发表机构
Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences; Institute of Applied Physics and Computational Mathematics; College of Engineering, Peking University（中国科学院数学与系统科学研究院计算数学与科学工程计算研究所; 应用物理与计算数学研究所; 北京大学工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出图神经网络原子间势的多层完备性理论，证明超图神经网络是势能面通用近似器，为实际应用的多层消息传递设置提供严格依据，并表明DPA3、CHGNet具备通用近似能力。
AI 中文摘要
我们证明了具有三体消息传递的不变架构超图神经网络（Hypergraph Neural Network）是势能面的通用近似器。我们的主要贡献是一套多层完备性理论：在构型为通用构型、满足重叠条件和连通性条件的前提下，基于稀疏截断图的L层消息传递，可达到访问完整L跳邻域的同等表示能力。这为“使用每层截断小于物理相互作用范围的多层消息传递”这一通用做法提供了首个严格依据，而该设置几乎是所有基于图神经网络的机器学习原子间势的实际应用场景。作为直接结果，我们证明DPA3和CHGNet架构均继承了通用近似能力。
英文摘要
We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy surfaces. Our main contribution is a multi-layer completeness theory. We show that $L$ layers of message passing on sparse, cutoff-based graphs achieve the same representational power as having access to the full $L$-hop neighborhood, provided the configurations are generic, satisfy an overlap condition and a connectivity condition. This provides the first rigorous justification for the common practice of using multi-layer message passing with a per-layer cutoff smaller than the physical interaction range, the setting used by virtually all practical graph neural network based machine-learned interatomic potentials. As immediate consequences, we show that both DPA3 and CHGNet architectures inherit universal approximation.
