Automatic-Differentiation-Enabled Finite Element Model Updating: Learning Constitutive Neural Networks from Structural Deformation Data

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.