Abstract: The ensemble Kalman filter (EnKF) is a widely used methodology for data assimilation problems and has been recently generalized to inverse problems, known as ensemble Kalman inversion (EKI). We view the method as a derivative free optimization method for a least-squares misfit functional and discuss various variants of the scheme such as variance inflation and regularization. This opens up the perspective to use the method for a wide range of applications, e.g.~imaging, groundwater flow problems, biological problems as well as in the context of the training of neural networks. We formulate the scheme in a discrete time setting and verify the convergence to its continuous time limit, which is given by a system of coupled stochastic differential equations. Based on the continuous time formulation we show well-posedness of the scheme and present accuracy results of the EKI estimate.
Bio: I am a postdoctoral researcher at the University of Heidelberg and a member of the research center "Interdisciplinary Center for Scientific Computing" (IWR) in the work group Machine Learning. I have received my PhD on sampling and optimization methods for inverse problems at the University of Mannheim as a member of the research training group "Statistical Modeling of Complex Systems and Processes". My research interests lie at the interface between probability theory, optimization and numerical analysis. In particular, I am working on particle based methods for solving (Bayesian) inverse problems.