  Bayesian optimal experimental design (OED) seeks to conduct the most
informative experiment under budget constraints to update the prior knowledge
of a system to its posterior from the experimental data in a Bayesian
framework. Such problems are computationally challenging because of (1)
expensive and repeated evaluation of some optimality criterion that typically
involves a double integration with respect to both the system parameters and
the experimental data, (2) suffering from the curse-of-dimensionality when the
system parameters and design variables are high-dimensional, (3) the
optimization is combinatorial and highly non-convex if the design variables are
binary, often leading to non-robust designs. To make the solution of the
Bayesian OED problem efficient, scalable, and robust for practical
applications, we propose a novel joint optimization approach. This approach
performs simultaneous (1) training of a scalable conditional normalizing flow
(CNF) to efficiently maximize the expected information gain (EIG) of a jointly
learned experimental design (2) optimization of a probabilistic formulation of
the binary experimental design with a Bernoulli distribution. We demonstrate
the performance of our proposed method for a practical MRI data acquisition
problem, one of the most challenging Bayesian OED problems that has
high-dimensional (320 $\times$ 320) parameters at high image resolution,
high-dimensional (640 $\times$ 386) observations, and binary mask designs to
select the most informative observations.
