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

2026-03-20 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Computational Mechanics, Materials Science · Depth: Expert, extended

Summary

A new hybrid deep learning framework, cDDPM–DeepONet, has been developed to accurately predict stress fields in hyperelastic materials with complex microstructural features. This framework addresses limitations of traditional deep learning surrogates like UNet and standalone diffusion models, which struggle with simultaneously capturing sharp stress concentrations and wide dynamic ranges. The cDDPM–DeepONet decouples stress morphology from stress magnitude: a conditional denoising diffusion probabilistic model (cDDPM) generates high-fidelity normalized von Mises stress fields, while a modified DeepONet predicts global scaling parameters (minimum and maximum von Mises stress). This separation allows the diffusion model to focus on spatial structure and the operator network to correct global amplitude. Evaluated on two nonlinear hyperelastic datasets with single and multiple polygonal voids, the hybrid model outperforms UNet, DeepONet, and standalone cDDPM baselines by one to two orders of magnitude across various metrics, including MAE, RMSE, PAE, PV, and LSG. Spectral analysis confirms its superior agreement with finite element reference solutions across the full wavenumber spectrum.

Key takeaway

For research scientists developing computational mechanics surrogates, the cDDPM–DeepONet framework offers a robust solution for high-fidelity stress prediction in hyperelastic materials. You should consider this hybrid approach to overcome the trade-offs between capturing fine-scale features and maintaining accurate global scaling, especially when dealing with complex microstructures and nonlinear material responses. This method significantly reduces errors compared to traditional models, making it suitable for applications requiring precise stress field analysis.

Key insights

Decoupling stress morphology and magnitude via a hybrid cDDPM–DeepONet framework significantly improves stress field prediction.

Principles

• Diffusion models excel at fine-scale feature recovery.
• Neural operators accurately predict global scaling parameters.
• Hybrid models overcome individual architectural biases.

Method

A cDDPM generates normalized stress fields, conditioned on geometry and loading, while a DeepONet predicts global minimum and maximum von Mises stresses. These are then combined to reconstruct the full physical stress map.

In practice

• Use cDDPM for high-fidelity spatial structure generation.
• Employ DeepONet for accurate global amplitude prediction.
• Apply this hybrid approach for complex hyperelastic material analysis.

Topics

• Hybrid AI Models
• Stress Prediction
• Hyperelastic Materials
• Diffusion Models
• Neural Operators

Best for: Research Scientist, AI Researcher, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.