A survey of geometric graph neural networks: data structures, models and applications
Abstract 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.
Authors
- Tingyang Xu (ORCID: https://orcid.org/0000-0002-8487-9045)
- Zongzhao Li
- Jiaqi Han (ORCID: https://orcid.org/0000-0003-1786-3817)
- Wenbing Huang (ORCID: https://orcid.org/0000-0002-2566-4159)
- Hongteng Xu (ORCID: https://orcid.org/0000-0003-4192-5360)
- Rui Jiao (ORCID: https://orcid.org/0000-0002-7516-0469)
- Ziyang Yu (ORCID: https://orcid.org/0000-0002-9237-6552)
- Zhewei Wei (ORCID: https://orcid.org/0000-0003-3620-5086)
- Liming Wu (ORCID: https://orcid.org/0000-0002-5738-0468)
- Fandi Wu (ORCID: https://orcid.org/0000-0003-1615-3004)
- Yang Liu (ORCID: https://orcid.org/0000-0003-3761-0104)
- Yu Rong (ORCID: https://orcid.org/0000-0001-7387-302X)
- Zihe Wang (ORCID: https://orcid.org/0009-0005-8493-7152)
- Deli Zhao (ORCID: https://orcid.org/0000-0002-8838-578X)
- Xiangzhe Kong (ORCID: https://orcid.org/0009-0005-7047-1910)
- Jiacheng Cen
Institutions
- Tencent (China) (CN)
- Zhejiang Lab (CN)
- Alibaba Group (China) (CN)
- Renmin University of China (CN)
- Stanford University (US)
- Tsinghua University (CN)
Publication Details
- Journal
- Frontiers of Computer Science
- Published
- 2025-05-28
- DOI
- https://doi.org/10.1007/s11704-025-41426-w
- Citations
- 29
- Primary Topic
- Advanced Graph Neural Networks
- Type
- article
- Field-Weighted Citation Impact
- 71.95
Funders
- Tencent
- National Natural Science Foundation of China
- Renmin University of China
- Beijing Nova Program
- Fundamental Research Funds for the Central Universities