The aim of this talk is to give an overview of the classical framework for Ensemble Kalman Inversion (EKI) and some of its modern applications. I will start the talk introducing the EKI framework to identify parameters in PDEs given partial (noisy) measurements of the solution of the PDE. I will consider a generic setting where the underlying PDE describes a physical system, and for which the unknown parameter is a function that characterises a spatially variable physical property of the system. I will discuss a level-set random field parameterisation within the EKI framework that enable us to infer unknown physical properties that may display discontinuities due to the presence of anomalies within the medium. I will show several examples of applications of EKI to solve inverse problems arising in (i) non-destructive testing of composite materials, (ii) electrical resistivity tomography and (iii) magnetic resonance elastography.  

Short Bio: Marco Iglesias holds a PhD in Computational and Applied Mathematics from the Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin. He held postdoctoral positions at the Department of Civil and Environmental Engineering at MIT and the Mathematics Institute at Warwick University. He joined the School of Mathematical Sciences at Nottingham in 2013 where he is currently Associate Professor in Scientific Computation.