A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications
This survey organizes and synthesizes existing research on geometric GNNs to facilitate future methodology development and experimental evaluation for researchers in machine learning and related scientific domains.
This paper conducts a comprehensive survey of geometric graph neural networks (GNNs), addressing the challenge of processing geometric graphs with physical symmetries that current GNNs handle ineffectively, by formalizing data structures, providing a unified model view, and summarizing applications and datasets.
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.