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

arXiv: https://arxiv.org/abs/2206.11343 · HTML: https://mlsanity.com/paper/2206.11343/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 131 references that are in the map.
- First posted on arXiv 22 Jun 2022.

## Builds on (most cited first, 20 of 20)

- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [Inference via low-dimensional couplings](https://mlsanity.com/paper/1703.06131/) (2017)
- [A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversion](https://mlsanity.com/paper/1308.1313/) (2013)
- [A layered multiple importance sampling scheme for focused optimal Bayesian experimental design](https://mlsanity.com/paper/1903.11187/) (2019)
- [A fast and scalable computational framework for large-scale and high-dimensional Bayesian optimal experimental design](https://mlsanity.com/paper/2010.15196/) (2020)
- [hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs; Part I: Deterministic Inversion and Linearized Bayesian Inference](https://mlsanity.com/paper/1909.03948/) (2019)
- [Pseudo-Marginal Hamiltonian Monte Carlo](https://mlsanity.com/paper/1607.02516/) (2016)
- [Mitigating the Influence of the Boundary on PDE-based Covariance Operators](https://mlsanity.com/paper/1610.05280/) (2016)
- [High-dimensional ABC](https://mlsanity.com/paper/1802.09725/) (2018)
- [A globally convergent modified Newton method for the direct minimization of the Ohta-Kawasaki energy with application to the directed self-assembly of diblock copolymers](https://mlsanity.com/paper/2010.15271/) (2020)
- [A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions](https://mlsanity.com/paper/1501.04739/) (2015)
- [On Consistency of Approximate Bayesian Computation](https://mlsanity.com/paper/1508.05178/) (2015)
- [Bayesian Deconvolution of Scanning Electron Microscopy Images Using Point-spread Function Estimation and Non-local Regularization](https://mlsanity.com/paper/1810.09739/) (2018)

## Built on by (most cited first, 11 of 11)

- [On minimax density estimation via measure transport](https://mlsanity.com/paper/2207.10231/) (2022)
- [Score-based generative models are provably robust: an uncertainty quantification perspective](https://mlsanity.com/paper/2405.15754/) (2024)
- [LazyDINO: Fast, scalable, and efficiently amortized Bayesian inversion via structure-exploiting and surrogate-driven measure transport](https://mlsanity.com/paper/2411.12726/) (2024)
- [Expected information gain estimation via density approximations: Sample allocation and dimension reduction](https://mlsanity.com/paper/2411.08390/) (2024)
- [A friendly introduction to triangular transport](https://mlsanity.com/paper/2503.21673/) (2025)
- [Nonlinear denoising score matching for enhanced learning of structured distributions](https://mlsanity.com/paper/2405.15625/) (2024)
- [A transport approach to sequential simulation-based inference](https://mlsanity.com/paper/2308.13940/) (2023)
- [Coupled Input-Output Dimension Reduction: Application to Goal-oriented Bayesian Experimental Design and Global Sensitivity Analysis](https://mlsanity.com/paper/2406.13425/) (2024)
- [Optimal Experimental Design for Reliable Learning of History-Dependent Constitutive Laws](https://mlsanity.com/paper/2603.12365/) (2026)
- [Learning the Structure of Triangular Transport Maps](https://mlsanity.com/paper/2609.37122/) (2026)
- [Multifidelity Formulations for Triangular Transport](https://mlsanity.com/paper/2610.00698/) (2026)

## Abstract (arXiv)

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.