Machine learning action parameters in lattice quantum chromodynamics

Shanahan, Phiala E.; Trewartha, Daniel; Detmold, William

doi:10.1103/PhysRevD.97.094506

Title: Machine learning action parameters in lattice quantum chromodynamics

Abstract

Numerical lattice quantum chromodynamics studies of the strong interaction are important in many aspects of particle and nuclear physics. Such studies require significant computing resources to undertake. A number of proposed methods promise improved efficiency of lattice calculations, and access to regions of parameter space that are currently computationally intractable, via multi-scale action-matching approaches that necessitate parametric regression of generated lattice datasets. The applicability of machine learning to this regression task is investigated, with deep neural networks found to provide an efficient solution even in cases where approaches such as principal component analysis fail. The high information content and complex symmetries inherent in lattice QCD datasets require custom neural network layers to be introduced and present opportunities for further development.

Authors:: Shanahan, Phiala E.; Trewartha, Daniel; Detmold, William

Publication Date:: Wed May 16 00:00:00 EDT 2018

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

OSTI Identifier:: 1437340

Alternate Identifier(s):: OSTI ID: 1438377; OSTI ID: 1635166

Report Number(s):: JLAB-THY-18-2627; DOE/OR/23177-4325; arXiv:1801.05784; MIT-CTP/4980
Journal ID: ISSN 2470-0010; PRVDAQ; 094506

Grant/Contract Number:: SC0010495; SC0011090; SC0018121; AC05-06OR23177; 0922770

Resource Type:: Published Article

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Name: Physical Review. D. Journal Volume: 97 Journal Issue: 9; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Shanahan, Phiala E., Trewartha, Daniel, and Detmold, William. Machine learning action parameters in lattice quantum chromodynamics.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.97.094506.

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                    Shanahan, Phiala E., Trewartha, Daniel, & Detmold, William. Machine learning action parameters in lattice quantum chromodynamics.  United States.  https://doi.org/10.1103/PhysRevD.97.094506

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                    Shanahan, Phiala E., Trewartha, Daniel, and Detmold, William. Wed .  
"Machine learning action parameters in lattice quantum chromodynamics".  United States.  https://doi.org/10.1103/PhysRevD.97.094506.

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@article{osti_1437340,

  title        = {Machine learning action parameters in lattice quantum chromodynamics},

  author       = {Shanahan, Phiala E. and Trewartha, Daniel and Detmold, William},

  abstractNote = {Numerical lattice quantum chromodynamics studies of the strong interaction are important in many aspects of particle and nuclear physics. Such studies require significant computing resources to undertake. A number of proposed methods promise improved efficiency of lattice calculations, and access to regions of parameter space that are currently computationally intractable, via multi-scale action-matching approaches that necessitate parametric regression of generated lattice datasets. The applicability of machine learning to this regression task is investigated, with deep neural networks found to provide an efficient solution even in cases where approaches such as principal component analysis fail. The high information content and complex symmetries inherent in lattice QCD datasets require custom neural network layers to be introduced and present opportunities for further development.},

  doi          = {10.1103/PhysRevD.97.094506},

  journal      = {Physical Review. D.},

  number       = 9,

  volume       = 97,

  place        = {United States},

  year         = {Wed May 16 00:00:00 EDT 2018},

  month        = {Wed May 16 00:00:00 EDT 2018}

}

Copy to clipboard

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Works referenced in this record:

Multigrid Monte Carlo Method for Lattice Field Theories
journal, March 1986

Goodman, Jonathan; Sokal, Alan D.
Physical Review Letters, Vol. 56, Issue 10
DOI: 10.1103/PhysRevLett.56.1015

Hybrid Monte Carlo
journal, September 1987

Duane, Simon; Kennedy, A. D.; Pendleton, Brian J.
Physics Letters B, Vol. 195, Issue 2
DOI: 10.1016/0370-2693(87)91197-X

Multigrid Monte Carlo algorithms for SU(2) lattice gauge theory: Two versus four dimensions
journal, December 1994

Grabenstein, Martin; Pinn, Klaus
Physical Review D, Vol. 50, Issue 11
DOI: 10.1103/PhysRevD.50.6998

