Past Event: Oden Institute Seminar

Ensemble Kalman Inversion: from subsurface environments to composite materials

Marco Iglesias Hernandez, University of Nottingham, United Kingdom

Abstract

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 in EnKF, Ensemble Kalman Inversion (EKI) is a computational framework that has been recently proposed 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 regularisation strategies for EKI that can improve accuracy and performance of large-scale inversions. 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 geoelectrical characterisation of the subsurface.