Computational Mathematics and Scientific Computing Seminar
Model uncertainty issues in nonlinear inverse problems
Speaker: Kui Ren, Columbia
Location: Warren Weaver Hall 1302
Date: April 26, 2019, 10 a.m.
In model-based inverse problems, it is often the case that only a portion of the relevant physical quantities in the model can be reconstructed. The rest of the model parameters are assumed to be known. In practice, these parameters are often only known partially (up to a certain accuracy). It is therefore important to characterize the dependence of the inversion/imaging results on the accuracy of these parameters. This is a challenging uncertainty quantification problem due to the fact that both the map from the uncertainty parameters (the ones we assumed partially known) to the measured data and the map from the measured data to the quantities to be imaged are difficult to analyze. This talk presents some recent computational studies on the characterization of such model uncertainty in nonlinear inverse problems for an elliptic PDE.