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Addressing non-linearity in PDE-constrained inverse problems

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RNTW01 - Rich and Nonlinear Tomography (RNT) in Radar, Astronomy and Geophysics

Many inverse problems can be posed as a PDE -constrained optimisation problem. Due to the multi-experimental and high-dimensional nature of the data, the resulting Constrained optimisation problem is often tackled using a reduced-space approach. Here, the state is eliminated from the problem by solving the PDE , resulting in a non-linear optimisation problem for the parameters. This non-linearity makes the approach very sensitive to initialisation. To tackle this issue, I will discuss two separate lines of research; constraint relaxation and reduced-order-modelling. The first borrows ideas from data-assimilation to allow for model-errors and implicitly enlarges the search space. The second proceeds in the spirit of the classical direct inverse scattering methods. Finally, I will sketch some connections between these two.

This talk is part of the Isaac Newton Institute Seminar Series series.

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