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This talk proposes new methods for reducing high-dimensional parameter and state spaces in large-scale Bayesian inverse problems. We focus on problems with spatially-concentrated observations or dynamics which have high uncertainty in areas far from the domain of interest. We first solve the deterministic inverse problem to estimate the uncertainty, and then solve the statistical Bayesian inverse problem only over the domain with low uncertainty. Numerical tests with a PDE-constrained inverse problem show improved recovery over the full domain.
This presentation is part of Minisymposium “MS54 - Hybrid Approaches that Combine Deterministic and Statistical Regularization for Applied Inverse Problems (4 parts)”
organized by: Cristiana Sebu (University of Malta) , Taufiquar Khan (Clemson University) .