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We consider the Bayesian calibration of models describing the phenomenon ofblock copolymer (BCP) self-assembly using image data produced by microscopy orX-ray scattering techniques. To account for the random long-range disorder inBCP equilibrium structures, we introduce auxiliary variables to represent thisaleatory uncertainty. These variables, however, result in an integratedlikelihood for high-dimensional image data that is generally intractable toevaluate. We tackle this challenging Bayesian inference problem using alikelihood-free approach based on measure transport together with theconstruction of summary statistics for the image data. We also show thatexpected information gains (EIGs) from the observed data about the modelparameters can be computed with no significant additional cost. Lastly, wepresent a numerical case study based on the Ohta--Kawasaki model for diblockcopolymer thin film self-assembly and top-down microscopy characterization. Forcalibration, we introduce several domain-specific energy- and Fourier-basedsummary statistics, and quantify their informativeness using EIG. Wedemonstrate the power of the proposed approach to study the effect of datacorruptions and experimental designs on the calibration results.

Bayesian model calibration for block copolymer self-assembly:  Likelihood-free inference and expected information gain computation via  measure transport