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
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:2610.08475v1 Announce Type: new
Abstract: In many-query scenarios, data-driven surrogate models provide an efficient alternative to high-fidelity solvers for simulating physical systems governe...
By Stefano Maria Pizzamiglio, Stefano Pagani, Francesco Regazzoni
arXiv:2601. 07742v4 Announce Type: replace-cross Abstract: Many materials properties depend on higher-order derivatives of the potential energy surface, yet machine learned interatomic potentials (MLIPs) trained with a standard loss on energy, force, and stress errors can exhibit error in curvature, degrading the prediction of vibrational properties.
By Teddy Koker, Abhijeet Gangan, Mit Kotak, Jaime Marian, Tess Smidt
The paper presents a data‑efficient pre‑training framework for neural surrogate models solving PDEs on unstructured 3D geometries. It introduces a geometry‑driven strategy for steady‑state problems that uses intrinsic shape descriptors, and a physics‑driven approach for transient problems that generates synthetic PDE data online. Experiments show faster convergence, higher data efficiency, and improved accuracy during fine‑tuning, especially in low‑data settings.
By Luis Medrano-Navarro, Giacomo Baldan, Qiang Liu, Benjamin Holzschuh, Jan Hagnberger, Mathias Niepert, Nils Thuerey
The paper introduces a data‑driven constitutive modeling framework that treats a material as a functional mapping from its entire strain history to stress response. It uses neural operators with causal attention and spectral convolutions to predict full stress trajectories in a single parallel forward pass, enforcing temporal path dependence without relying on internal state variables. The method is validated on multidimensional, rate‑independent plasticity and ductile damage models, achieving accurate, resolution‑invariant predictions with excellent parallel efficiency.
By Rishabh Arora, Lisa Scheunemann, Tim Brepols, Shahed Rezaei
arXiv:2603.29515v3 Announce Type: replace
Abstract: The increasingly wide use of deep machine learning techniques in computational mechanics has significantly accelerated simulations of problems that...
By David Gonzalez, Alba Muixi, Beatriz Moya, Elias Cueto