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

TL;DR

This work tackles identifying microstructural attributions to extreme stress events in polycrystals by formulating a tail-focused Bayesian inference framework. It integrates a physics-informed stress model with extreme-value theory within a variational inference scheme that operates in a dimension-reduced latent space represented by Gaussian mixtures. The approach yields reliable tail predictions and interpretable mechanisms of failure, demonstrated through bicrystal simulations and data-scarce scenarios, while quantifying uncertainty in the tail. The framework offers computational efficiency and physical consistency, enabling better-informed material design under uncertainty and suggesting avenues for extending to more complex polycrystal configurations.

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 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.

Figures (8)

• Figure 1: Overview diagram of the general physics-informed variational inference framework.
• Figure 2: Comparison of posterior distributions in PCA latent space across different inference methods. The figure shows PDF contours and scatter plots for three pairs of principal components. (a) Prior GMM distribution fitted to all training data, (b) Variational inference (GMM-VI) posterior targeting extreme events, (c) MCMC posterior samples for the same target distribution, and (d) Empirical GMM fitted directly to observed extreme events. Colored density maps (purple to yellow) indicate probability density from low to high. Red scatter points show the locations of extreme events.
• Figure 3: Performance evaluation of extreme event classification using three different inference methods: (a) GMM-VI posterior, (b) MCMC posterior, and (c) Empirical distribution estimation. Top row shows confusion matrices for binary classification (Normal vs. Extreme). Numbers in cells represent counts of true positives, false positives, true negatives, and false negatives. Bottom row displays LLR scores plotted against true stress values for each method, where points are colored by prediction correctness (red = correct, blue = incorrect). The vertical dashed line indicates the stress threshold $S_{th}$, while the horizontal line shows the LLR decision threshold.
• Figure 4: False negative rate and false positive rate as functions of LLR threshold for three methods in the perfect model test.
• Figure 5: BIC analysis for GMM fitting of prior distribution $\mathbf{z}$ in the latent space, and stress distributions for for both bicrystal configurations. Panel (a) and (b): Bayesian Information Criterion (BIC) as a function of mixture components. Panel (c) and (d): Stress PDFs showing 95th percentile thresholds (red dashed lines), used to define extreme events.