Speaker
Description
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 es-
timator 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 Split-
ting 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. We present a sampling and interpolation scheme
that is able to predict the variances associated with Frequency Splitting un-
der 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 dis-
plays significant speedups over multigrid deflation, and that these shifts can
be used for multiple configurations within the same ensemble with no penalty
to performance.
