Polycrystalline metal failure often begins with stress concentration at grain boundaries. Identifying which microstructural features trigger these events is important but challenging because these extreme damage events are rare and the failure mechanisms involve multiple complex processes across scales. Most existing inference methods focus on average behavior rather than rare events, whereas standard sample-based methods are computationally expensive for high-dimensional complex systems. In this paper, we develop a new variational inference framework that integrates a recently developed computationally efficient physics-informed statistical model with extreme value statistics to significantly facilitate the identification of material failure attributions. First, we reformulate the objective to emphasize observed exceedances by incorporating extreme-value theory into the likelihood, thereby highlighting tail behavior. Second, we constrain inference via a physics-informed statistical model that characterizes microstructure-stress relationships, which uniquely provides physically consistent predictions for these rare events. Third, mixture models in a reduced latent space are developed to capture the non-Gaussian characteristics of microstructural features, allowing the identification of multiple underlying mechanisms. In both controlled and realistic experimental tests for the bicrystal configuration, the framework achieves reliable extreme-event prediction and reveals the microstructural features associated with material failure, providing physical insights for material design with uncertainty quantification.

翻译：多晶金属的失效通常始于晶界处的应力集中。识别哪些微观结构特征会触发这些事件至关重要，但由于这些极端损伤事件较为罕见，且失效机制涉及跨尺度的多个复杂过程，这一任务极具挑战性。现有的大多数推理方法侧重于平均行为而非罕见事件，而标准的基于抽样的方法对于高维复杂系统计算成本高昂。本文提出了一种新的变分推理框架，该框架将近期开发的计算高效的物理信息统计模型与极值统计相结合，从而显著促进了材料失效归因的识别。首先，我们通过将极值理论融入似然函数，重构了强调观测超限值的目标函数，从而突出了尾部行为。其次，我们通过一个描述微观结构-应力关系的物理信息统计模型来约束推理，该模型独特地为这些罕见事件提供了物理一致的预测。第三，我们在降维的潜空间中开发了混合模型，以捕捉微观结构特征的非高斯特性，从而能够识别多种潜在机制。在双晶构型的受控和实际实验测试中，该框架实现了可靠的极端事件预测，并揭示了与材料失效相关的微观结构特征，为考虑不确定性量化的材料设计提供了物理见解。