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

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