Identifying parameters of computational models from experimental data, or model calibration, is fundamental for assessing and improving the predictability and reliability of computer simulations. In this work, we propose a method for Bayesian calibration of models that predict morphological patterns of diblock copolymer (Di-BCP) thin film self-assembly while accounting for various sources of uncertainties in pattern formation and data acquisition. This method extracts the azimuthally-averaged power spectrum (AAPS) of the top-down microscopy characterization of Di-BCP thin film patterns as summary statistics for Bayesian inference of model parameters via the pseudo-marginal method. We derive the analytical and approximate form of a conditional likelihood for the AAPS of image data. We demonstrate that AAPS-based image data reduction retains the mutual information, particularly on important length scales, between image data and model parameters while being relatively agnostic to the aleatoric uncertainties associated with the random long-range disorder of Di-BCP patterns. Additionally, we propose a phase-informed prior distribution for Bayesian model calibration. Furthermore, reducing image data to AAPS enables us to efficiently build surrogate models to accelerate the proposed Bayesian model calibration procedure. We present the formulation and training of two multi-layer perceptrons for approximating the parameter-to-spectrum map, which enables fast integrated likelihood evaluations. We validate the proposed Bayesian model calibration method through numerical examples, for which the neural network surrogate delivers a fivefold reduction of the number of model simulations performed for a single calibration task.

翻译：从实验数据中辨识计算模型的参数（即模型标定）是评估并提升计算机模拟预测性与可靠性的基础。本研究提出一种贝叶斯模型标定方法，用于预测嵌段共聚物薄膜自组装形态模式，同时考虑模式形成与数据采集过程中的多种不确定性来源。该方法提取嵌段共聚物薄膜自上而下显微表征的方位角平均功率谱作为汇总统计量，通过伪边际方法进行模型参数的贝叶斯推断。我们推导了图像数据方位角平均功率谱的条件似然函数的解析形式及近似形式。研究表明：基于方位角平均功率谱的图像数据降维方法能够保留图像数据与模型参数之间的互信息（尤其在重要长度尺度上），同时相对不受嵌段共聚物图案随机长程序无序所关联的偶然不确定性影响。此外，我们提出一种相位感知先验分布用于贝叶斯模型标定。进一步地，将图像数据降维为方位角平均功率谱使我们能够高效构建代理模型以加速所提出的贝叶斯模型标定流程。我们给出了两个多层感知机的构建与训练方法，用于逼近参数-频谱映射关系，从而实现快速的综合似然评估。通过数值算例验证了所提出的贝叶斯模型标定方法，其中神经网络代理模型使单次标定任务所需的模型模拟次数减少了五倍。