混合模型精准预测复杂材料应力分布,突破传统方法精度瓶颈。
A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materials
- 分离结构与幅值:扩散模型生成应力形态,深度算子网络修正全局尺度。
- 相比基线模型,误差降低一到两个数量级,保留局部高应力集中特征。
- 适合需要高保真应力预测的结构力学仿真,如多孔弹性材料设计。
预测具有复杂微观结构的超弹性材料中的应力场对传统深度学习代理模型仍具挑战性,因其难以同时捕捉尖锐的应力集中和广泛的应力幅度动态范围。卷积架构如UNet易导致高频梯度过度平滑,而神经算子如DeepONet存在频谱偏差并低估局部极端值。扩散模型虽能恢复细粒度结构,但常引入低频幅值漂移,破坏物理量纲一致性。为此,我们提出一种混合代理框架cDDPM-DeepONet,将应力形态与幅值解耦。基于UNet主干的条件去噪扩散概率模型(cDDPM)在几何与载荷条件下生成归一化的冯·米塞斯应力场;同时,改进的DeepONet预测全局缩放参数(最小与最大应力),实现全分辨率物理应力图重建。该分离机制使扩散模型专注空间结构,算子网络修正全局幅值,有效缓解频谱与尺度偏差。我们在含单个与多个多边形孔洞的非线性超弹性数据集上评估该框架,结果表明其始终优于UNet、DeepONet及独立cDDPM基线模型,误差降低一至两个数量级。谱分析显示,各波数下与有限元解高度一致,既保持整体行为又精确保留局部应力集中。
原文摘要 · Abstract (English)
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.
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