The paper presents a hyperreduction technique that accelerates finite element model updating for discovering neural constitutive models from structural experiments. By combining proper orthogonal decomposition, energy‑conserving sampling, and adjoint sensitivities, the method adapts the reduced trial space and sampled elements during training, enabling a polyconvex neural network to maintain accuracy while drastically reducing computational cost. Experiments on two experimental datasets and a synthetic 3‑D example show training times drop from hours to minutes without sacrificing predictive fidelity.
arXiv:2606. 05199v1 Announce Type: cross 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.
The paper introduces a differentiable finite element framework that discovers hyperelastic constitutive laws from limited experimental data, such as boundary-only displacement measurements and global reaction forces. By embedding the nonlinear finite element equilibrium problem into the learning loop, the method evaluates candidate strain‑energy densities through the deformation fields they produce, enforcing mechanical equilibrium as a constraint. The constitutive response is modeled with Hyperelastic Neural Networks, a structure‑preserving class that guarantees physical admissibility, including residual energy and stress‑free conditions, frame indifference, isotropic symmetry, polyconvexity, coercivity, and controlled volumetric growth. Numerical experiments in two and three dimensions show accurate recovery of hyperelastic isotropic responses, robustness to noise, and generalization across geometries, loading, and boundary conditions.
The paper introduces ADE‑FEMU, an end‑to‑end differentiable framework that embeds a constitutive neural network within a JAX‑based finite element solver and learns its parameters by minimizing a measurement‑mismatch loss using automatic differentiation. It demonstrates two neural network architectures—a flexible grey‑box CANN and an interpretable white‑box CANN—for incompressible isotropic hyperelastic materials, and validates the approach on three experimental datasets, including full‑field DIC, reduced‑data stretch profiles, and a heterogeneous matrix‑inclusion system.
This paper introduces a polyconvex physics‑augmented neural network (PANN) that uses learned paired directional features to model the anisotropic hyperelastic response of a representative volume element. The network’s energy functions are constructed with convex, componentwise nondecreasing cores (ICNN or ICKAN) and satisfy objectivity, stress‑free reference, two‑dimensional polyconvexity, and prescribed growth conditions. Experiments on multicavity and single‑cavity periodic cells show that the constrained PANN achieves sub‑percent stress and displacement errors, while an unconstrained model loses rank‑one convexity and under‑predicts compression stresses beyond the training data.
arXiv:2606. 10909v1 Announce Type: cross Abstract: Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations.
arXiv:2606. 14565v1 Announce Type: cross Abstract: Constitutive artificial neural networks (CANNs) provide interpretable material model discovery, but have so far been used in stress-supervised settings based on apparent stress-strain data from homogeneous tests.
The paper introduces the Constitutive Parameterized Deep Energy Method (CPDEM), a physics‑driven neural network that embeds stochastic material parameters directly into the strain energy density functional. By training via expected energy minimization over the parameter domain, CPDEM learns a continuous solution manifold, enabling zero‑shot, real‑time inference of displacement fields for any material parameters without retraining or dataset generation. The method is validated on linear elasticity, finite‑strain hyperelasticity, and highly nonlinear contact mechanics, marking the first purely physics‑driven deep learning approach that efficiently handles continuous multi‑parameter variations in solid mechanics.
Extending the neural-operator element method from individually trained, fixed-geometry neural elements to a library of reusable, geometry-parameterized element types fails structurally: a field-predicting operator trained by value regression induces an energy whose assembled Hessian is indefinite, and Newton converges to spurious minima (247% error) even with 1%-accurate field predictions. We introduce convex neural energy elements: each element exports a scalar energy E(g,U), architecturally convex in its boundary degrees of freedom U and smoothly parameterized by its geometry g, realized as a hypernetwork-generated positive-semidefinite quadratic form (an input-convex correction is reserved for non-quadratic physics).
arXiv:2605. 24651v2 Announce Type: replace-cross Abstract: We propose a Weak-form Physics-Informed Neural Operator (WINO), a data-free framework that combines the efficiency of neural operators with the geometric flexibility of the $\varphi$-finite element method ($\varphi$-FEM).
arXiv:2608. 14063v1 Announce Type: new Abstract: Machine learning is rapidly reshaping constitutive modeling, offers new ways to learn material behavior directly from experimental data, and challenges long-established modeling paradigms.
arXiv:2606. 08287v1 Announce Type: new Abstract: Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios.
arXiv:2608. 02036v1 Announce Type: new Abstract: Extending the neural-operator element method from individually trained, fixed-geometry neural elements to a library of reusable, geometry-parameterized element types fails structurally: a field-predicting operator trained by value regression induces an energy whose assembled Hessian is indefinite, and Newton converges to spurious minima (247% error) even with 1%-accurate field predictions.