 1994 it has seen a wide applicability to various mathematical disciplines. In this talk we discuss how the EnKF has been used to tackle statistical inverse problems, referred to as ensemble Kalman inversion (EKI). Prior information is of crucial importance, and one way to alleviate issues such as the over-fitting of data is to add some form of regularization. In this talk we discuss one form of regularization, being Tikhonov, which has strong connections with Bayesian inversion. By incorporating Tikhonov regularization, this can improve the overall inversion, specific to Gaussian priors. Various analytical results are derived, where we present numerical experiments highlighting the importance of regularization for EKI.
Dr. Neil Chada National Univerity of Singapore