arXiv AI By Manuel Ricardo Guevara Garban, Yves Chemisky, \'Etienne Pruli\`ere, Micha\"el Cl\'ement

Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity

Read the original on arXiv AI →

The Flow has not summarised this story yet — read it at arXiv AI.

arXiv Machine Learning
Jun 10

Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks

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 Machine Learning
Jun 19

A Hybrid GNN-FEM Framework for Phase-Field Fracture Simulation. Physics-Preserving Hybridization for Generalizable Surrogate Modeling

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 Machine Learning
Sep 17

ADAPT: Lightweight, Long-Range Machine Learning Force Fields Without Graphs

The paper introduces ADAPT, a lightweight machine‑learning force field that replaces graph neural networks with a direct coordinates‑in‑space Transformer encoder to model all pairwise atomic interactions. Applied to silicon point defects, ADAPT reduces force prediction error by about 22% and energy prediction error by roughly 40% compared to a state‑of‑the‑art GNN model, while also cutting computational cost. This approach addresses common GNN issues such as oversmoothing, oversquashing, and poor long‑range interaction representation, which are especially problematic for point defect modeling.

By Evan Dramko, Yihuang Xiong, Yizhi Zhu, Geoffroy Hautier, Thomas Reps, Christopher Jermaine, Anastasios Kyrillidis
arXiv Machine Learning
Sep 10

Hyperelastic constitutive model discovery with differentiable finite elements and structure-preserving neural networks

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 Machine Learning
Oct 15

Constitutive parameterized deep energy method for solid mechanics problems with random material parameters

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