论文标题
使用数据一致的反转和机器学习来解决属性结构链接的随机逆问题
Solving stochastic inverse problems for property-structure linkages using data-consistent inversion and machine learning
论文作者
论文摘要
确定过程结构 - 专业链接是材料科学中的关键目标之一，不确定性量化在理解过程结构和结构 - 培训链接方面起着至关重要的作用。在这项工作中，我们试图学习微观结构参数的分布，这些参数是一致的，从某种意义上说，通过晶体可塑性有限元模型（CPFEM）对该分布的正向传播与材料属性上的目标分布匹配。与确定性解决方案相反，这种随机反演提出的表达式呈现了可接受/一致的微观结构的分布，该解决方案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，我们采用了基于推送前向概率度量的最近开发的不确定性定量（UQ）框架，该框架结合了措施理论和贝叶斯规则的技术来定义独特且数值稳定的解决方案。这种方法需要使用对模型输入的分布并解决随机远期问题的初始猜测进行初始预测。为了减少解决随机前向和随机反问题的计算负担，我们将这种方法与基于高斯过程的机器学习（ML）贝叶斯回归模型相结合，并在结构 - 跨性别链接中的两种代表性案例研究中证明了拟议的方法。
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.
