Uncertainty quantification (UQ) plays a critical role in verifying and validating forward integrated computational materials engineering (ICME) models. Among numerous ICME models, the crystal plasticity finite element method (CPFEM) is a powerful tool that enables one to assess microstructure-sensitive behaviors and thus, bridge material structure to performance. Nevertheless, given its nature of constitutive model form and the randomness of microstructures, CPFEM is exposed to both aleatory uncertainty (microstructural variability), as well as epistemic uncertainty (parametric and model-form error). Therefore, the observations are often corrupted by the microstructure-induced uncertainty, as well as the ICME approximation and numerical errors. In this work, we highlight several ongoing research topics in UQ, optimization, and machine learning applications for CPFEM to efficiently solve forward and inverse problems.

翻译：不确定性量化（UQ）在验证和确认前向集成计算材料工程（ICME）模型中起着关键作用。在众多ICME模型中，晶体塑性有限元方法（CPFEM）是一种强大工具，能够评估微观结构敏感行为，从而桥接材料结构与性能。然而，鉴于其本构模型形式及微观结构的随机性，CPFEM同时面临偶发不确定性（微观结构变异性）与认知不确定性（参数误差和模型形式误差）。因此，观测结果常受微观结构诱发的不确定性以及ICME近似误差和数值误差的影响。本文重点阐述了CPFEM中不确定性量化、优化及机器学习应用的若干前沿研究课题，旨在高效解决正向与逆向问题。