# A review of graph neural network applications in mechanics-related domains

arXiv: https://arxiv.org/abs/2407.11060 · HTML: https://mlsanity.com/paper/2407.11060/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 157 references that are in the map.
- First posted on arXiv 10 Jul 2024.

## Builds on (most cited first, 30 of 61)

- [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)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [A Critical Review of Recurrent Neural Networks for Sequence Learning](https://mlsanity.com/paper/1506.00019/) (2015)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directions](https://mlsanity.com/paper/2109.12843/) (2021)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [Everything is Connected: Graph Neural Networks](https://mlsanity.com/paper/2301.08210/) (2023)
- [Computing Graph Neural Networks: A Survey from Algorithms to Accelerators](https://mlsanity.com/paper/2010.00130/) (2020)

## Built on by (most cited first, 14 of 14)

- [A graph neural network surrogate model for mesh-based crashworthiness prediction of vehicle panel components](https://mlsanity.com/paper/2503.17386/) (2025)
- [On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL condition](https://mlsanity.com/paper/2507.08861/) (2025)
- [Rapid training of Hamiltonian graph networks using random features](https://mlsanity.com/paper/2506.06558/) (2025)
- [Parameter-Efficient Conditioning for Material Generalization in Graph-Based Simulators](https://mlsanity.com/paper/2511.05456/) (2025)
- [Rigid-Deformation Decomposition AI Framework for 3D Spatio-Temporal Prediction of Vehicle Collision Dynamics](https://mlsanity.com/paper/2503.19712/) (2025)
- [A Mesh-Adaptive Hypergraph Neural Network for Unsteady Flow Around Oscillating and Rotating Structures](https://mlsanity.com/paper/2503.22252/) (2025)
- [Towards Robust Surrogate Models: Benchmarking Machine Learning Approaches to Expediting Phase Field Simulations of Brittle Fracture](https://mlsanity.com/paper/2507.07237/) (2025)
- [Recurrent U-Net-Based Graph Neural Network (RUGNN) for Accurate Deformation Predictions in Sheet Material Forming](https://mlsanity.com/paper/2507.11547/) (2025)
- [Graph Network-based Structural Simulator: Graph Neural Networks for Structural Dynamics](https://mlsanity.com/paper/2510.25683/) (2025)
- [Adaptive Fusion Graph Network for 3D Strain Field Prediction in Solid Rocket Motor Grains](https://mlsanity.com/paper/2512.23443/) (2025)
- [A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws](https://mlsanity.com/paper/2604.15617/) (2026)
- [Differentiable Multiphysics Co-Optimization via Implicit Neural Representations: A Transient Hamburger-Cooking Benchmark](https://mlsanity.com/paper/2605.01040/) (2026)
- [GNN for Structural Displacement Prediction](https://mlsanity.com/paper/2605.08303/) (2026)
- [A variational physics-informed graph neural network for heterogeneous solid mechanics](https://mlsanity.com/paper/2609.10983/) (2026)

## Abstract (arXiv)

Mechanics-related problems often present unique challenges in achieving accurate geometric and physical representations, particularly for non-uniform structures. Graph neural networks (GNNs) have emerged as a promising tool to tackle these challenges by adeptly learning from graph data with irregular underlying structures. Consequently, recent years have witnessed a surge in complex mechanics-related applications inspired by the advancements of GNNs. Despite this process, there is a notable absence of a systematic review addressing the recent advancement of GNNs in solving mechanics-related problems. To bridge this gap, this review article aims to provide an in-depth overview of the GNN applications in mechanics-related domains while identifying key challenges and outlining potential future research directions. In this review article, we begin by introducing the fundamental algorithms of GNNs that are widely employed in mechanics-related applications. We provide a concise explanation of their underlying principles to establish a solid understanding that will serve as a basis for exploring the applications of GNNs in mechanics-related domains. The scope of this paper is intended to cover the categorisation of literature into solid mechanics, fluid mechanics, and interdisciplinary mechanics-related domains, providing a comprehensive summary of graph representation methodologies, GNN architectures, and further discussions in their respective subdomains. Additionally, open data and source codes relevant to these applications are summarised for the convenience of future researchers. This article promotes an interdisciplinary integration of GNNs and mechanics and provides a guide for researchers interested in applying GNNs to solve complex mechanics-related problems.