A STABILIZATION OF A CONTINUOUS LIMIT OF THE ENSEMBLE KALMAN INVERSION

Dieter Armbruster, Michael Herty, Giuseppe Visconti

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 iterations 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 is observed also in the multidimensional 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.

Original languageEnglish (US)
Pages (from-to)1494-1515
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume60
Issue number3
DOIs
StatePublished - 2022

Keywords

  • dynamical systems
  • inverse problems
  • moment equations
  • nonlinear filtering methods
  • regularization
  • stabilization

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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