Quantifying uncertainty associated with the microstructure variation of a material can be a computationally daunting task, especially when dealing with advanced constitutive models and fine mesh resolutions in the crystal plasticity finite element method (CPFEM). Numerous studies have been conducted regarding the sensitivity of material properties and performance to the mesh resolution and choice of constitutive model. However, a unified approach that accounts for various fidelity parameters, such as mesh resolutions, integration time-steps, and constitutive models simultaneously is currently lacking. This paper proposes a novel uncertainty quantification (UQ) approach for computing the properties and performance of homogenized materials using CPFEM, that exploits a hierarchy of approximations with different levels of fidelity. In particular, we illustrate how multi-level sampling methods, such as multi-level Monte Carlo (MLMC) and multi-index Monte Carlo (MIMC), can be applied to assess the impact of variations in the microstructure of polycrystalline materials on the predictions of homogenized materials properties. We show that by adaptively exploiting the fidelity hierarchy, we can significantly reduce the number of microstructures required to reach a certain prescribed accuracy. Finally, we show how our approach can be extended to a multi-fidelity framework, where we allow the underlying constitutive model to be chosen from either a phenomenological plasticity model or a dislocation-density-based model.
Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学研究所）；Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）；Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Technical University of Munich（慕尼黑工业大学）
Microstructure-based Variational Neural Networks for Robust Uncertainty Quantification in Materials Digital Twins
Center for Integrated Nanotechnologies（集成纳米技术中心）；Sandia National Laboratories（桑塔纳国家实验室）；Theoretical Division（理论 division）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Department of Mechanical Engineering（机械工程系）；Pohang University of Science and Technology（釜山科学技术大学）
Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification
Institute for Mathematical Innovation University of Bath, Bath, UK（数学创新研究所 英国巴斯大学）；Department of Mathematical Sciences University of Bath, Bath, UK（数学科学系 英国巴斯大学）
Uncertainty Propagation in a Multiscale CALPHAD-Reinforced Elastochemical Phase-field Model
ICME方法通过建立定量的工艺-结构-性能关系，为材料设计提供决策支持。然而，必须通过在ICME模型链中建立不确定性界限来实现对决策支持的信心。然而，计算材料科学中不确定性的量化和传播仍然是计算材料科学方法的一个相当未探索的方面。此外，传统的不确定性传播框架往往是有限的情况下，计算昂贵的模拟。一个相当常见和重要的模型链是基于CALPHAD的相稳定性热力学模型与相场模型耦合的微观结构演化模型。在这些情况下，不确定性的传播是具有挑战性的，不仅是由于纯粹的模拟计算成本，而且还因为输入空间的高维数。在这项工作中，我们提出了一个框架的量化和传播的不确定性，在基于CALPHAD的弹性化学相场模型。我们通过研究Mg $_2$（Si $_x$ Sn $_{1-x}$）热电材料的微观结构演变来激发我们的工作。我们首先进行了马尔可夫链蒙特卡洛为基础的推断的CALPHAD模型参数的伪二进制系统，然后使用先进的采样方案传播的不确定性在高维模拟输入空间。通过高通量相场模拟，我们生成了200，000个合成微结构的时间序列，并使用机器学习方法来了解传播的不确定性对所研究系统的微结构景观的影响。微观结构数据集已在开放相场微观结构数据库（OPMD）中整理，可在\href{http://microstructures.net}{http://microstructures.net}获得。
Quantification of 3D spatial correlations between state variables and distances to the grain boundary network in full-field crystal plasticity spectral method simulations
Microstructure Generation via Generative Adversarial Network for Heterogeneous, Topologically Complex 3D Materials
U.S. DOE National Energy Technology Laboratory（美国能源部国家能源技术实验室）；Carnegie Mellon University（卡内基梅隆大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Leidos Research Support Team（莱多斯研究支持团队）
On Strong-Scaling and Open-Source Tools for High-Throughput Quantification of Material Point Cloud Data: Composition Gradients, Microstructural Object Reconstruction, and Spatial Correlations
Machine learning materials physics: Deep neural networks trained on elastic free energy data from martensitic microstructures predict homogenized stress fields with high accuracy
Real-time quantification of fluid flows around bubbles during directional solidification
Université Lyon 1, CNRS Institut Lumière Matière UMR5306（里昂第一大学，CNRS光与物质研究所）；Sciences et Ingénierie de La Matière Molle UMR 7615, ESPCI Paris, PSL Research University, CNRS, Sorbonne Universités（软物质科学与工程UMR 7615，巴黎高等物理化工学院，PSL研究大学，CNRS，索邦大学）
Mapping Microstructure: Manifold Construction for Accelerated Materials Exploration
The Ohio State University（俄亥俄州立大学）；US Naval Research Laboratory（美国海军研究实验室）；Air Force Research Laboratory（空军研究实验室）；Blue Quartz Software, LLC（蓝石英软件有限责任公司）
