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

2026-03-18

AI Summary

This work addresses the challenge that conventional deep learning surrogate models struggle to simultaneously capture stress concentration zones and the wide dynamic range of stress magnitudes in hyperelastic materials. To overcome this limitation, the authors propose a hybrid cDDPM-DeepONet framework that innovatively decouples the stress field into spatial morphology and global amplitude: the normalized spatial morphology is generated by a UNet-based conditional denoising diffusion probabilistic model (cDDPM), while a modified DeepONet predicts the corresponding scaling parameter. This decomposition effectively mitigates spectral bias and amplitude drift, achieving one to two orders of magnitude higher accuracy than standalone UNet, DeepONet, or cDDPM on both single- and multi-hole hyperelastic datasets, with excellent agreement against finite element solutions across the full wavenumber spectrum.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• hyperelastic materials
• stress prediction
• stress concentration
• dynamic range
• microstructure

Innovation

• conditional diffusion model
• DeepONet
• stress field prediction
• hyperelastic materials
• hybrid neural operator