Light asymmetric dark matter on the lattice: SU(2) technicolor with two fundamental flavors
journal, January 2012

Lewis, Randy; Pica, Claudio; Sannino, Francesco
Physical Review D, Vol. 85, Issue 1
DOI: 10.1103/PhysRevD.85.014504

Lattice QCD input for nuclear structure and reactions
journal, January 2018

Davoudi, Zohreh
EPJ Web of Conferences, Vol. 175
DOI: 10.1051/epjconf/201817501022

Applications of neural networks to the studies of phase transitions of two-dimensional Potts models
journal, April 2018

Li, C. -D.; Tan, D. -R.; Jiang, F. -J.
Annals of Physics, Vol. 391
DOI: 10.1016/j.aop.2018.02.018

Critical slowing down and error analysis in lattice QCD simulations
journal, April 2011

Schaefer, Stefan; Sommer, Rainer; Virotta, Francesco
Nuclear Physics B, Vol. 845, Issue 1
DOI: 10.1016/j.nuclphysb.2010.11.020

LIII. On lines and planes of closest fit to systems of points in space
journal, November 1901

Pearson, Karl
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 2, Issue 11
DOI: 10.1080/14786440109462720

Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory
journal, November 2017

Wetzel, Sebastian J.; Scherzer, Manuel
Physical Review B, Vol. 96, Issue 18
DOI: 10.1103/PhysRevB.96.184410

Machine Learning Phases of Strongly Correlated Fermions
journal, August 2017

Ch’ng, Kelvin; Carrasquilla, Juan; Melko, Roger G.
Physical Review X, Vol. 7, Issue 3
DOI: 10.1103/PhysRevX.7.031038

Principles of neurodynamics. Perceptrons and the theory of brain mechanisms
report, March 1961

Rosenblatt, Frank
DOI: 10.21236/AD0256582

Finite-lattice approximations to renormalization groups
journal, May 1975

Bell, Thomas L.; Wilson, Kenneth G.
Physical Review B, Vol. 11, Issue 9
DOI: 10.1103/PhysRevB.11.3431

Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position
journal, April 1980

Fukushima, Kunihiko
Biological Cybernetics, Vol. 36, Issue 4
DOI: 10.1007/BF00344251

Discovering phase transitions with unsupervised learning
journal, November 2016

Wang, Lei
Physical Review B, Vol. 94, Issue 19
DOI: 10.1103/PhysRevB.94.195105

The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk
journal, January 1988

Madras, Neal; Sokal, Alan D.
Journal of Statistical Physics, Vol. 50, Issue 1-2
DOI: 10.1007/BF01022990

Multiscale Monte Carlo equilibration: Two-color QCD with two fermion flavors
journal, December 2016

Detmold, William; Endres, Michael G.
Physical Review D, Vol. 94, Issue 11
DOI: 10.1103/PhysRevD.94.114502

$I = 2$ $π π$ scattering from fully-dynamical mixed-action lattice QCD
journal, March 2006

Beane, Silas R.; Bedaque, Paulo F.; Orginos, Kostas
Physical Review D, Vol. 73, Issue 5
DOI: 10.1103/PhysRevD.73.054503

Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit
journal, June 2000

Hahnloser, Richard H. R.; Sarpeshkar, Rahul; Mahowald, Misha A.
Nature, Vol. 405, Issue 6789
DOI: 10.1038/35016072

Finding Minimum Entropy Codes
journal, September 1989

Barlow, H. B.; Kaushal, T. P.; Mitchison, G. J.
Neural Computation, Vol. 1, Issue 3
DOI: 10.1162/neco.1989.1.3.412

Measurement of the $π^{-} p$ elastic scattering cross section near 180° between 600 and 1280 MeV/ c
journal, July 1974

Richards, T. J.; Crabb, D. G.; Keller, R.
Physical Review D, Vol. 10, Issue 1
DOI: 10.1103/PhysRevD.10.45

A new Directed Divergence Measure and its Characterization∗
journal, May 1990

Lin, J.; Wong, S. K. M.
International Journal of General Systems, Vol. 17, Issue 1
DOI: 10.1080/03081079008935097

