Bayesian geometric inverse problems

This project will be based at the University of Nottingham in the School of
Mathematical Sciences.

The aim of this project is to develop computational Bayesian techniques for the solution of geometric inverses problems that arise in a wide range of applications such as subsurface geophysics, manufacturing engineering and the built environment. Examples of geometric inverse problem that will be addressed with the techniques developed in this project are: (i) inference of fracture networks and/or conduits in Karst aquifers during the injection of CO2 for its geologic storage; (ii) detection of defects in reinforced preform during the resin infusion process in the fabrication of composite materials; (iii) inference of internal structures (e.g. cavities) in building structures such as walls with the aim of improving estimates of energy consumption. These problems have an underlying (forward) model described by Partial Differential Equation(s) (PDE) with input parameters associated to some (unknown) physical property of interest; the inverse problem is to infer this property from noisy observations of the solution of the PDE. In the context of problems (i)-(iii), sophisticated geometric parameterizations are often required to enable an accurate and realistic characterization of these properties (e.g. channelized structures in Karst networks). This project will develop computational hierarchical Bayesian methodologies to infer those geometry-constrained properties within an infinite-dimensional Bayesian framework for PDE-constrained inverse problems.
Depending on the applicant’s interest and academic background, the project could include the development of geometric parameterizations based on computer vision, image reconstruction and segmentation (e.g. level-sets) techniques; in this case, the project could be potentially co-supervised by Dr. Bai Li, Computer Science at Nottingham.

UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.