22-24 September 2021
Alpen-Adria-Universität Klagenfurt
Europe/Vienna timezone

Deterministic Dynamics of Ensemble Kalman Inversion

24 Sep 2021, 15:40
20m
HS 1 (Alpen-Adria-Universität Klagenfurt)

HS 1

Alpen-Adria-Universität Klagenfurt

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

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