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

Ricardo Baptista, Lianghao Cao+5 more|arXiv (Cornell University)|Jun 22, 2022

Markov Chains and Monte Carlo Methods4 citations

TL;DR

This paper proposes a likelihood-free Bayesian inference framework using measure transport via triangular transport maps to calibrate the Ohta–Kawasaki model for block copolymer self-assembly from top-down microscopy images. By constructing energy- and Fourier-based summary statistics and leveraging amortized inference, the method enables efficient posterior estimation and exact expected information gain (EIG) computation, demonstrating robust calibration under data corruption and varying experimental conditions.

ABSTRACT

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.

Motivation & Objective

• Address the challenge of intractable likelihoods in Bayesian calibration of block copolymer self-assembly models due to high-dimensional, disordered image data.
• Account for aleatoric uncertainty in BCP equilibrium structures through auxiliary variables while maintaining tractable inference.
• Develop a scalable inference framework that enables efficient posterior estimation and expected information gain (EIG) computation with minimal computational overhead.
• Quantify the informativeness of different summary statistics and experimental designs (e.g., noise, magnification) for model calibration.
• Enable optimal experimental design by assessing how data quality and measurement settings affect parameter inference accuracy and uncertainty.

Proposed method

• Employ a probabilistic data model that incorporates both measurement uncertainty and aleatoric disorder in BCP self-assembly via auxiliary random fields.
• Use low-dimensional, domain-specific summary statistics—energy-based and Fourier-based—to reduce high-dimensional image data while preserving parameter-informative features.
• Apply triangular transport maps (Knothe–Rosenblatt rearrangement) to learn the joint distribution of parameters and summary statistics from limited joint samples.
• Perform amortized likelihood-free inference: once transport maps are trained, posterior inference for any new data realization is fast and consistent.
• Compute expected information gain (EIG) with no additional cost by leveraging the same transport map structure used for posterior inference.
• Use hierarchical uniform priors informed by the forward operator to ensure physically plausible parameter space exploration.

Experimental results

Research questions

• RQ1 How can Bayesian calibration be performed when the likelihood function is intractable due to high-dimensional image data and auxiliary variables modeling long-range disorder?
• RQ2 Which summary statistics (energy-based vs. Fourier-based) are most informative for calibrating the Ohta–Kawasaki model parameters from microscopy images?
• RQ3 How do data corruptions such as noise and blurring affect the expected information gain and posterior uncertainty in model calibration?
• RQ4 How does the magnification level of the microscope influence the informativeness of observed data for parameter inference?
• RQ5 Can expected information gain be computed efficiently alongside posterior inference without significant computational overhead?

Key findings

• The proposed likelihood-free inference method via triangular transport maps enables consistent and efficient posterior estimation for block copolymer model calibration with minimal sample requirements.
• Energy-based summary statistics (e.g., spatial averages) were found to be more informative than Fourier-based statistics for calibrating the Ohta–Kawasaki model parameters, particularly for learning the parameter $m$.
• Expected information gain (EIG) was computed with no significant additional cost, enabling systematic evaluation of data quality and experimental design impacts.
• EIG decreased with increasing noise and blurring, and the $(Q_2, Q_4)$ summary statistics were more sensitive to noise than $(Q_1, Q_3)$ or full observables, especially at low spatial average values.
• Higher magnification levels led to increased EIG, indicating that finer spatial resolution improves parameter inference accuracy and reduces uncertainty.
• Posterior predictive samples confirmed that the calibrated model accurately reproduces observed microstructures, validating the effectiveness of the chosen summary statistics.