The 2024 Nobel Prize in Chemistry was recently granted to David Baker, Demis Hassabis and John M. Jumper, renowned for their pioneering works in protein design. In addition, Nature has recently spotlighted significant progress in biochemistry, such as the protein generation method Chroma and the material design method MatterGen, both of which use geometric graph neural networks (GNNs) as a representation tool. In fact, geometric GNNs, have always been important for the study of AI for Science. This is because physical systems such as particles, molecules and proteins in the scientific field can be modeled into a special data structure - geometric graphs. 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 GNNs. To better understand geometric GNNs, a research team formed by collaborators affiliated with Renmin University of China, Alibaba, Hupan Lab, Tsinghua University Tencent and Stanford University, published their new survey on 15 November 2025 in Frontiers of Computer Science co-published by Higher Education Press and Springer Nature.

This survey provides a general overview throughout data structure, model design, and applications, which constitutes an entire input-output pipeline that is instructive for machine learning practitioners to employ geometric GNNs on various scientific tasks.
Then, they divide geometric graph neural networks into three categories: invariant models, equivariant models, and geometric graph transformer. The equivariant model is further divided into scalarization-based models and high-degree steerable models
based on spherical harmonics. According to the above rules, the article collects and classifies the well-known geometric graph neural network models in recent years.

In terms of scientific applications, the survey covers multiple application scenarios such as physics (particles), biochemistry (small molecules, proteins) and other applications such as crystals. The article summarizes various geometric GNNs for different tasks and introduces the commonly used data sets in each task.
Overall, the authors review over 300 references, present three geometric GNNs models, discuss methodologies for 23 tasks on scientific data such as particles, molecules, and proteins, and compile more than 50 evaluation datasets.

Finally, the authors discuss the following open research directions.

1. Developing geometric graph foundation models considering the spaces of task, data and model, is an engaging area of research.
2. Enhance the efficiency and autonomy of the loop connecting model training and real-world experimental validation.
3. Integrate large language models (LLMs) into geometric GNNs to harness the wealth of extensive knowledge.

Explore approaches that strike a balance between maintaining equivariance and accommodating adaptability.
DOI:10.1007/s11704-025-41426-w