Optimizing Shift Selection in Multilevel Monte Carlo for Disconnected Diagrams in Lattice QCD

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• Travis Whyte, DAMTP
• Tuesday 16 May 2023, 10:00-11:00
• MR11 (B1.39), Pavilion B, CMS.

If you have a question about this talk, please contact Christopher Thomas.

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 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, however there is no a priori way to select the shifts that minimize the cost of the multilevel trace estimation. 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 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. I will 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.

This talk is part of the Lattice field theory informal seminars series.

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