Determining process-structure-property linkages is one of the key objectives in material science, and uncertainty quantification plays a critical role in understanding both process-structure and structure-property linkages. In this work, we seek to learn a distribution of microstructure parameters that are consistent in the sense that the forward propagation of this distribution through a crystal plasticity finite element model (CPFEM) matches a target distribution on materials properties. This stochastic inversion formulation infers a distribution of acceptable/consistent microstructures, as opposed to a deterministic solution, which expands the range of feasible designs in a probabilistic manner. To solve this stochastic inverse problem, we employ a recently developed uncertainty quantification (UQ) framework based on push-forward probability measures, which combines techniques from measure theory and Bayes rule to define a unique and numerically stable solution. This approach requires making an initial prediction using an initial guess for the distribution on model inputs and solving a stochastic forward problem. To reduce the computational burden in solving both stochastic forward and stochastic inverse problems, we combine this approach with a machine learning (ML) Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure-property linkages.

翻译：确定工艺-结构-性能关联是材料科学的关键目标之一，而不确定性量化在理解工艺-结构及结构-性能关联中起着重要作用。本研究旨在学习微观结构参数的分布，其核心要求是该分布通过晶体塑性有限元模型（CPFEM）正向传播后，能够与材料性能的目标分布保持一致。这种随机逆推公式推断出可接受/一致微观结构的分布（而非确定性解），从而以概率化方式扩展了可行设计的范围。为求解该随机逆问题，我们采用基于前推概率测度的最新不确定性量化（UQ）框架，该框架融合测度论与贝叶斯规则以定义唯一且数值稳定的解。该方法需先利用模型输入的初始猜测分布进行预测，并求解随机正问题。为降低求解随机正问题与随机逆问题的计算成本，我们将该框架与基于高斯过程的机器学习（ML）贝叶斯回归模型相结合，并通过两个代表性的结构-性能关联案例研究验证所提方法的有效性。