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SUMMARY:Addressing non-linearity in PDE-constrained inverse problems - Tri
 stan van Leeuwen (Centrum voor Wiskunde en Informatica (CWI))
DTSTART:20230131T090000Z
DTEND:20230131T094500Z
UID:TALK194509@talks.cam.ac.uk
DESCRIPTION:Many inverse problems can be posed as a PDE-constrained optimi
 sation problem. Due to the multi-experimental and high-dimensional nature 
 of the data\, the resulting Constrained optimisation problem is often tack
 led using a reduced-space approach. Here\, the state is eliminated from th
 e problem by solving the PDE\, resulting in a non-linear optimisation prob
 lem for the parameters. This non-linearity makes the approach very sensiti
 ve to initialisation. To tackle this issue\, I will discuss two separate l
 ines of research\; constraint relaxation and reduced-order-modelling. The 
 first borrows ideas from data-assimilation to allow for model-errors and i
 mplicitly enlarges the search space. The second proceeds in the spirit of 
 the classical direct inverse scattering methods. Finally\, I will sketch s
 ome connections between these two.
LOCATION:Seminar Room 1\, Newton Institute
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