用于本构模型中不确定性量化和传播的区间与模糊物理增强神经网络（iPANN和fPANN）

中文摘要 AI 辅助

在不确定性下的本构建模仍是可靠力学模拟的核心挑战，尤其是在可用应力 - 变形数据稀疏、有噪声或不均匀时。我们提出区间和模糊物理增强神经网络（iPANNs和fPANNs）用于不确定性感知的超弹性本构建模。iPANNs学习稀疏的自由能密度分支，fPANNs通过α - 截集插值将其嵌入模糊集表示。它们编码机械约束并采用平滑L0正则化。通过两阶段转移学习训练模型。在合成数据上评估框架，结果表明学习到的边界能包围有噪声的应力观测值并推广到测试集，还能在有限元设置中进行不确定性传播。该框架为超弹性本构建模中无分布的偶然不确定性量化及下游有限元模拟中的传播提供了紧凑且符合物理的途径。

英文摘要

Constitutive modeling under uncertainty remains a central challenge for reliable mechanics simulations, particularly when the available stress-deformation data are sparse, noisy, or heterogeneous. We propose interval and fuzzy physics-augmented neural networks (iPANNs and fPANNs) for uncertainty-aware hyperelastic constitutive modeling. iPANNs learn sparse lower, mean, and upper free energy density branches whose stresses, obtained by automatic differentiation, ultimately enclose noisy stress observations. In contrast to this deterministic interval description, fPANNs embed the learned iPANN branches into a fuzzy-set representation through membership-level (alpha-cut) interpolation, yielding a nested family of admissible responses. iPANNs and fPANNs encode mechanistic constraints by preserving objectivity, consistency and promoting polyconvexity and, smoothed L0 regularization promoting interpretable energy representations. The bound models are trained through a two-stage transfer-learning procedure in which a sparse mean constitutive response is learned first and then fine-tuned into lower and upper energy branches. We evaluate the framework on synthetic isotropic hyperelastic data with heteroscedastic noise, varying random realizations, shifted noise means, and varying noise magnitudes. The results show that the learned bounds enclose noisy stress observations while generalizing to the test set. Further, we examine the propagation of uncertainty through the mean, upper and lower bound predictions of the learned iPANN models in a finite element setting. The proposed framework provides a compact, physics-consistent route for distribution-free aleatoric uncertainty quantification in hyperelastic constitutive modeling, and propagation in downstream finite element simulations.

发表机构

• Cornell University（康奈尔大学）
• Ecole Polytechnique Federale de Lausanne (EPFL)（洛桑联邦理工学院）
• Sandia National Laboratories（桑迪亚国家实验室）
• University of Southern California（南加州大学）
• Pasteur Labs（巴斯德实验室）

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