# Graph Neural Network-based Surrogate Models for Finite Element Analysis

arXiv: https://arxiv.org/abs/2211.09373 · HTML: https://mlsanity.com/paper/2211.09373/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2022.

## Built on by (most cited first, 7 of 7)

- [Physics-Informed Graph Convolutional Networks: Towards a generalized framework for complex geometries](https://mlsanity.com/paper/2310.14948/) (2023)
- [Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks](https://mlsanity.com/paper/2502.08783/) (2025)
- [Graph Network-based Structural Simulator: Graph Neural Networks for Structural Dynamics](https://mlsanity.com/paper/2510.25683/) (2025)
- [A Hybrid GNN approach for predicting node data for 3D meshes](https://mlsanity.com/paper/2310.14707/) (2023)
- [Predicting Wall Thickness Changes in Cold Forging Processes: An Integrated FEM and Neural Network approach](https://mlsanity.com/paper/2411.13366/) (2024)
- [Learning Mappings in Mesh-based Simulations](https://mlsanity.com/paper/2506.12652/) (2025)
- [A Research Prototype for Closed-Loop Generative Design of Customized Foot Orthoses via Semantic-Physics Alignment](https://mlsanity.com/paper/2607.16631/) (2026)

## Abstract (arXiv)

Current simulation of metal forging processes use advanced finite element methods. Such methods consist of solving mathematical equations, which takes a significant amount of time for the simulation to complete. Computational time can be prohibitive for parametric response surface exploration tasks. In this paper, we propose as an alternative, a Graph Neural Network-based graph prediction model to act as a surrogate model for parameters search space exploration and which exhibits a time cost reduced by an order of magnitude. Numerical experiments show that this new model outperforms the Point-Net model and the Dynamic Graph Convolutional Neural Net model.