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SUMMARY:Optimizing Shift Selection in Multilevel Monte Carlo for Disconnec
 ted Diagrams in Lattice QCD - Travis Whyte\, DAMTP
DTSTART:20230516T090000Z
DTEND:20230516T100000Z
UID:TALK200665@talks.cam.ac.uk
CONTACT:Christopher Thomas
DESCRIPTION:The calculation of disconnected diagram contributions to physi
 cal 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 varia
 nce of the stochastic estimator is large\, variance reduction techniques m
 ust 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 o
 f shifted operators to estimate the trace\, however there is no a priori w
 ay to select the shifts that minimize the cost of the multilevel trace est
 imation. In this talk\, I will 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 interpolati
 on scheme is able to predict the variances to high accuracy and therefore 
 choose shifts that correspond to an approximate minimum of the cost for th
 e trace estimation. I will show that Frequency Splitting with the chosen s
 hifts displays significant speedups over multigrid deflation\, and that th
 ese shifts can be used for multiple configurations within the same ensembl
 e with no penalty to performance.
LOCATION:MR11 (B1.39)\, Pavilion B\, CMS
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