Hessian-free force-gradient integrators

TL;DR

This paper introduces Hessian-free force-gradient integrators that avoid computing the Hessian, making them efficient for complex Hamiltonian systems like molecular dynamics and lattice QCD simulations.

Contribution

The paper presents a novel class of integrators for Hamiltonian systems that do not require Hessian evaluations, reducing computational cost in certain applications.

Findings

Effective in molecular dynamics simulations

Applicable to lattice QCD and Schwinger model

Verified through numerical experiments on N-body problems

Abstract

We propose a new framework of Hessian-free force-gradient integrators that do not require the analytical expression of the force-gradient term based on the Hessian of the potential. Due to that the new class of decomposition algorithms for separable Hamiltonian systems with quadratic kinetic energy may be particularly useful when applied to Hamiltonian systems where an evaluation of the Hessian is significantly more expensive than an evaluation of its gradient, e.g. in molecular dynamics simulations of classical systems. Numerical experiments of an N-body problem, as well as applications to the molecular dynamics step in the Hybrid Monte Carlo (HMC) algorithm for lattice simulations of the Schwinger model and Quantum Chromodynamics (QCD) verify these expectations.