发表机构
School of Physical Science and Technology, ShanghaiTech University, Shanghai, China; School of Chemistry, Nanjing University, Nanjing, China（物理科学与技术学院，上海科技大学，上海，中国; 化学学院，南京大学，南京，中国）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对机器学习原子间势的SO(2)理论局限性，提出维格纳D矩阵构造及两个新相互作用构建块，包括边复积基和径向旋转复注意力，改进原子簇扩展模块，训练的模型在Matbench Discovery上达最优性能。
AI 中文摘要
在本文中，我们对用于机器学习原子间势（MLIPs）的SO(2)理论进行了系统研究，并确定了传统SO(2)线性架构相对于SO(3)克莱布什 - 戈尔丹张量积（CGTP）的局限性。基于这些见解，我们提出了维格纳D矩阵的直接笛卡尔构造和递归克莱布什 - 戈尔丹构造，并引入了两个新颖的相互作用构建块。首先，基于广义不对称收缩提出了边复积基，这是一种多体展开的新公式，通过复值等变乘法直接在边上构建高阶相互作用。其次，引入了径向旋转复注意力（RRA），它提高了外推性能并超越了现有的注意力向量公式。我们还对原子簇扩展模块进行了一些改进。在此基础上，我们在OMat24、sAlex和MPTrj上训练模型，并推出了TECE - OAM - RRA - 1.0，在Matbench Discovery上实现了最优性能。
英文摘要
In this paper, we provide a systematic investigation of SO(2) theory to machine learning interatomic potentials (MLIPs) and identify the limitations of conventional SO(2) Linear architectures relative to SO(3) Clebsch-Gordan Tensor Products (CGTP). Building on these insights, we propose direct Cartesian construction and recursive Clebsch-Gordan construction of Wigner D-matrices and introduce two novel interaction building blocks. First, we propose the Edge Complex Product Basis based on Generalized Asymmetric Contraction, a new formulation for many-body expansion that directly constructs higher-order interactions on edges through complex-valued equivariant multiplications. Second, we introduce Radial Rotary Complex Attention(RRA), which enhances extrapolation performance and surpasses existing attention vector formulations. We also introduce several improvements to the Atomic Cluster Expansion module. Building on these advances, we train our models on OMat24, sAlex, and MPTrj, and introduce TECE-OAM-RRA-1.0, which achieve state-of-the-art (SOTA) performance on the Matbench Discovery.
