FEM-Informed Hypergraph Neural Networks for Efficient Elastoplasticity

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.