Abstract

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Speeding up HMC with better integrators

Presenter: Anthony Kennedy — University of Edinburgh

A D Kennedy, Mike Clark

We shall discuss how dynamical fermion computations may be made yet cheaper by using symplectic integrators that conserve energy much more accurately without increasing the integration step size. We will first explain why symplectic integrators exactly conserve a "shadow" Hamiltonian close to the desired one, and how this Hamiltonian may be computed in terms of Poisson brackets. We shall then discuss how classical mechanics may be implemented on Lie groups and derive the form of the Poisson brackets and force terms for some interesting integrators such as those making use of second derivatives of the action (Hessian or force gradient integrators). These will be seen to greatly improved energy conservation for only a small additional cost (one extra inversion of the Dirac operator), and we hope to show that their use significantly reduces the cost of dynanical fermion computations.