Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage -- such as physical symmetries and chemical properties -- to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures:(1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

翻译：近期，涵盖分子、蛋白质和材料的原子系统计算建模进展，将这些系统表示为几何图，其中原子作为节点嵌入3D欧几里得空间。在这些图中，几何属性根据3D原子系统固有的物理对称性（包括欧几里得空间中的旋转和平移，以及节点置换）进行变换。近年来，几何图神经网络已成为从蛋白质结构预测到分子模拟和材料生成等应用领域首选的机器学习架构。其特异性在于利用归纳偏置（如物理对称性和化学性质）来学习这些几何图的信息化表示。在这篇观点性论文中，我们全面且自成体系地概述了用于3D原子系统的几何图神经网络领域。我们涵盖基础背景材料，并引入一种教学式几何图神经网络架构分类法：（1）不变网络，（2）笛卡尔基等变网络，（3）球面基等变网络，（4）无约束网络。此外，我们概述了关键数据集和应用领域，并提出了未来研究方向。本工作的目标是提供该领域的结构化视角，使其易于入门者理解，并帮助从业者直观掌握其数学抽象。