A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materials

Abstract: Predicting stress fields in hyperelastic materials with complex microstructures remains challenging for traditional deep learning surrogates, which struggle to capture both sharp stress concentrations and the wide dynamic range of stress magnitudes. Convolutional architectures such as UNet tend to oversmooth high-frequency gradients, while neural operators like DeepONet exhibit spectral bias and underpredict localized extremes. Diffusion models can recover fine-scale structure but often introduce low-frequency amplitude drift, degrading physical scaling. To address these limitations, we propose a hybrid surrogate framework, cDDPM-DeepONet, that decouples stress morphology from magnitude. A conditional denoising diffusion probabilistic model (cDDPM), built on a UNet backbone, generates normalized von Mises stress fields conditioned on geometry and loading. In parallel, a modified DeepONet predicts global scaling parameters (minimum and maximum stress), enabling reconstruction of full-resolution physical stress maps. This separation allows the diffusion model to focus on spatial structure while the operator network corrects global amplitude, mitigating spectral and scaling biases. We evaluate the framework on nonlinear hyperelastic datasets with single and multiple polygonal voids. The proposed model consistently outperforms UNet, DeepONet, and standalone cDDPM baselines by one to two orders of magnitude. Spectral analysis shows strong agreement with finite element solutions across all wavenumbers, preserving both global behavior and localized stress concentrations.