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.