Applying polynomial filtering to mass preconditioned Hybrid Monte Carlo

TL;DR

This paper explores polynomial filtering in mass preconditioned Hybrid Monte Carlo to improve efficiency and simplify tuning, introducing a multi-scale integration scheme that enhances performance.

Contribution

It introduces polynomial filtering to mass preconditioning in HMC, enabling easier parameter tuning and improved performance with a new multi-scale integration scheme.

Findings

Polynomial filtering performs as well or better than standard mass preconditioning.

The method requires less fine tuning of parameters.

A generalized multi-scale integration scheme is proposed.

Abstract

The use of mass preconditioning or Hasenbusch filtering in modern Hybrid Monte Carlo simulations is common. At light quark masses, multiple filters (three or more) are typically used to reduce the cost of generating dynamical gauge fields; however, the task of tuning a large number of Hasenbusch mass terms is non-trivial. The use of short polynomial approximations to the inverse has been shown to provide an effective UV filter for HMC simulations. In this work we investigate the application of polynomial filtering to the mass preconditioned Hybrid Monte Carlo algorithm as a means of introducing many time scales into the molecular dynamics integration with a simplified parameter tuning process. A generalized multi-scale integration scheme that permits arbitrary step- sizes and can be applied to Omelyan-style integrators is also introduced. We find that polynomial-filtered mass-preconditioning (PF-MP) performs as well as or better than standard mass preconditioning, with significantly less fine tuning required.