The paper introduces a variational, label‑free physics‑informed graph neural network (PI‑GNN) that models heterogeneous solid mechanics by embedding material heterogeneity into the discretization rather than the neural network’s trial field. The PI‑GNN operates on a conforming adaptive mesh graph, assigns constitutive behavior per element, and minimizes the discrete total potential energy without penalty terms or interface weights, yielding a discrete energy equivalent to the finite element Ritz functional. Across small‑strain elasticity and finite‑strain Neo‑Hookean hyperelasticity in 2D and 3D, the method achieves von Mises errors below 3.58 % over a wide stiffness‑contrast range, outperforming strong‑form PINNs and reducing displacement errors significantly.
By Aashay Rajan Yadav, Amiya Prakash Das, Ratna Kumar Annabattula
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.
By Matthias Knipper, Chenyi Ji, Malte Brand, Kevin Linka
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.
By S. Ares de Parga, A. Cornejo, J. A. Hern\'andez, R. Rossi
arXiv:2606. 16624v2 Announce Type: replace Abstract: Plate and shell structures are widely used in engineering fields.
By Siqi Wang, Daobo Sun, Yizheng Wang, Yilong Zhang, Yabin Jin, Xiaoying Zhuang, Timon Rabczuk
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.
By Matthias Knipper, Chenyi Ji, Malte Brand, Kevin Linka
arXiv:2606. 19378v1 Announce Type: new Abstract: Scientific machine learning (SciML) has emerged as a promising approach for accelerating simulations of complex physical systems, yet achieving physically consistent and generalizable predictions for nonlinear, history-dependent problems remains a central challenge.
By Hyeonbin Moon, Yongjin Choi, Seunghwa Ryu