One World Virtual Seminar Series - Stochastic Numerics and Inverse Problems
Marco Iglesias (University of Nottingham)
Title: Ensemble Kalman Inversion: from subsurface environments to composite materials
The Ensemble Kalman filter (EnKF) developed by Evensen and co-workers in the 1990s has had enormous impact in the geosciences and various engineering disciplines. EnKF has been historically used for data assimilation problems, where the objective is to infer the state of a partially observed dynamic system from observational data. Motivated by algorithmic ideas from EnKF, Ensemble Kalman Inversion (EKI) is a computational framework that has been proposed and applied for solving PDE-constrained inverse problems (i.e. to infer inputs from outputs of a PDE model) in a derivative-free fashion. In this talk I will introduce EKI from a framework that unifies both the Bayesian and the classical (deterministic) approach for inverse problems. I will present a regularisation strategy for EKI that can improve its accuracy and performance. I will further discuss recent parameterisations within EKI which enable to efficiently infer geometric features of the underlying (unknown) field. Numerical examples will be used to show the potential advantages of these parameterisations in various application areas including the non-destructive evaluation of composite materials as well as the geo-electrical characterisation of the subsurface.
The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336, VAT Registration Number GB 592 9507 00, and is acknowledged by the UK authorities as a “Recognised body” which has been granted degree awarding powers.