论文标题
通过主要成分分析的保护法律和旋转系统建模
Conservation Laws and Spin System Modeling through Principal Component Analysis
论文作者
论文摘要
本文研究了主要组件分析（PCA）对物理系统的几种应用。其中的第一个表明，可以使用适当的系统变量的主要组件来识别物理保守的数量。也就是说，如果已知物理对称定律的一般形式，则PCA可以从观察到的系统轨迹中确定对称性的代数表达。其次，发现同质周期性自旋系统的主要成分光谱的特征值光谱反映了边界的几何形状。最后，使用PCA在能量磁化空间中产生具有概率分布的合成自旋实现，尽管统计量不准确，但与输入实现非常相似。
This paper examines several applications of principal component analysis (PCA) to physical systems. The first of these demonstrates that the principal components in a basis of appropriate system variables can be employed to identify physically conserved quantities. That is, if the general form of a physical symmetry law is known, the PCA can identify an algebraic expression for the symmetry from the observed system trajectories. Secondly, the eigenvalue spectrum of the principal component spectrum for homogeneous periodic spin systems is found to reflect the geometric shape of the boundary. Finally, the PCA is employed to generate synthetic spin realizations with probability distributions in energy-magnetization space that closely resemble that of the input realizations although statistical quantities are inaccurately reproduced.
