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.
By Zhangyong Liang, Jihong Zhu, Huanhuan Gao
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
arXiv:2606. 04000v1 Announce Type: cross Abstract: We present a probabilistic modeling framework for incorporating small-scale spatial heterogeneity into macroscopic descriptions of material behavior for polycrystalline metallic materials.
By Pouria Behnoudfar, Deekshith Naidu Ponnana, Noah J. Schmelzer, Janith Wanni, George T. Gray III, Dan J. Thoma, Curt A. Bronkhorst, Nan Chen, Wenxiao Pan
arXiv:2606. 01179v1 Announce Type: cross Abstract: Entropy production governs irreversibility and uncertainty in both physical and information-theoretic systems.
By Biswajeet Sahoo, Debadutta Patra
arXiv:2607. 06479v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) provide a promising framework for solving partial differential equations while embedding the underlying physical laws directly into the learning process.
By Sonal Ankush Chibire, Jenn-Terng Gau, Bo Zhang
The paper introduces the mesh-based neural energy method (M‑NEM) for simulating heterogeneous composites, extending the neural energy method (NEM) by discretizing the displacement field on a mesh. By interpolating nodal displacements with shape functions, M‑NEM suppresses displacement oscillations, replaces automatic differentiation with algebraic shape‑function derivatives for strain, and uses high‑order Gaussian quadrature for energy integration. Benchmarks show that M‑NEM reduces stress errors by up to three orders of magnitude and is one to two orders faster than the conventional collocation‑based NEM, while also converging on problems with extreme stiffness contrasts where the conventional method fails.
By Pius J. M. Wichmann, Stefan Hildebrand, Sandra Klinge
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:2604. 13354v2 Announce Type: replace-cross Abstract: The discovery of inorganic crystal structures with targeted properties is a significant challenge in materials science.
By Auguste de Lambilly, Vladimir Baturin, David Portehault, Guillaume Lambard, Nataliya Sokolovska, Florence d'Alch\'e-Buc, Jean-Claude Crivello
arXiv:2603. 28707v3 Announce Type: replace-cross Abstract: We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics.
By Hagen Holthusen, Paul Steinmann, Ellen Kuhl
arXiv:2607. 19198v1 Announce Type: cross Abstract: Amorphous materials exhibit exceptional mechanical and functional properties, yet their rugged energy landscapes are notoriously difficult to sample.
By Mouyang Cheng, Denis Blessing, Botao Yu, Gerhard Neumann, Mingda Li, Carles Domingo-Enrich, Yuanqi Du
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.
By Francesco Regazzoni
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