The dropout learning algorithm
journal, May 2014

Baldi, Pierre; Sadowski, Peter
Artificial Intelligence, Vol. 210
DOI: 10.1016/j.artint.2014.02.004

The Contiguity Ratio and Statistical Mapping
journal, November 1954

Geary, R. C.
The Incorporated Statistician, Vol. 5, Issue 3
DOI: 10.2307/2986645

Block renormalization group for Euclidean Fermions
journal, June 1989

Balaban, Tadeusz; O'Carroll, Michael; Schor, Ricardo
Communications in Mathematical Physics, Vol. 122, Issue 2
DOI: 10.1007/BF01257414

Solving the quantum many-body problem with artificial neural networks
journal, February 2017

Carleo, Giuseppe; Troyer, Matthias
Science, Vol. 355, Issue 6325
DOI: 10.1126/science.aag2302

Machine learning phases of matter
journal, February 2017

Carrasquilla, Juan; Melko, Roger G.
Nature Physics, Vol. 13, Issue 5
DOI: 10.1038/nphys4035

Notes on Continuous Stochastic Phenomena
journal, January 1950

Moran, P. A. P.
Biometrika, Vol. 37, Issue 1-2
DOI: 10.1093/biomet/37.1-2.17

Exploring cluster Monte Carlo updates with Boltzmann machines
journal, November 2017

Wang, Lei
Physical Review E, Vol. 96, Issue 5
DOI: 10.1103/PhysRevE.96.051301

Self-learning Monte Carlo method
journal, January 2017

Liu, Junwei; Qi, Yang; Meng, Zi Yang
Physical Review B, Vol. 95, Issue 4
DOI: 10.1103/PhysRevB.95.041101

Nuclear physics from lattice QCD
journal, January 2011

Beane, S. R.; Detmold, W.; Orginos, K.
Progress in Particle and Nuclear Physics, Vol. 66, Issue 1
DOI: 10.1016/j.ppnp.2010.08.002

Multi-grid Monte Carlo (II). Two-dimensional XY model
journal, May 1991

Edwards, Robert G.; Goodman, Jonathan; Sokal, Alan D.
Nuclear Physics B, Vol. 354, Issue 2-3
DOI: 10.1016/0550-3213(91)90357-4

A new class of metric divergences on probability spaces and its applicability in statistics
journal, September 2003

Österreicher, Ferdinand; Vajda, Igor
Annals of the Institute of Statistical Mathematics, Vol. 55, Issue 3
DOI: 10.1007/BF02517812

Accelerated Monte Carlo simulations with restricted Boltzmann machines
journal, January 2017

Huang, Li; Wang, Lei
Physical Review B, Vol. 95, Issue 3
DOI: 10.1103/PhysRevB.95.035105

Self-organization in a perceptual network
journal, March 1988

Linsker, R.
Computer, Vol. 21, Issue 3
DOI: 10.1109/2.36

Machine Learning Topological Invariants with Neural Networks
journal, February 2018

Zhang, Pengfei; Shen, Huitao; Zhai, Hui
Physical Review Letters, Vol. 120, Issue 6
DOI: 10.1103/PhysRevLett.120.066401

Dark nuclei. II. Nuclear spectroscopy in two-color QCD
journal, December 2014

Detmold, William; McCullough, Matthew; Pochinsky, Andrew
Physical Review D, Vol. 90, Issue 11
DOI: 10.1103/PhysRevD.90.114506

Multi-grid Monte Carlo (III). Two-dimensional O(4)-symmetric non-linear σ-model
journal, August 1992

Edwards, Robert G.; JoséFerreira, Sabino; Goodman, Jonathan
Nuclear Physics B, Vol. 380, Issue 3
DOI: 10.1016/0550-3213(92)90262-A

Moments of nucleon spin-dependent generalized parton distributions
journal, March 2004

Schroers, W.; Brower, R. C.; Dreher, P.
Nuclear Physics B - Proceedings Supplements, Vol. 129-130
DOI: 10.1016/S0920-5632(03)02750-6

Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
journal, December 2015

Endres, Michael G.; Brower, Richard C.; Detmold, William
Physical Review D, Vol. 92, Issue 11
DOI: 10.1103/PhysRevD.92.114516

