格点量子色动力学中不连通图多能级Monte Carlo的最佳位移选择
Optimizing Shift Selection in Multilevel Monte Carlo for Disconnected Diagrams in Lattice QCD
摘要：
在格点量子色动力学中，计算不连通图对物理信号的贡献是一项计算量很大的工作。为了提取物理信号，必须随机估计逆格点狄拉克算子的迹，这是一个大型稀疏矩阵。由于随机估计量的方差通常很大，因此必须采用方差缩减技术。多级蒙特卡罗（MLMC）方法通过利用估计量的伸缩序列来降低迹估计量的方差。频率分裂是一种这样的方法，其使用移位算子的逆序列来估计逆晶格狄拉克算子的迹，然而，没有先验方式来选择使多级迹估计的成本最小化的移位。在这篇文章中，我们提出了一个采样和插值方案，能够预测与频率分裂下的位移的基础时空晶格的方差。插值方案能够高精度地预测方差，因此选择对应于迹估计的成本的近似最小值的移位。我们发现，频率分裂与选定的移位显示显着的加速比多重网格紧缩，这些移位可以用于同一合奏内的多个配置，而不会对性能造成损失。
英文摘要：
The calculation of disconnected diagram contributions to physical signals is a computationally expensive task in Lattice QCD. To extract the physical signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix, must be stochastically estimated. Because the variance of the stochastic estimator is typically large, variance reduction techniques must be employed. Multilevel Monte Carlo (MLMC) methods reduce the variance of the trace estimator by utilizing a telescoping sequence of estimators. Frequency Splitting is one such method that uses a sequence of inverses of shifted operators to estimate the trace of the inverse lattice Dirac operator, however there is no a priori way to select the shifts that minimize the cost of the multilevel trace estimation. In this article, we present a sampling and interpolation scheme that is able to predict the variances associated with Frequency Splitting under displacements of the underlying space time lattice. The interpolation scheme is able to predict the variances to high accuracy and therefore choose shifts that correspond to an approximate minimum of the cost for the trace estimation. We show that Frequency Splitting with the chosen shifts displays significant speedups over multigrid deflation, and that these shifts can be used for multiple configurations within the same ensemble with no penalty to performance.
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