Multifidelity sensor placement in Bayesian inverse problems

Mentors:
Lead: Arvind K. Saibaba (Mathematics, NC State)
Collaborator: Julianne Chung (Mathematics, Emory University)

Intellectual merit and significance:
Reconstructing spatial functions from sparse sensor measurements  is an important task in data science with many applications. We assume that there are two types, or fidelities, of sensors: a large number of cheap but low signal-to-noise ratio, and a small number of expensive but high  signal-to-noise ratio. We want to determine optimal multifidelity sensor placement which is a cost-constrained optimization problem and is known to be NP-hard, even in the single-fidelity case. We will explore several algorithms for solving this optimization problem, and build on recent work in optimal sensor placement involving column subset selection. The methods will target flow reconstruction in fluid dynamics, but other applications to Bayesian inverse problems will be considered. 

Objectives:
(i) Preliminary implementation on fluid reconstruction problem, (ii) develop and explore different algorithms and compare the performance, (iii) demonstrate performance on several application problems, including Bayesian inverse problems, and (iv) integrate the implementations into a software package that is currently under development.

Outcomes:
Upon successful completion of the project, the students will submit a paper to the SIAM Undergraduate Research Online (SIURO) journal. They will also integrate their implementations into an existing software package.