The paper introduces Thermodynamically Consistent Latent Dynamics Identification (tLaSDI) using parametric GENERIC Formalism-Informed Neural Networks (pGFINNs) to predict fracture patterns and evolution in heterogeneous materials. By embedding thermodynamic principles—such as total energy conservation and entropy generation—directly into the neural network architecture, the model operates in a lower‑dimensional latent space and maintains thermodynamic consistency on unseen data. A Geometry‑Conditioned Autoencoder further enhances geometry‑guided learning, and results show that tLaSDI‑pGFINNs outperform a purely data‑driven AE‑LSTM model in accurately capturing fracture behavior.
By Muhamad Alim, Xiaolong He, Mei-Na Tsao, Chi-Hua Yu, J. S. Chen
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
arXiv:2608. 04778v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) incorporate governing equations into neural-network training and can approximate PDE solutions without requiring large observational datasets.
By Xujia Chen, Xinyue Hu, Letian Chen, Yi Liu, Wenhui Fan
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.
By Manuel Ricardo Guevara Garban, Yves Chemisky, \'Etienne Pruli\`ere, Micha\"el Cl\'ement, Martin Abendroth, Bj\"orn Kiefer
arXiv:2609.26426v1 Announce Type: new
Abstract: Finite Element Analysis (FEA) is widely used for transient mechanical simulations, but its high computational cost limits real-time and high-resolution...
By Georgios Triantafyllou, Panagiotis G. Kalozoumis, Dimitris K. Iakovidis
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