Abstract
AbstractThe recent introduction of machine learning techniques, especially normalizing flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional hybrid Monte Carlo (HMC) algorithm. In this work we study a modified HMC algorithm that draws on the seminal work on trivializing flows by Lüscher. Autocorrelations are reduced by sampling from a simpler action that is related to the original action by an invertible mapping realised through Normalizing Flows models with a minimal set of training parameters. We test the algorithm in a$$\phi ^{4}$$ϕ4theory in 2D where we observe reduced autocorrelation times compared with HMC, and demonstrate that the training can be done at small unphysical volumes and used in physical conditions. We also study the scaling of the algorithm towards the continuum limit under various assumptions on the network architecture.
Funder
Ministerio de Ciencia e Innovación
Horizon 2020 Framework Programme
Conselleria de Innovación, Universidades, Ciencia y Sociedad Digital, Generalitat Valenciana
Science and Technology Facilities Council
University of Edinburgh
Publisher
Springer Science and Business Media LLC
Subject
Physics and Astronomy (miscellaneous),Engineering (miscellaneous)
Reference43 articles.
1. M. Campostrini, P. Rossi, E. Vicari, Monte Carlo simulation of $$\rm CP ^{N-1}$$ models. Phys. Rev. D 46, 2647 (1992). https://doi.org/10.1103/PhysRevD.46.2647
2. E. Vicari, Monte carlo simulation of lattice $${\mathbb{C}\mathbb{P} }^{N-1}$$ models at large $$N$$. Phys. Lett. B 309, 139 (1993). https://doi.org/10.1016/0370-2693(93)91517-Q. arXiv:9209025 [hep-lat]
3. L. Del Debbio, G.M. Manca, E. Vicari, Critical slowing down of topological modes. Phys. Lett. B 594, 315 (2004). https://doi.org/10.1016/j.physletb.2004.05.038. arXiv:hep-lat/0403001
4. G.P. Engel, S. Schaefer, Testing trivializing maps in the Hybrid Monte Carlo algorithm. Comput. Phys. Commun. 182, 2107 (2011). https://doi.org/10.1016/j.cpc.2011.05.004. arXiv:1102.1852 [hep-lat]
5. J. Flynn, A. Jüttner, A. Lawson, F. Sanfilippo, Precision study of critical slowing down in lattice simulations of the $${\mathbb{C}\mathbb{P}}^{N-1}$$ model (2015). arXiv:1504.06292 [hep-lat]
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