Confinement of quarks
journal, October 1974

Wilson, Kenneth G.
Physical Review D, Vol. 10, Issue 8
DOI: 10.1103/PhysRevD.10.2445

Quantum Chromodynamics on the Lattice
book, January 2010

Gattringer, Christof; Lang, Christian B.
Lecture Notes in Physics
DOI: 10.1007/978-3-642-01850-3

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG)
journal, February 2017

Aoki, S.; Aoki, Y.; Bečirević, D.
The European Physical Journal C, Vol. 77, Issue 2
DOI: 10.1140/epjc/s10052-016-4509-7

Fixed point actions for Wilson fermions
journal, October 1993

Wiese, U. -J.
Physics Letters B, Vol. 315, Issue 3-4
DOI: 10.1016/0370-2693(93)91634-Y

On Information and Sufficiency
journal, March 1951

Kullback, S.; Leibler, R. A.
The Annals of Mathematical Statistics, Vol. 22, Issue 1
DOI: 10.1214/aoms/1177729694

Perfect Actions: From the Theoretical Background to Recent Developments
journal, January 1998

Hasenfratz, Peter
Progress of Theoretical Physics Supplement, Vol. 131
DOI: 10.1143/PTPS.131.189

Relations Between two sets of Variates
journal, December 1936

Hotelling, H.
Biometrika, Vol. 28, Issue 3-4
DOI: 10.1093/biomet/28.3-4.321

Learning thermodynamics with Boltzmann machines
journal, October 2016

Torlai, Giacomo; Melko, Roger G.
Physical Review B, Vol. 94, Issue 16
DOI: 10.1103/PhysRevB.94.165134

Thermodynamics of strong-interaction matter from lattice QCD
journal, October 2015

Ding, Heng-Tong; Karsch, Frithjof; Mukherjee, Swagato
International Journal of Modern Physics E, Vol. 24, Issue 10
DOI: 10.1142/S0218301315300076

A new metric for probability distributions
journal, July 2003

Endres, D. M.; Schindelin, J. E.
IEEE Transactions on Information Theory, Vol. 49, Issue 7
DOI: 10.1109/TIT.2003.813506

Perfect lattice action for asymptotically free theories
journal, February 1994

Hasenfratz, P.; Niedermayer, F.
Nuclear Physics B, Vol. 414, Issue 3
DOI: 10.1016/0550-3213(94)90261-5

Representations of the rotation reflection symmetry group of the four-dimensional cubic lattice
journal, November 1983

Mandula, Jeffrey E.; Zweig, George; Govaerts, Jan
Nuclear Physics B, Vol. 228, Issue 1
DOI: 10.1016/0550-3213(83)90399-1

Divergence measures based on the Shannon entropy
journal, January 1991

Lin, J.
IEEE Transactions on Information Theory, Vol. 37, Issue 1
DOI: 10.1109/18.61115

Erratum: Properties and uses of the Wilson flow in lattice QCD
journal, March 2014

Lüscher, Martin
Journal of High Energy Physics, Vol. 2014, Issue 3
DOI: 10.1007/JHEP03(2014)092

Lattice QCD with mixed actions
journal, August 2005

collaboration, Ukqcd; Bowler, Ken C.; Joó, Balint
Journal of High Energy Physics, Vol. 2005, Issue 08
DOI: 10.1088/1126-6708/2005/08/003

Properties and uses of the Wilson flow in lattice QCD
journal, August 2010

Lüscher, Martin
Journal of High Energy Physics, Vol. 2010, Issue 8
DOI: 10.1007/JHEP08(2010)071

Analysis of a complex of statistical variables into principal components.
journal, January 1933

Hotelling, H.
Journal of Educational Psychology, Vol. 24, Issue 6
DOI: 10.1037/h0071325

The renormalization group and the ε expansion
journal, August 1974

Wilson, K.
Physics Reports, Vol. 12, Issue 2
DOI: 10.1016/0370-1573(74)90023-4

The Chroma Software System for Lattice QCD
journal, March 2005

Edwards, Robert G.; Joó, Bálint
Nuclear Physics B - Proceedings Supplements, Vol. 140
DOI: 10.1016/j.nuclphysbps.2004.11.254

