Young-E(3)张量积分解用于旋转和置换等变的团簇展开

中文摘要 AI 辅助

提出了一种固定晶格团簇展开（CE）和原子团簇展开（ACE）的推广形式，该形式同时表达了旋转和置换对称性。通过在Young子群稳定的载体中进行Schur-Weyl分解，随后对旋转和置换表示进行联合耦合，生成了任意的$S_N\ imes SO(3)$张量积载体。这使得我们能够为任意张量积秩以及任意角度和径向张量积内容解析出完整的、正交的联合旋转和置换适配基。我们表明，这一非常通用的Young-E(3)（YE3T）张量积基包含ACE基作为其子集，对应于置换对称性特征被限制为完全对称载体的特殊情况。与构建过完备的旋转和置换不变基并事后约简不同，Barthelemy等人最近展示了通过不构建过完备基而获得的缩放优势。YE3T直接产生一个完整的正交基，无需过完备步骤，并严格扩展到超越置换对称特征的置换特征。YE3T分解产生了新的联合不可约旋转和置换等变基集，在速度和精度上均超越了现有的旋转适配展开，为机器学习原子间势定义了新的帕累托前沿。我们表明，置换对称性特征的可调性使得该基既适用于原子模拟，也适用于电子结构模拟。

英文摘要

A generalization of fixed-lattice cluster expansions (CE) and atomic cluster expansions (ACE) is presented that expresses both rotation and permutation symmetries. By performing Schur--Weyl decomposition in Young subgroup-stabilized carriers, followed by joint coupling of rotation and permutation representations, arbitrary $S_N\times SO(3)$ tensor product carriers are generated. This allows us to resolve complete, orthonormal joint rotation and permutation-adapted bases for arbitrary tensor product ranks and arbitrary angular and radial tensor product content. We show that this very general Young--E(3) (YE3T) tensor product basis contains the ACE basis as a subset, corresponding to the special case where permutation symmetry character is restricted to the fully symmetric carrier. Rather than constructing an overcomplete rotation and permutation-invariant basis and reducing it \textit{a posteriori}, Barthelemy \textit{et al.} recently demonstrated scaling benefits by not constructing an overcomplete basis. YE3T directly produces a complete orthonormal basis without an overcomplete step and rigorously extends to permutation characters beyond permutation-symmetric features. The YE3T decomposition yields new joint irreducible rotation- and permutation-equivariant basis sets that surpass existing rotation-adapted expansions in both speed and accuracy, defining a new Pareto front for machine-learned interatomic potentials. We show that the tunability of the permutation symmetry character makes the basis useful for both atomistic and electronic-structure simulations.

发表机构

• Center for Computing Research, Sandia National Laboratories（桑迪亚国家实验室计算研究中心）

机构由 AI 辅助整理，请以论文原文为准。