# 2nd Alps-Adriatic Inverse Problems Workshop 2021 (AAIP 2021) Chemnitz Inverse Problems Symposium on tour

22-24 September 2021
Europe/Vienna timezone

## Deterministic Dynamics of Ensemble Kalman Inversion

24 Sep 2021, 15:40
20m

### Speaker

Leon Bungert (University of Bonn)

### Description

The Ensemble Kalman inversion (EKI) is a powerful tool for the solution of Bayesian inverse problems of type $y=Au^\dagger+\varepsilon$, with $u^\dagger$ being an unknown parameter and $y$ a given datum subject to measurement noise $\varepsilon$. It evolves an ensemble of particles, sampled from a prior measure, towards an approximate solution of the inverse problem. In this talk I will provide a complete description of the dynamics of EKI, utilizing a spectral decomposition of the particle covariance. In particular, I will demonstrate that, despite the common folklore that EKI creates samples from the posterior measure, this is only true for its mean field limit and will suggest modifications of EKI that overcome this drawback.

### Primary authors

Leon Bungert (University of Bonn) Dr Philipp Wacker (FAU Erlangen-Nürnberg)

### Presentation Materials

There are no materials yet.