FEM-Informed Hypergraph Neural Networks for Efficient Elastoplasticity

• URL: http://arxiv.org/abs/2602.07364v1
• Date: Sat, 07 Feb 2026 05:11:12 GMT
• Title: FEM-Informed Hypergraph Neural Networks for Efficient Elastoplasticity
• Authors: Jianchuan Yang, Xi Chen, Jidong Zhao,
• Abstract summary: Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations.<n>Motivated by discrete physics losses, we embed finite-element computations at nodes and Gauss points directly into message-passing layers.<n>We propose a numerically consistent FEM-Informed Hypergraph Neural Networks (FHGNN)
• Score: 3.211924713637672
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and Hierarchical Deep Learning Neural Network (HiDeNN) constructions, we embed finite-element (FEM) computations at nodes and Gauss points directly into message-passing layers and propose a numerically consistent FEM-Informed Hypergraph Neural Networks (FHGNN). Similar to conventional physics-informed neural networks (PINNs), training is purely physics-driven and requires no labeled data: the input is a node element hypergraph whose edges encode mesh connectivity. Guided by empirical results and condition-number analysis, we adopt an efficient variational loss. Validated on 3D benchmarks, including cyclic loading with isotropic/kinematic hardening, the proposed method delivers substantially improved accuracy and efficiency over recent, competitive PINN variants. By leveraging GPU-parallel tensor operations and the discrete representation, it scales effectively to large elastoplastic problems and can be competitive with, or faster than, multi-core FEM implementations at comparable accuracy. This work establishes a foundation for scalable, physics-embedded learning in nonlinear solid mechanics.

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