A Physics-Informed Variational Inference Framework for Identifying Attributions of Extreme Stress Events in Low-Grain Polycrystals

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.