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

2024-03-01

arXiv.org

AI Summary

Conventional graph neural networks (GNNs) struggle to model geometric graphs exhibiting physical symmetries—such as translation, rotation, and reflection invariance—critical in molecular and materials science. Method: This work presents a systematic survey of geometric GNNs (Geo-GNNs), introducing a unified analytical framework grounded in geometric message passing. It is the first to coherently integrate invariant and equivariant model designs through the lens of symmetry constraints. Contribution/Results: We structurally categorize data modeling paradigms, symmetry-preserving mechanisms, and scientific applications (e.g., molecular property prediction, materials discovery), constructing a knowledge graph covering mainstream models and benchmark datasets. We identify key challenges—including scalability, high-order geometric representation, and cross-domain generalization—and outline future directions: Lie group/algebra-driven equivariant architectures and dynamic geometric awareness. This survey provides theoretical foundations and practical guidelines for Geo-GNN design, standardized evaluation, and geometrically aware AI development in physics, chemistry, and biology.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Social Networks and Social Media: Computational social science

Abstract

Geometric graph is a special kind of graph with geometric features, which is 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 tackle this issue, researchers proposed a variety of Geometric Graph Neural Networks 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 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.

Problem

• Addressing GNN limitations on geometric graphs
• Surveying geometric GNN models and applications
• Exploring future directions in geometric GNN research

Innovation

• Geometric GNNs with invariant properties
• Unified view of geometric message passing
• Survey of geometric graph data structures