论文标题
群集扩展方法来自物理概念
Cluster expansion methods from physical concepts
论文作者
论文摘要
材料科学中使用的集群扩展形式主义是在公理的基础上重建的，目的是阐明潜在的概念并改善计算程序，并且不使用常规的群集功能。取而代之的是，以内在方式定义了配置函数的群集组件，可以将其视为有条件期望的Moebius反转。将模型拟合到配置样品的相关方法完全基于希尔伯特空间几何形状。通过直接从给定的数据构建模型，我们避免了常规方法是主题的不确定问题。张量可观察物在标量观测值的平等基础上进行处理。
The cluster expansion formalism used in materials science is reconstructed on an axiomatic basis with the aims of clarifying underlying concepts and improving computational procedures, and without using conventional cluster functions. Instead, cluster components of configuration functions are defined in an intrinsic manner, which can be viewed as Moebius inversion of conditional expectation. The associated method for fitting a model to a configurational sample is grounded entirely in Hilbert space geometry. By constructing models directly from the given data, we avoid an underdetermination problem to which the conventional approach is subject. Tensor observables are treated on an equal footing with scalar observables.
