10 papers
Multi-type Sensor Placement for PDE-based Bayesian Inverse Problems
Steven Maio, Alen Alexanderian, Karina Koval +1
We address optimal placement of multi-type sensors for Bayesian inverse problems governed by partial differential equations (PDEs). The proposed framework allows for sensors with d…
Submodularity of the expected information gain in infinite-dimensional linear inverse problems
Alen Alexanderian, Steven Maio
We consider infinite-dimensional linear Gaussian Bayesian inverse problems with uncorrelated measurement errors and focus on the problem of selecting sensor placements that maximiz…
A brief note on submodular optimization
Alen Alexanderian
We consider some basic concepts concerning the optimization of monotone submodular functions, including a detailed discussion of submodularity. Illustrative examples are included t…
FlexTrace: Exchangeable Randomized Trace Estimation for Matrix Functions
Madhusudan Madhavan, Alen Alexanderian, Arvind K. Saibaba
We consider the task of estimating the trace of a matrix function, , of a large symmetric positive semi-definite matrix . This problem arises in mult…
Preconditioned pseudo-time continuation for parameterized inverse problems
Joseph Hart, Alen Alexanderian, Bart van Bloemen Waanders
We consider parameterized variational inverse problems that are constrained by partial differential equations (PDEs). We seek to efficiently compute the solution of the inverse pro…
Path-OED for infinite-dimensional Bayesian linear inverse problems governed by PDEs
J. Nicholas Neuberger, Alen Alexanderian, Bart van Bloemen Waanders +1
We consider infinite-dimensional Bayesian linear inverse problems governed by time-dependent partial differential equations (PDEs) and develop a mathematical and computational fram…