Normalizing flows and the real-time sign problem
Abstract
Normalizing flows have recently been applied to the problem of accelerating Markov chains in lattice field theory. We propose a generalization of normalizing flows that allows them to applied to theories with a sign problem. These complex normalizing flows are closely related to contour deformations (i.e., the generalized Lefschetz thimble method), which been applied to sign problems in the past. We discuss the question of the existence of normalizing flows; they do not exist in the most general case, but we argue that exact normalizing flows are likely to exist for many physically interesting problems, including cases where the Lefschetz thimble decomposition has an intractable sign problem. Finally, normalizing flows can be constructed in perturbation theory. We give numerical results on their effectiveness across a range of couplings for the Schwinger-Keldysh sign problem associated to a real scalar field in 0+1 dimensions.
- Publication Date:
- Research Org.:
- Univ. of Colorado, Boulder, CO (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1788141
- Alternate Identifier(s):
- OSTI ID: 1788225
- Grant/Contract Number:
- SC0017905; FG02-93ER-40762
- Resource Type:
- Published Article
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 103 Journal Issue: 11; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Ab initio calculations; Lattice field theory; Metropolis algorithm
Citation Formats
Lawrence, Scott, and Yamauchi, Yukari. Normalizing flows and the real-time sign problem. United States: N. p., 2021.
Web. doi:10.1103/PhysRevD.103.114509.
Lawrence, Scott, & Yamauchi, Yukari. Normalizing flows and the real-time sign problem. United States. https://doi.org/10.1103/PhysRevD.103.114509
Lawrence, Scott, and Yamauchi, Yukari. Mon .
"Normalizing flows and the real-time sign problem". United States. https://doi.org/10.1103/PhysRevD.103.114509.
@article{osti_1788141,
title = {Normalizing flows and the real-time sign problem},
author = {Lawrence, Scott and Yamauchi, Yukari},
abstractNote = {Normalizing flows have recently been applied to the problem of accelerating Markov chains in lattice field theory. We propose a generalization of normalizing flows that allows them to applied to theories with a sign problem. These complex normalizing flows are closely related to contour deformations (i.e., the generalized Lefschetz thimble method), which been applied to sign problems in the past. We discuss the question of the existence of normalizing flows; they do not exist in the most general case, but we argue that exact normalizing flows are likely to exist for many physically interesting problems, including cases where the Lefschetz thimble decomposition has an intractable sign problem. Finally, normalizing flows can be constructed in perturbation theory. We give numerical results on their effectiveness across a range of couplings for the Schwinger-Keldysh sign problem associated to a real scalar field in 0+1 dimensions.},
doi = {10.1103/PhysRevD.103.114509},
journal = {Physical Review D},
number = 11,
volume = 103,
place = {United States},
year = {Mon Jun 14 00:00:00 EDT 2021},
month = {Mon Jun 14 00:00:00 EDT 2021}
}
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