Robust A-Optimal Experimental Design for Bayesian Inverse Problems
Ahmed Attia Sven Leyffer Todd Munson
Optimal design of experiments for Bayesian inverse problems has recently
gained wide popularity and attracted much attention, especially in the
computational science and Bayesian inversion communities. An optimal design
maximizes a predefined utility function that is formulated in terms of the
elements of an inverse problem, an example being optimal sensor placement for
parameter identification. The state-of-the-art algorithmic approaches following
this simple formulation generally overlook misspecification of the elements of
the inverse problem, such as the prior or the measurement uncertainties. This
work presents an efficient algorithmic approach for designing optimal
experimental design schemes for Bayesian inverse problems such that the optimal
design is robust to misspecification of elements of the inverse problem.
Specifically, we consider a worst-case scenario approach for the uncertain or
misspecified parameters, formulate robust objectives, and propose an
algorithmic approach for optimizing such objectives. Both relaxation and
stochastic solution approaches are discussed with detailed analysis and insight
into the interpretation of the problem and the proposed algorithmic approach.
Extensive numerical experiments to validate and analyze the proposed approach
are carried out for sensor placement in a parameter identification problem.