Non-linear Material Response Prediction Using Diffusion and Neural Operator Models

The high computational cost of finite element analysis (FEA) often limits its application to heterogeneous and complex materials, where intricate behaviors and interactions lead to time-extensive and computationally intensive simulations. As a result, data-driven approaches based on deep learning (DL) have emerged as promising, cost-effective surrogates that aim to bypass the heavy reliance on physics-based solvers. However, existing DL methods frequently struggle with generalization across diverse geometries and loading conditions, especially when the material response is non-linear. This study presents a novel DL framework designed to efficiently predict stress fields in hyperelastic material systems. This framework integrates a U-Net-based conditional denoising diffusion model, which produces normalized stress maps, with a neural operator model that simultaneously learns the scaling required to rescale these maps accurately. This two-pronged approach effectively addresses the restriction of applying traditional normalization techniques to materials responses over a wide range. Overall, this study validates the framework through experiments on hyperelastic and polycrystalline material models of varying complexity.