mlsanityData to 7 Oct 2026

A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications

arXiv 2403.00485 ↗First posted 1 Mar 2024cs.LGcited by 28

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Abstract (arXiv)

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections, making them ineffectively processed by current Graph Neural Networks (GNNs). To address this issue, researchers proposed a variety of geometric GNNs equipped with invariant/equivariant properties to better characterize the geometry and topology of geometric graphs. Given the current progress in this field, it is imperative to conduct a comprehensive survey of data structures, models, and applications related to geometric GNNs. In this paper, based on the necessary but concise mathematical preliminaries, we formalize geometric graph as the data structure, on top of which we provide a unified view of existing models from the geometric message passing perspective. Additionally, we summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation. We also discuss the challenges and future potential directions of geometric GNNs at the end of this survey.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Builds on 181 of its 374 references that are in the map. First posted on arXiv 1 Mar 2024.

Builds on

181 of 374 references.

References · 181

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38 more
  1. 2019Strategies for Pre-training Graph Neural Networkscited by 964
  2. 2021E(n) Equivariant Graph Neural Networkscited by 951
  3. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
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  6. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
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  16. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
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50 most cited of 181 All 181 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 9; 2025: 15; 2026: 4.

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  1. 2024E(n) Equivariant Topological Neural Networkscited by 22
  2. 2024Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?cited by 18
  3. 2025A Survey of Graph Transformers: Architectures, Theories and Applicationscited by 12
  4. 2024AI-driven inverse design of materials: Past, present and futurecited by 10
  5. 2025Materials Generation in the Era of Artificial Intelligence: A Comprehensive Surveycited by 9
  6. 2024On the Expressive Power of Sparse Geometric MPNNscited by 7
  7. 2024Learning local equivariant representations for quantum operatorscited by 7
  8. 2025A Survey of AI for Materials Science: Foundation Models, LLM Agents, Datasets, and Toolscited by 7
  9. 2025Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learningcited by 6
  10. 2024Using pretrained graph neural networks with token mixers as geometric featurizers for conformational dynamicscited by 5
  11. 2025DualEquiNet: A Dual-Space Hierarchical Equivariant Network for Large Biomoleculescited by 5
  12. 2024WGFormer: An SE(3)-Transformer Driven by Wasserstein Gradient Flows for Molecular Ground-State Conformation Predictioncited by 4
16 more
  1. 2025InvDesFlow-AL: active learning-based workflow for inverse design of functional materialscited by 4
  2. 2025Zero-Shot Cyclic Peptide Design via Composable Geometric Constraintscited by 4
  3. 2025Dynami-CAL GraphNet: A Physics-Informed Graph Neural Network Conserving Linear and Angular Momentum for Dynamical Systemscited by 3
  4. 2025Universally Invariant Learning in Equivariant GNNscited by 3
  5. 2024Subequivariant Reinforcement Learning in 3D Multi-Entity Physical Environmentscited by 2
  6. 2024KA-GNN: Kolmogorov-Arnold Graph Neural Networks for Molecular Property Predictioncited by 2
  7. 2025Topotein: Topological Deep Learning for Protein Representation Learningcited by 2
  8. 2025PAINET: A Principled Efficient Transformer for 3D Dynamics Modelingcited by 2
  9. 2025Geometric Mixture Models for Electrolyte Conductivity Predictioncited by 2
  10. 2026Equivariant Neural Networks for Force-Field Models of Lattice Systemscited by 2
  11. 2025CrystalFramer: Rethinking the Role of Frames for SE(3)-Invariant Crystal Structure Modelingcited by 0
  12. 2025Parameter-Free Structural-Diversity Message Passing for Graph Neural Networkscited by 0
  13. 2025A Conformation-Centric Generative Foundation Model for Linear Polymer Modeling and Designcited by 0
  14. 2026Cross-Chirality Generalization by Axial Vectors for Hetero-Chiral Protein-Peptide Interaction Designcited by 0
  15. 2026Symmetry-Structured Neural Completion of Islamic Geometric Patterns from Sparse Control Geometrycited by 0
  16. 2026Reducing Symmetry Increase in Equivariant Neural Networkscited by 0