mlsanityData to 7 Oct 2026

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

arXiv 2407.11060 ↗First posted 10 Jul 2024cs.LG math-ph math.MPcited by 14

Not on the map. Why?

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.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 61 of its 157 references that are in the map. First posted on arXiv 10 Jul 2024.

Builds on

61 of 157 references.

References · 61

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2017Inductive Representation Learning on Large Graphscited by 6,284
  4. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  5. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  6. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  7. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  8. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  9. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  10. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  11. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  12. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
38 more
  1. 2014Deep Learning in Neural Networks: An Overviewcited by 765
  2. 2020Graph Neural Networks in Recommender Systems: A Surveycited by 493
  3. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  4. 2018Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separationcited by 400
  5. 2019Machine Learning for Fluid Mechanicscited by 380
  6. 2021Graph Neural Network for Traffic Forecasting: A Surveycited by 260
  7. 2020DeeperGCN: All You Need to Train Deeper GCNscited by 249
  8. 2018Graph networks as learnable physics engines for inference and controlcited by 242
  9. 2015A Critical Review of Recurrent Neural Networks for Sequence Learningcited by 223
  10. 2022Graph neural networks for materials science and chemistrycited by 181
  11. 2022Graph Neural Networks for Graphs with Heterophily: A Surveycited by 175
  12. 2019Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networkscited by 144
  13. 2021A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directionscited by 144
  14. 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 137
  15. 2019A Gentle Introduction to Deep Learning for Graphscited by 107
  16. 2021Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problemscited by 100
  17. 2023Everything is Connected: Graph Neural Networkscited by 85
  18. 2020Computing Graph Neural Networks: A Survey from Algorithms to Acceleratorscited by 81
  19. 2020Graph Neural Networks: Taxonomy, Advances and Trendscited by 48
  20. 2022Learning rigid dynamics with face interaction graph networkscited by 43
  21. 2020How to Build a Graph-Based Deep Learning Architecture in Traffic Domain: A Surveycited by 38
  22. 2022Physical Design using Differentiable Learned Simulatorscited by 37
  23. 2022GNN-Surrogate: A Hierarchical and Adaptive Graph Neural Network for Parameter Space Exploration of Unstructured-Mesh Ocean Simulationscited by 32
  24. 2021Constraint-based graph network simulatorcited by 27
  25. 2017Application of Convolutional Neural Network to Predict Airfoil Lift Coefficientcited by 26
  26. 2021Machine learning and deep learningcited by 26
  27. 2022MAgNET: A Graph U-Net Architecture for Mesh-Based Simulationscited by 26
  28. 2018Stress Field Prediction in Cantilevered Structures Using Convolutional Neural Networkscited by 25
  29. 2021Boundary Graph Neural Networks for 3D Simulationscited by 24
  30. 2023Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modelingcited by 21
  31. 2021Large-scale graph representation learning with very deep GNNs and self-supervisioncited by 18
  32. 2020Graph Convolutional Neural Networks for Body Force Predictioncited by 16
  33. 2021A Deep Emulator for Secondary Motion of 3D Characterscited by 16
  34. 2022A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulationscited by 14
  35. 2022Flow Completion Network: Inferring the Fluid Dynamics from Incomplete Flow Information using Graph Neural Networkscited by 13
  36. 2021What machine learning can do for computational solid mechanicscited by 12
  37. 2024Multiscale graph neural networks with adaptive mesh refinement for accelerating mesh-based simulationscited by 12
  38. 2022On the use of graph neural networks and shape-function-based gradient computation in the deep energy methodcited by 10

50 most cited of 61 All 61 (JSON)

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 10; 2026: 4.

14 papers.

Sort:

  1. 2025A graph neural network surrogate model for mesh-based crashworthiness prediction of vehicle panel componentscited by 4
  2. 2025On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL conditioncited by 4
  3. 2025Rapid training of Hamiltonian graph networks using random featurescited by 2
  4. 2025Parameter-Efficient Conditioning for Material Generalization in Graph-Based Simulatorscited by 2
  5. 2025Rigid-Deformation Decomposition AI Framework for 3D Spatio-Temporal Prediction of Vehicle Collision Dynamicscited by 1
  6. 2025Towards Robust Surrogate Models: Benchmarking Machine Learning Approaches to Expediting Phase Field Simulations of Brittle Fracturecited by 1
  7. 2025Recurrent U-Net-Based Graph Neural Network (RUGNN) for Accurate Deformation Predictions in Sheet Material Formingcited by 1
  8. 2025Graph Network-based Structural Simulator: Graph Neural Networks for Structural Dynamicscited by 1
  9. 2025A Mesh-Adaptive Hypergraph Neural Network for Unsteady Flow Around Oscillating and Rotating Structurescited by 0
  10. 2025Adaptive Fusion Graph Network for 3D Strain Field Prediction in Solid Rocket Motor Grainscited by 0
  11. 2026A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Lawscited by 0
  12. 2026Differentiable Multiphysics Co-Optimization via Implicit Neural Representations: A Transient Hamburger-Cooking Benchmarkcited by 0
2 more
  1. 2026GNN for Structural Displacement Predictioncited by 0
  2. 2026A variational physics-informed graph neural network for heterogeneous solid mechanicscited by 0