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：近年来，计算建模在分子、蛋白质及材料等原子系统领域取得显著进展，将原子系统表示为几何图——原子作为节点嵌入三维欧几里得空间。在此类图中，几何属性根据三维原子系统的固有物理对称性（包括欧几里得空间中的旋转与平移，以及节点置换）进行变换。近年，几何图神经网络已成为支撑蛋白质结构预测、分子模拟及材料生成等应用的首选机器学习架构。其独特之处在于利用归纳偏置（如物理对称性与化学性质）学习几何图的表征。在本文中，我们针对三维原子系统的几何图神经网络领域，以自成一体的视角提供全面概述。涵盖基础背景知识，并引入一套教学分类法：（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，概述关键数据集与应用领域，并提出未来研究方向。本文旨在构建该领域的结构化认知框架，降低新手入门门槛，并助力实践者深入理解其数学抽象本质。