8 papers
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…
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…
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…
On submodularity of the expected information gain
Steven Maio, Alen Alexanderian
We consider finite-dimensional linear Gaussian Bayesian inverse problems with uncorrelated sensor measurements. In this setting, it is known that the expected information gain, qua…
Bridging the Gap Between Deterministic and Probabilistic Approaches to State Estimation
Lev Kakasenko, Alen Alexanderian, Mohammad Farazmand +1
We consider the problem of state estimation from limited discrete and noisy measurements. In particular, we focus on modal state estimation, which approximates the unknown state of…
A control-oriented approach to optimal sensor placement
Madhusudan Madhavan, Alen Alexanderian, Arvind K. Saibaba +2
We propose a control-oriented optimal experimental design (cOED) approach for linear PDE-constrained Bayesian inverse problems. In particular, we consider optimal control problems…