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Title: Machine learning action parameters in lattice quantum chromodynamics

Abstract

Citation Formats

Multigrid Monte Carlo Method for Lattice Field Theories journal, March 1986

Hybrid Monte Carlo journal, September 1987

Multigrid Monte Carlo algorithms for SU(2) lattice gauge theory: Two versus four dimensions journal, December 1994

Light asymmetric dark matter on the lattice: SU(2) technicolor with two fundamental flavors journal, January 2012

Lattice QCD input for nuclear structure and reactions journal, January 2018

Applications of neural networks to the studies of phase transitions of two-dimensional Potts models journal, April 2018

Critical slowing down and error analysis in lattice QCD simulations journal, April 2011

LIII. On lines and planes of closest fit to systems of points in space journal, November 1901

Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory journal, November 2017

Machine Learning Phases of Strongly Correlated Fermions journal, August 2017

Principles of neurodynamics. Perceptrons and the theory of brain mechanisms report, March 1961

Finite-lattice approximations to renormalization groups journal, May 1975

Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position journal, April 1980

Discovering phase transitions with unsupervised learning journal, November 2016

The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk journal, January 1988

Multiscale Monte Carlo equilibration: Two-color QCD with two fermion flavors journal, December 2016

I = 2 π π scattering from fully-dynamical mixed-action lattice QCD journal, March 2006

Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit journal, June 2000

Finding Minimum Entropy Codes journal, September 1989

Measurement of the π − p elastic scattering cross section near 180° between 600 and 1280 MeV/ c journal, July 1974

A new Directed Divergence Measure and its Characterization∗ journal, May 1990

The dropout learning algorithm journal, May 2014

The Contiguity Ratio and Statistical Mapping journal, November 1954

Block renormalization group for Euclidean Fermions journal, June 1989

Solving the quantum many-body problem with artificial neural networks journal, February 2017

Machine learning phases of matter journal, February 2017

Notes on Continuous Stochastic Phenomena journal, January 1950

Exploring cluster Monte Carlo updates with Boltzmann machines journal, November 2017

Self-learning Monte Carlo method journal, January 2017

Nuclear physics from lattice QCD journal, January 2011

Multi-grid Monte Carlo (II). Two-dimensional XY model journal, May 1991

A new class of metric divergences on probability spaces and its applicability in statistics journal, September 2003

Accelerated Monte Carlo simulations with restricted Boltzmann machines journal, January 2017

Self-organization in a perceptual network journal, March 1988

Machine Learning Topological Invariants with Neural Networks journal, February 2018

Dark nuclei. II. Nuclear spectroscopy in two-color QCD journal, December 2014

Multi-grid Monte Carlo (III). Two-dimensional O(4)-symmetric non-linear σ-model journal, August 1992

Moments of nucleon spin-dependent generalized parton distributions journal, March 2004

Multiscale Monte Carlo equilibration: Pure Yang-Mills theory journal, December 2015

Confinement of quarks journal, October 1974

Quantum Chromodynamics on the Lattice book, January 2010

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG) journal, February 2017

Fixed point actions for Wilson fermions journal, October 1993

On Information and Sufficiency journal, March 1951

Perfect Actions: From the Theoretical Background to Recent Developments journal, January 1998

Relations Between two sets of Variates journal, December 1936

Learning thermodynamics with Boltzmann machines journal, October 2016

Thermodynamics of strong-interaction matter from lattice QCD journal, October 2015

A new metric for probability distributions journal, July 2003

Perfect lattice action for asymptotically free theories journal, February 1994

Representations of the rotation reflection symmetry group of the four-dimensional cubic lattice journal, November 1983

Divergence measures based on the Shannon entropy journal, January 1991

Erratum: Properties and uses of the Wilson flow in lattice QCD journal, March 2014

Lattice QCD with mixed actions journal, August 2005

Properties and uses of the Wilson flow in lattice QCD journal, August 2010

Analysis of a complex of statistical variables into principal components. journal, January 1933

