A Fast and Scalable Method for A-Optimal Design of Experiments for Infinite-dimensional Bayesian Nonlinear Inverse Problems

Understand

We address the problem of optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by PDEs.

• The goal is to find a placement of sensors, at which experimental data are collected, so as to minimize the uncertainty in the inferred parameter field.
• We formulate the OED objective function by generalizing the classical A-optimal experimental design criterion using the expected value of the trace of the posterior covariance.
• We seek a method that solves the OED problem at a cost (measured in the number of forward PDE solves) that is independent of both the parameter and sensor dimensions.