Ensemble Quasi-Newton HMC

2019/04/22 by Xiao-Yong Jin, Jin, Xiao-Yong, James C. Osborn +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #hep-lat

paper · pdf · doi:10.48550/arxiv.1904.10039

7 pages, 2 figures, Proceedings of the 36th Annual International Symposium on Lattice Field Theory (Lattice 2018), 22-28 July 2018, Michigan State University, East Lansing, Michigan USA

arxiv created 2019/04/22 · arxiv updated 2019/04/24

Abstract

We present a modification of the Hybrid Monte Carlo algorithm for tackling the critical slowing down of generating Markov chains of lattice gauge configurations towards the continuum limit. We propose a new method to exchange information within an ensemble of Markov chains, and use it to construct an approximate inverse Hessian matrix of the action inspired from quasi-Newton algorithms for optimization. The kinetic term of the molecular dynamics evolution includes the approximate Hessian for long distance couplings among the momenta. We show the result of applying the new algorithm to the U(1) gauge theory in two dimensions, and discuss our future plans.

Related

• Extended framework for the hybrid Monte Carlo in lattice gauge theory
• Riemannian manifold hybrid Monte Carlo in lattice QCD
• Machine Learning and Variational Algorithms for Lattice Field Theory
• MLMC: Machine Learning Monte Carlo for Lattice Gauge Theory
• Playing with the kinetic term in the HMC