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.
翻译:我们认为,利用通过显微镜或X光散射技术产生的图像数据,对描述成块共聚(BCP)现象的模型进行巴耶斯校准;为了说明BCP均衡结构中的随机长距离紊乱,我们引入了辅助变量来代表这种悬浮的不确定性;然而,这些变量导致高维图像数据的综合可能性,而这些数据通常难以评估;我们采用基于测量传输的无可能性方法,与为图像数据构建摘要统计,解决了这个具有挑战性的贝耶斯推断问题;我们还表明,从观察到的模型参数数据中获取的信息收益(EIGs)可以不增加大笔费用进行计算;最后,我们介绍了基于Ota-Kawasaki模型的数值案例研究,用于对共聚聚合薄胶片自我组装和上下自下显微镜定性。关于校准,我们引入了几个特定域的能量和四基综合统计数据,并用EIG量化其信息性。我们展示了拟议方法研究数据腐败和实验性设计对校准结果的影响的力度。