Diffusion Models for Predicting Uncertainty in Full-field Material Response
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Microstructure-sensitive material response is inherently high-dimensional and spatially heterogeneous, with similar macroscopic behavior often arising from distinct microstructures while local stress fields differ significantly. Accurately capturing this variability is essential for micromechanics-driven modeling, yet remains challenging for data-driven approaches that aim to predict full-field responses. This work presents a data-driven generative modeling framework based on a conditional denoising diffusion probabilistic model (cDDPM) for predicting full-field von Mises stress distributions in polycrystalline microstructures. Rather than learning a deterministic input–output mapping, the model learns a conditional distribution of stress fields given microstructural geometry and loading conditions. The reverse diffusion process is parameterized by an attention-based UNet architecture, enabling multi-scale representation of micromechanical features such as grain boundaries and stress localization regions. Due to the stochastic nature of diffusion sampling, the framework generates multiple physically consistent stress realizations for a given input, allowing uncertainty quantification through ensemble statistics and Bayesian model averaging without imposing explicit distributional assumptions. The model is trained on synthetically generated polycrystalline microstructures with orthotropic grains and random orientations. Results show that the cDDPM accurately reproduces stress patterns across unseen microstructures, capturing localized stress concentrations and sharp geometric features. The predicted uncertainty fields are spatially heterogeneous and align with regions of high stress gradients and elevated prediction error, providing physically interpretable confidence measures. Ensemble averaging further improves predictive accuracy compared to individual diffusion samples. Overall, this work demonstrates that diffusion-based generative models provide a scalable and effective approach for uncertainty-aware full-field prediction in computational micromechanics, supporting data-driven exploration of microstructure–response relationships.
