应变泛函：表征原子构型的完备且对称自适应的描述符集合
Strain Functionals: A Complete and Symmetry-adapted Set of Descriptors to Characterize Atomistic Configurations
AI总结：
提出应变泛函描述符框架，利用高斯核映射原子量并构造完备的旋转不变描述符，可区分晶体对称性、识别缺陷并测量变形，适用于原子模拟数据分析。
摘要：
从原子模拟中提取相关信息依赖于对原子构型的完备且准确的表征。我们提出一个框架，用以在完备且对称自适应的基组（称为应变泛函）下表征原子构型。在该方法中，使用高斯核将离散的原子量（如数密度、速度和力）映射为连续场。随后，利用局部数密度的n阶中心矩来表征局部原子构型。初始的笛卡尔矩通过SO(3)分解被幺正地重构为固体谐波多项式基组。利用Clebsch-Gordan耦合，从SO(3)分解的各项构造旋转不变度量，称为应变泛函描述符（SFDs）。与相关方法的一个关键区别在于，我们识别出最小但完备的描述符集合。这些描述符以形状、尺寸和取向描述符的形式数值地表征局部几何结构，能够识别n重对称轴以及诸如三角、立方、六方等净形状。它们可以轻松区分大多数不同的晶体对称性（使用n=4），识别缺陷（如位错和层错），测量局部变形，并可结合机器学习技术用于有限温度原子模拟数据的原位分析及缺陷动力学量化。
英文摘要：
Extracting relevant information from atomistic simulations relies on a complete and accurate characterization of atomistic configurations. We present a framework for characterizing atomistic configurations in terms of a complete and symmetry-adapted basis, referred to as strain functionals. In this approach a Gaussian kernel is used to map discrete atomic quantities, such as number density, velocities, and forces, to continuous fields. The local atomic configurations are then characterized using nth order central moments of the local number density. The initial Cartesian moments are recast unitarily into a Solid Harmonic Polynomial basis using SO(3) decompositions. Rotationally invariant metrics, referred to as Strain Functional Descriptors (SFDs), are constructed from the terms in the SO(3) decomposition using Clebsch-Gordan coupling. A key distinction compared to related methods is that a minimal but complete set of descriptors is identified. These descriptors characterize the local geometries numerically in terms of shape, density, and orientation descriptors that recognize n-fold symmetry axes and net shapes such as trigonal, cubic, hexagonal, etc. They can easily distinguish between most different crystal symmetries using n = 4, identify defects (such as dislocations and stacking faults), measure local deformation, and can be used in conjunction with machine learning techniques for in situ analysis of finite temperature atomistic simulation data and quantification of defect dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
