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

In this talk, we consider Bayesian calibration of models describing the phenomenon of block copolymer (BCP) self-assembly, a first step towards enhancing and controlling quality, validity, and reliability of computer simulations of BCP self-assembly. The goal of model calibration is to infer model parameters via Bayes’ rule from image characterizations of block copolymer melts obtained via microscopy or X-ray scattering techniques. To account for aleatory uncertainties represented by the random metastability and defectivity in BCP self-assembly, auxiliary variables are introduced in the models. 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 image feature extraction. We show that expected information gains from the summary statistics can be computed with no significant additional cost, and they can be used as means to assess the utility of summary statistics choices. Lastly, we present a numerical case study based on top-down microscopy characterizations of unguided diblock copolymer thin film self-assembly. We demonstrate that the proposed approach not only efficiently executes the calibration task while taking into account metastability of BCP self-assembly, but also helps us quantify the effects of image corruptions and experimental designs on the calibration results.