PoS - Proceedings of Science
Volume 430 - The 39th International Symposium on Lattice Field Theory (LATTICE2022) - Poster
Interpolation as a means of shift selection for multilevel Monte Carlo with lattice displacements
T. Whyte*, A. Stathopoulos, E. Romero and K. Orginos
Full text: pdf
Pre-published on: November 07, 2022
Published on: April 06, 2023
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 of the lattice Dirac operator,
however there is no a priori way to select the shifts that minimize the cost of the multilevel trace
estimation. 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
DOI: https://doi.org/10.22323/1.430.0255
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