  Optimal Bayesian design techniques provide an estimate for the best
parameters of an experiment in order to maximize the value of measurements
prior to the actual collection of data. In other words, these techniques
explore the space of possible observations and determine an experimental setup
that produces maximum information about the system parameters on average.
Generally, optimal Bayesian design formulations result in multiple
high-dimensional integrals that are difficult to evaluate without incurring
significant computational costs as each integration point corresponds to
solving a coupled system of partial differential equations. In the present
work, we propose a novel approach for development of polynomial chaos expansion
(PCE) surrogate model for the design utility function. In particular, we
demonstrate how the orthogonality of PCE basis polynomials can be utilized in
order to replace the expensive integration over the space of possible
observations by direct construction of PCE approximation for the expected
information gain. This novel technique enables the derivation of a reasonable
quality response surface for the targeted objective function with a
computational budget comparable to several single-point evaluations. Therefore,
the proposed technique reduces dramatically the overall cost of optimal
Bayesian experimental design. We evaluate this alternative formulation
utilizing PCE on few numerical test cases with various levels of complexity to
illustrate the computational advantages of the proposed approach.
