Introduction to Normalizing Flows for Lattice Field Theory

Albergo, Michael S.; Boyda, Denis; Hackett, Daniel C.; Kanwar, Gurtej; Cranmer, Kyle; Racanière, Sébastien; Rezende, Danilo Jimenez; Shanahan, Phiala E.

Introduction to Normalizing Flows for Lattice Field Theory

Michael S. Albergo
(
- New York U.
)
,
Denis Boyda
(
- MIT, Cambridge, CTP and
- IAIFI, Cambridge
)
,
Daniel C. Hackett
(
- MIT, Cambridge, CTP and
- IAIFI, Cambridge
)
,
Gurtej Kanwar
(
- MIT, Cambridge, CTP and
- IAIFI, Cambridge
)
,
Kyle Cranmer
(
- New York U.
)

Jan 20, 2021

38 pages

e-Print:

2101.08176 [hep-lat]

Report number:

MIT-CTP/5272

View in:

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Abstract: (arXiv)

This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072, arXiv:2002.02428, and arXiv:2003.06413 are reviewed and a concrete implementation of the framework is presented. We apply this framework to a lattice scalar field theory and to U(1) gauge theory, explicitly encoding gauge symmetries in the flow-based approach to the latter. This presentation is intended to be interactive and working with the attached Jupyter notebook is recommended.

Note:

38 pages, 5 numbered figures, Jupyter notebook included as ancillary file

field theory: scalar
gauge field theory: U(1)
symmetry: gauge
lattice field theory
flow
lattice

References(29)

Figures(5)

[1]

Flow-based generative models for Markov chain Monte Carlo in lattice field theory

M.S. Albergo
(
- Perimeter Inst. Theor. Phys. and
- Cambridge U. and
- Waterloo U.
)
,
G. Kanwar
(
- MIT, Cambridge, CTP
)
,
P.E. Shanahan
(
- MIT, Cambridge, CTP and
- Perimeter Inst. Theor. Phys.
)

- Phys.Rev.D 100 (2019) 3, 034515
•
e-Print:
- 1904.12072
•
DOI:
- 10.1103/PhysRevD.100.034515

[2]

Normalizing Flows on Tori and Spheres

et al.

e-Print:
- 2002.02428

[3]

Equivariant flow-based sampling for lattice gauge theory

Gurtej Kanwar
(
- MIT
)
,
Michael S. Albergo
(
- New York U., CCPP
)
,
Denis Boyda
(
- MIT
)
,
Kyle Cranmer
(
- New York U., CCPP
)
,
Daniel C. Hackett
(
- MIT
)

et al.

- Phys.Rev.Lett. 125 (2020) 12, 121601
•
e-Print:
- 2003.06413
•
DOI:
- 10.1103/PhysRevLett.125.121601

[4]

Normalizing Flows for Probabilistic Modeling and Inference

George Papamakarios
(
- Google Inc.
)
,
Eric Nalisnick
(
- Google Inc.
)
,
Danilo Jimenez Rezende
(
- Google Inc.
)
,
Shakir Mohamed
(
- Google Inc.
)
,
Balaji Lakshminarayanan
(
- Google Inc.
)

- J.Machine Learning Res. 22 (2021) 1, 2617-2680
•
e-Print:
- 1912.02762
•
DOI:
- 10.5555/3546258.3546315

[5]

Simulation of phi 4 theory in the strong coupling expansion beyond the Ising Limit, Master’s thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I