Prof. Karen Veroy-Grepl, Ph.D.
In this project, we focus on goal-oriented Bayesian inversion of problems governed by partial differential equations, particularly for applications with high-dimensional parameter spaces. The solution of the discretized inverse problem is often prohibitive due to the need to solve the forward problem numerous times. We thus build upon our expertise on Bayesian inversion for large-scale systems and model order reduction to investigate the use of model order reduction methods to accelerate the solution of Bayesian inverse problems. We intend to use the reduced-basis method and trust region methods to reduce the computational cost in problems with high-dimensional parameter spaces.
The aims of this project are:
• Reduction of the computational cost to solve Bayesian inverse problems governed by partial differential equations.
• Quantification of the uncertainty caused by the use of surrogate reduced-order models.
• Application to large-scale inverse problems with high-dimensional parameter spaces, for instance in the geosciences.