# Heterogeneous Graph Representation of Stiffened Panels with Non-Uniform Boundary Conditions and Loads

arXiv: https://arxiv.org/abs/2510.02472 · HTML: https://mlsanity.com/paper/2510.02472/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 80 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Heterogeneous Graph Transformer](https://mlsanity.com/paper/2003.01332/) (2020)
- [Scene Graph Generation by Iterative Message Passing](https://mlsanity.com/paper/1701.02426/) (2017)
- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [Spectrally approximating large graphs with smaller graphs](https://mlsanity.com/paper/1802.07510/) (2018)
- [Graph Coarsening with Neural Networks](https://mlsanity.com/paper/2102.01350/) (2021)
- [A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method](https://mlsanity.com/paper/2206.13103/) (2022)
- [A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations](https://mlsanity.com/paper/2212.14545/) (2022)
- [Towards Reusable Surrogate Models: Graph-Based Transfer Learning on Trusses](https://mlsanity.com/paper/2109.02689/) (2021)
- [Learning the nonlinear dynamics of soft mechanical metamaterials with graph networks](https://mlsanity.com/paper/2202.13775/) (2022)
- [Separable Physics-Informed Neural Networks for the solution of elasticity problems](https://mlsanity.com/paper/2401.13486/) (2024)
- [LatticeGraphNet: A two-scale graph neural operator for simulating lattice structures](https://mlsanity.com/paper/2402.01045/) (2024)
- [Graph Neural Network for Stress Predictions in Stiffened Panels Under Uniform Loading](https://mlsanity.com/paper/2309.13022/) (2023)

## Built on by (most cited first, 2 of 2)

- [Physics-Guided Dual-Stream Heterogeneous Graph Neural Network for Predicting Full-Field Structural Response of Stiffened Panels](https://mlsanity.com/paper/2606.20916/) (2026)
- [One-Step Flow Matching for Generative Modeling of Path-Dependent Physical Fields](https://mlsanity.com/paper/2606.22752/) (2026)

## Abstract (arXiv)

Surrogate models are essential in structural analysis and optimization. We propose a heterogeneous graph representation of stiffened panels that accounts for geometrical variability, non-uniform boundary conditions, and diverse loading scenarios, using heterogeneous graph neural networks (HGNNs). The structure is partitioned into multiple structural units, such as stiffeners and the plates between them, with each unit represented by three distinct node types: geometry, boundary, and loading nodes. Edge heterogeneity is introduced by incorporating local orientations and spatial relationships of the connecting nodes. Several heterogeneous graph representations, each with varying degrees of heterogeneity, are proposed and analyzed. These representations are implemented into a heterogeneous graph transformer (HGT) to predict von Mises stress and displacement fields across stiffened panels, based on loading and degrees of freedom at their boundaries. To assess the efficacy of our approach, we conducted numerical tests on panels subjected to patch loads and box beams composed of stiffened panels under various loading conditions. The heterogeneous graph representation was compared with a homogeneous counterpart, demonstrating superior performance. Additionally, an ablation analysis was performed to evaluate the impact of graph heterogeneity on HGT performance. The results show strong predictive accuracy for both displacement and von Mises stress, effectively capturing structural behavior patterns and maximum values.