2020/06/27 by Dieter Armbruster, Armbruster, Dieter, Michaël Herty +3
Earth and Planetary Sciences · Environmental Science · #37N35 #65N21 #93E11 #Arctic and Antarctic ice dynamics #Cryospheric studies and observations #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Urban Heat Island Mitigation
paper · pdf · doi:10.48550/arxiv.2006.15390
openalex publication_date 2020/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In recent years several continuous limits in the number of iteration and particles have been performed in order to study properties of the method. In particular, a one--dimensional linear stability analysis reveals possible drawbacks in the phase space of moments provided by the continuous limits of the EKI, but observed also in the multi--dimensional setting. In this work we address this issue by introducing a stabilization of the dynamics which leads to a method with globally asymptotically stable solutions. We illustrate the performance of the stabilized version by using test inverse problems from the literature and comparing it with the classical continuous limit formulation of the method.