Automatic-Differentiation-Enabled Finite Element Model Updating: Learning Constitutive Neural Networks from Structural Deformation Data
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 36 of its 87 references that are in the map. First posted on arXiv 22 May 2026.
Builds on
36 of 87 references.
References · 36
- 2021Convex optimizationcited by 2,515
- 2016Input Convex Neural Networkscited by 414
- 2021Polyconvex anisotropic hyperelasticity with neural networkscited by 55
- 2020Unsupervised discovery of interpretable hyperelastic constitutive lawscited by 51
- 2022A new family of Constitutive Artificial Neural Networks towards automated model discoverycited by 49
- 2023Neural networks meet hyperelasticity: A guide to enforcing physicscited by 46
- 2022JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data sciencecited by 41
- 2024A review on data-driven constitutive laws for solidscited by 35
- 2022Automated discovery of generalized standard material models with EUCLIDcited by 31
- 2022NN-EUCLID: deep-learning hyperelasticity without stress datacited by 30
- 2021Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equationscited by 29
- 2022Discovering plasticity models without stress datacited by 28
24 more
- 2022Bayesian-EUCLID: discovering hyperelastic material laws with uncertaintiescited by 23
- 2024Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal variablescited by 17
- 2023On sparse regression, Lp-regularization, and automated model discoverycited by 15
- 2023Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteriacited by 14
- 2023Viscoelastic Constitutive Artificial Neural Networks (vCANNs) - a framework for data-driven anisotropic nonlinear finite viscoelasticitycited by 13
- 2022Automatic generation of interpretable hyperelastic material models by symbolic regressioncited by 12
- 2024Neural networks meet anisotropic hyperelasticity: A framework based on generalized structure tensors and isotropic tensor functionscited by 10
- 2024Inverse design of anisotropic microstructures using physics-augmented neural networkscited by 7
- 2024Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networkscited by 6
- 2024Automated model discovery of finite strain elastoplasticity from uniaxial experimentscited by 6
- 2024Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodelingcited by 6
- 2026Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material modelscited by 6
- 2024Reduced and All-at-Once Approaches for Model Calibration and Discovery in Computational Solid Mechanicscited by 5
- 2025A topology optimisation framework to design test specimens for one-shot identification or discovery of material modelscited by 5
- 2022Physics-Informed Neural Networks for Material Model Calibration from Full-Field Displacement Datacited by 4
- 2024Multiscale topology optimization of functionally graded lattice structures based on physics-augmented neural network material modelscited by 4
- 2025Material Fingerprinting: A shortcut to material model discovery without solving optimization problemscited by 4
- 2025A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strainscited by 4
- 2025Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energiescited by 3
- 2025Non-smooth optimization meets automated material model discoverycited by 3
- 2025Unsupervised Constitutive Model Discovery from Sparse and Noisy Datacited by 3
- 2026Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)cited by 3
- 2026Hyperelastic constitutive model discovery with differentiable finite elements and structure-preserving neural networkscited by 2
- 2026A Convex Route to Thermoelasticity: Learning Internal Energy and Dissipationcited by 1
Built on by
Not cited yet.