A physics-informed variational inference framework for identifying attributions of extreme stress events in polycrystals

Abstract

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 events are rare and the failure mechanisms involve multiple complex processes across length scales. To address this challenge, the problem is approached from an inverse perspective by developing a new variational inference (VI) framework that integrates a recently introduced computationally efficient physics-informed statistical model with extreme-value statistics to facilitate the identification of material-failure attributions. First, we reformulate the objective to emphasize exceedances by incorporating extreme-value theory into the likelihood, thereby highlighting tail behaviour. Second, we constrain the inference process via a physics-informed statistical model that characterizes microstructure–stress relationships, which uniquely provides physical consistency for extreme 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 that mismatched elastic strains and strong misorientation of the overall compression directions are key microstructural conditions associated with stress localization and failure. These results provide physical insights for material design with uncertainty quantification.