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 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 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 Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure–property linkages.

中文翻译：

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使用数据一致反演和机器学习解决属性-结构联系的随机逆问题

确定过程-结构-性质的联系是材料科学的关键目标之一，不确定性量化在理解过程-结构和结构-性质的联系方面起着关键作用。在这项工作中，我们寻求学习微观结构参数的分布，这些分布在这种分布通过晶体塑性有限元模型的前向传播与材料特性的目标分布相匹配的意义上是一致的。这种随机反演公式推断出可接受/一致微观结构的分布，而不是确定性解决方案，后者以概率方式扩展了可行设计的范围。为了解决这个随机逆问题，我们采用了最近开发的基于前推概率度量的不确定性量化框架，它结合了来自测度理论和贝叶斯规则的技术来定义一个独特且数值稳定的解决方案。这种方法需要使用模型输入分布的初始猜测进行初始预测，并解决随机前向问题。为了减少解决随机正向和随机逆向问题的计算负担，我们将这种方法与基于高斯过程的机器学习贝叶斯回归模型相结合，并在结构-性质联系的两个代表性案例研究中展示了所提出的方法。