Multilevel trace estimation via a multigrid hierarchy: improvements, structural tuning and probing

by Gustavo Ramírez Hidalgo (Forschungszentrum Juelich)

Tuesday 10 Jun 2025, 16:00 → 18:00 Europe/Zurich

4/2-037 - TH meeting room (CERN)

Trace estimation of functions that depend on the Dirac operator is crucial in Lattice QCD computations. And in most physically-relevant regimes, it is important to have good variance-reduction algorithms at hand. In this talk, we do a brief recapitulation of a method for deflation via a multigrid hierarchy, which we call here multigrid multilevel Monte Carlo for trace estimation. Then, we discuss improvements of the method via orthogonal projections. After that, we briefly point out how to try to maximize variance reduction by keeping in mind the interplay of the multigrid aggregation and how dense the per-site blocks in the coarse-grid operator are. Finally, we compare the impact of probing on our two ways of doing multigrid multilevel Monte Carlo with the impact on inexact deflation.