arXiv cs.AI· Matthias Knipper, Chenyi Ji, Malte Brand, Kevin Linka·· 6 天前AI 评分22
ADE-FEMU：用自动微分从结构变形数据学习本构神经网络
Automatic-Differentiation-Enabled Finite Element Model Updating: Learning Constitutive Neural Networks from Structural Deformation Data
AI 导读
ADE-FEMU 是一个端到端可微框架，将本构神经网络嵌入 JAX-FEM 非线性求解器，通过梯度最小化测量失配损失来识别参数，可在动力学信息有限的结构数据上训练。该框架用前向与反向自动微分自动计算 Newton 切线刚度和损失梯度，无需解析伴随或离线代理模型，并在穿孔试样 DIC、降维拉伸数据及基体-夹杂两相系统三个公开数据集上验证。
正文 · 原文
Abstract:The identification of constitutive neural network models from heterogeneous full-field deformation data provides a robust alternative to traditional calibration methods based on homogeneous stress-strain experiments, particularly given the high dimensionality of trainable parameters. This work presents ADE-FEMU (Automatic-Differentiation-Enabled Finite Element Model Updating), an end-to-end differentiable framework that integrates a constitutive neural network model within a JAX-FEM nonlinear solver and identifies its parameters through gradient-based minimization of a measurement-mismatch loss, allowing for training on structural data with limited kinetic information. Thus, it can be considered as an extension of finite element model updating (FEMU) for hyperelastic materials, implemented within a GPU-accelerated, fully automatically differentiable finite element framework Newton tangent stiffness and loss gradients are computed automatically using forward- and reverse-mode automatic differentiation throughout the entire pipeline, thereby removing the need for analytic adjoints or offline surrogate models. ADE-FEMU is demonstrated for two architectures: a grey-box Constitutive Artificial Neural Network (CANN), a polyconvex, fully connected model with high flexibility, and a white-box CANN, an expert-system network with phenomenologically interpretable strain-energy terms. Focusing on incompressible isotropic hyperelasticity, ADE-FEMU is evaluated on three open experimental datasets: (1) full digital image correlation (DIC) of a perforated tensile specimen, (2) a reduced-data scenario with a one-dimensional stretch profile and global force-displacement curve, and (3) a heterogeneous matrix-inclusion system in which both phases constitutive laws are identified and generalized to twenty-two previously unseen samples.
| Subjects: | Computational Physics (physics.comp-ph); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2606.05199 [physics.comp-ph] |
| (or arXiv:2606.05199v2 [physics.comp-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2606.05199 arXiv-issued DOI via DataCite |
Submission history
From: Matthias Knipper [view email]
[v1]
Fri, 22 May 2026 11:36:48 UTC (28,395 KB)
[v2]
Fri, 9 Oct 2026 09:17:45 UTC (24,166 KB)
来源：arXiv cs.AI · arxiv.org