Probabilistic Bayesian optimal experimental design using conditional
  normalizing flows
Rafael Orozco Felix J. Herrmann Peng Chen
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.