  We consider the Bayesian calibration of models describing the phenomenon of
block copolymer (BCP) self-assembly using image data produced by microscopy or
X-ray scattering techniques. To account for the random long-range disorder in
BCP equilibrium structures, we introduce auxiliary variables to represent this
aleatory uncertainty. These variables, however, result in an integrated
likelihood for high-dimensional image data that is generally intractable to
evaluate. We tackle this challenging Bayesian inference problem using a
likelihood-free approach based on measure transport together with the
construction of summary statistics for the image data. We also show that
expected information gains (EIGs) from the observed data about the model
parameters can be computed with no significant additional cost. Lastly, we
present a numerical case study based on the Ohta--Kawasaki model for diblock
copolymer thin film self-assembly and top-down microscopy characterization. For
calibration, we introduce several domain-specific energy- and Fourier-based
summary statistics, and quantify their informativeness using EIG. We
demonstrate the power of the proposed approach to study the effect of data
corruptions and experimental designs on the calibration results.
