The paper introduces a mesh‑free multiresolution deep energy method for phase‑field modeling of brittle fracture. A single neural network represents displacement and phase fields, trained by minimizing incremental energy with multiresolution B‑spline feature encoding and stratified Monte Carlo integration. Across six benchmark problems, the method reproduces load‑displacement curves and crack patterns with high accuracy, outperforming a deep Ritz baseline on a random multi‑crack dataset.
By Han Zhang, Mehrisadat Makki Alamdari, Babak Shahbodagh, Mohammad Vahab, Cosmin Anitescu, Timon Rabczuk, Elena Atroshchenko
Phase-field modeling of brittle fracture removes the need to track cracks explicitly by recasting their evolution as the minimization of an energy functional. In return it requires a discretization de...
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
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
arXiv:2607. 09382v1 Announce Type: new Abstract: This work aims to develop a fast and physically consistent surrogate model for real-time structural health monitoring of fractured elastic domains.
By Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz, St\'ephane Grieu
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. 12271v1 Announce Type: new Abstract: In this paper, a parametric physics-informed neural network for solving the heterogeneous soil thermal problem with borehole heat exchangers (BHEs) as singular sources is developed.
By Moke Rao, Thomas Hamacher, Smajil Halilovic
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:2507.05291v2 Announce Type: replace-cross
Abstract: We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale, in the contex...
By Manuel Ricardo Guevara Garban, Yves Chemisky, \'Etienne Pruli\`ere, Micha\"el Cl\'ement
arXiv:2606. 19375v1 Announce Type: new Abstract: Identifying anisotropic yield functions remains challenging since yielding is not directly observed in full-field mechanical measurements, directional calibration can require many loading directions, and selecting an appropriate analytical form is nontrivial.
By Hyeonbin Moon, Donghyuk Cho, Jecheon Yu, Jeong Whan Yoon, Seunghwa Ryu
arXiv:2604. 14562v2 Announce Type: replace Abstract: Accurate temperature field prediction in metal additive manufacturing (AM) is essential for understanding the process-structure-performance relationship.
By Hyeonsu Lee, Jihoon Jeong
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