III: Small: 3D Graph Neural Networks: Completeness, Efficiency, and Applications

许多现实世界的系统和现象可以用实体及其关系来描述。例如，社交网络由人和他们的关系组成，分子由化学键连接的原子组成。图通常用于编码这样的系统和现象，其中节点对应实体，边对应关系。图的计算分析多年来一直是一个活跃的研究领域，有大量卓有成效的结果和发现。然而，目前许多图分析研究只考虑图的拓扑（即这些关系的二维表示），而没有考虑重要的几何信息。在许多科学领域，物理系统最准确地描述几何图，也称为三维图，其中每个节点与三维物理空间中的坐标相关联。这些几何信息的精确编码在许多科学领域都是至关重要的。例如，分子中的原子占据物理空间，它们的位置决定了分子的三维几何形状。在药物发现中，药物的结合特性和有效性严重依赖于它们的3D形状，因为分子相互作用类似于锁和钥匙机制。该项目旨在通过开发能够准确有效地捕获图形的三维几何形状的算法来推进几何图形分析领域。该项目致力于通过吸引和激励K-12和代表性不足的学生参与人工智能和分子分析研究和教育，扩大对计算机的参与。在这个项目中，第一组研究任务旨在开发有原则的3D图形神经网络，该网络可以利用小分子的3D几何信息的力量来生成信息丰富和有区别的表示。本文将提出一种新颖的消息传递方案，以完整有效地整合三维几何信息。基于这一发展，一种新的3D图形神经网络架构将被设计用于促进大规模分子数据的表示学习，并提高大量现实世界任务的性能和效率。第二组研究任务将提出的完整和高效的三维图形神经网络扩展到蛋白质的表示学习，蛋白质是具有基本重要性的复杂大分子。现有的研究要么没有考虑蛋白质中存在的等级关系，要么存在严重的效率问题。为了克服这些限制，本项目将开发一种新的分层蛋白质图网络来学习不同层次的蛋白质表示。该方法忠实地整合了重要的层次关系，使蛋白质学习方案更加自然。利用所提出的小分子完备和高效的三维图神经网络作为基础模型，新的分层蛋白质图网络有望在不同层次上实现可证明的完备性和效率。拟议的研究将导致开源软件工具被研究人员和从业者使用。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Many real-world systems and phenomena can be described by entities and their relations. For example, social networks consist of people and their relationships, and molecules consist of atoms connected by chemical bonds. Graphs are commonly used to encode such systems and phenomena in which nodes correspond to entities, and edges correspond to relations. Computational analysis of graphs has been an active area of research for many years with a plethora of fruitful results and discoveries. However, many current graph analysis studies only consider topologies of graphs (i.e., a two-dimensional representations of these relationships), while important geometric information is not considered. In many scientific domains, physical systems are most accurately described by geometric graphs, also known as 3D graphs, in which each node is associated with a coordinate in 3D physical space. Accurate encoding of such geometric information is critical in many scientific domains. For example, atoms in a molecule occupy physical space, and their locations determine 3D molecular geometry. In drug discovery, the binding properties and thus effectiveness of drugs critically depend on their 3D shapes as molecular interactions act similarly to lock-and-key mechanisms. This project aims at advancing the field of geometric graph analysis by developing algorithms that can capture 3D geometries of graphs accurately and efficiently. The project is committed to broadening participation in computing by engaging and inspiring K-12 and underrepresented students in artificial intelligence and molecular analysis research and education. In this project, the first set of research tasks aim to develop principled 3D graph neural networks that can use the power of 3D geometric information of small molecules to generate informative and discriminative representations. A novel message passing scheme will be developed to incorporate 3D geometric information in a complete and efficient manner. Building on this development, a new 3D graph neural networks architecture will be designed to facilitate representation learning on large-scale molecule data and boost the performance and efficiency for a plethora of real-world tasks. The second set of research tasks extend the proposed complete and efficient 3D graph neural networks to representation learning of proteins, which are complex macromolecules of fundamental importance. Existing studies either fail to consider the hierarchical relations present in proteins or suffer from severe efficiency issues. To overcome these limitations, a novel hierarchical protein graph network to learn protein representations at different levels will be developed in this project. The proposed method faithfully integrates important hierarchical relations, resulting in a more natural protein learning scheme. By employing the proposed complete and efficient 3D graph neural networks for small molecules as a base model, the new hierarchical protein graph network is expected to achieve provable completeness and efficiency at different levels. The proposed research will result in open-source software tools to be used by researchers and practitioners.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.