The renormalization group and the ε expansion journal, August 1974

The Chroma Software System for Lattice QCD journal, March 2005

Multigrid Monte Carlo Method for Lattice Field Theories
journal, March 1986

Hybrid Monte Carlo
journal, September 1987

Multigrid Monte Carlo algorithms for SU(2) lattice gauge theory: Two versus four dimensions
journal, December 1994

Light asymmetric dark matter on the lattice: SU(2) technicolor with two fundamental flavors
journal, January 2012

Lattice QCD input for nuclear structure and reactions
journal, January 2018

Applications of neural networks to the studies of phase transitions of two-dimensional Potts models
journal, April 2018

Critical slowing down and error analysis in lattice QCD simulations
journal, April 2011

LIII. On lines and planes of closest fit to systems of points in space
journal, November 1901

Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory
journal, November 2017

Machine Learning Phases of Strongly Correlated Fermions
journal, August 2017

Principles of neurodynamics. Perceptrons and the theory of brain mechanisms
report, March 1961

Finite-lattice approximations to renormalization groups
journal, May 1975

Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position
journal, April 1980

Discovering phase transitions with unsupervised learning
journal, November 2016

The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk
journal, January 1988

Multiscale Monte Carlo equilibration: Two-color QCD with two fermion flavors
journal, December 2016

$I = 2$ $π π$ scattering from fully-dynamical mixed-action lattice QCD
journal, March 2006

Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit
journal, June 2000

Finding Minimum Entropy Codes
journal, September 1989

Measurement of the $π^{-} p$ elastic scattering cross section near 180° between 600 and 1280 MeV/ c
journal, July 1974

A new Directed Divergence Measure and its Characterization∗
journal, May 1990

The dropout learning algorithm
journal, May 2014

The Contiguity Ratio and Statistical Mapping
journal, November 1954

Block renormalization group for Euclidean Fermions
journal, June 1989

Solving the quantum many-body problem with artificial neural networks
journal, February 2017

Machine learning phases of matter
journal, February 2017

Notes on Continuous Stochastic Phenomena
journal, January 1950

Exploring cluster Monte Carlo updates with Boltzmann machines
journal, November 2017

Self-learning Monte Carlo method
journal, January 2017

Nuclear physics from lattice QCD
journal, January 2011

Multi-grid Monte Carlo (II). Two-dimensional XY model
journal, May 1991

A new class of metric divergences on probability spaces and its applicability in statistics
journal, September 2003

Accelerated Monte Carlo simulations with restricted Boltzmann machines
journal, January 2017

Self-organization in a perceptual network
journal, March 1988

Machine Learning Topological Invariants with Neural Networks
journal, February 2018

Dark nuclei. II. Nuclear spectroscopy in two-color QCD
journal, December 2014

Multi-grid Monte Carlo (III). Two-dimensional O(4)-symmetric non-linear σ-model
journal, August 1992

Moments of nucleon spin-dependent generalized parton distributions
journal, March 2004

Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
journal, December 2015

Confinement of quarks
journal, October 1974

Quantum Chromodynamics on the Lattice
book, January 2010

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG)
journal, February 2017

Fixed point actions for Wilson fermions
journal, October 1993

On Information and Sufficiency
journal, March 1951

Perfect Actions: From the Theoretical Background to Recent Developments
journal, January 1998

Relations Between two sets of Variates
journal, December 1936

Learning thermodynamics with Boltzmann machines
journal, October 2016

Thermodynamics of strong-interaction matter from lattice QCD
journal, October 2015

A new metric for probability distributions
journal, July 2003

Perfect lattice action for asymptotically free theories
journal, February 1994

Representations of the rotation reflection symmetry group of the four-dimensional cubic lattice
journal, November 1983

Divergence measures based on the Shannon entropy
journal, January 1991

Erratum: Properties and uses of the Wilson flow in lattice QCD
journal, March 2014

Lattice QCD with mixed actions
journal, August 2005

Properties and uses of the Wilson flow in lattice QCD
journal, August 2010

Analysis of a complex of statistical variables into principal components.
journal, January 1933

The renormalization group and the ε expansion
journal, August 1974

The Chroma Software System for Lattice QCD
journal, March 2005