A Stabilization of a Continuous Limit of the Ensemble Kalman Inversion

TL;DR

This paper introduces a stabilized version of the continuous limit of the Ensemble Kalman Inversion (EKI), enhancing its stability and reliability in solving inverse problems, demonstrated through tests and comparisons.

Contribution

The paper proposes a novel stabilization technique for the continuous limit of EKI, ensuring globally asymptotically stable solutions and improving its performance.

Findings

Stabilized EKI exhibits improved stability in inverse problem solving.

The method outperforms classical continuous limit formulations in tests.

Stability analysis confirms global asymptotic stability of the new approach.

Abstract

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.