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Regressive and generative neural networks for scalar field theory

Kai Zhou, Gergely Endrődi, Long-Gang Pang, and Horst Stöcker
Phys. Rev. D 100, 011501(R) – Published 9 July 2019

Abstract

We explore the perspectives of machine learning techniques in the context of quantum field theories. In particular, we discuss two-dimensional complex scalar field theory at nonzero temperature and chemical potential—a theory with a nontrivial phase diagram. A neural network is successfully trained to recognize the different phases of this system and to predict the values of various observables, based on the field configurations. We analyze a broad range of chemical potentials and find that the network is robust and able to recognize patterns far away from the point where it was trained. Aside from the regressive analysis, which belongs to supervised learning, an unsupervised generative network is proposed to produce new quantum field configurations that follow a specific distribution. An implicit local constraint fulfilled by the physical configurations was found to be automatically captured by our generative model. We elaborate on potential uses of such a generative approach for sampling outside the training region.

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  • Received 12 March 2019

DOI:https://doi.org/10.1103/PhysRevD.100.011501

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsInterdisciplinary PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Kai Zhou1,2,*, Gergely Endrődi2, Long-Gang Pang1,3,4, and Horst Stöcker1,2,5

  • 1Frankfurt Institute for Advanced Studies, 60438 Frankfurt am Main, Germany
  • 2Institut für Theoretische Physik, Goethe Universität, 60438 Frankfurt am Main, Germany
  • 3Department of Physics, University of California, Berkeley, California 94720, USA
  • 4Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 5GSI Helmholtzzentrum für Schwerionenforschung, 64291 Darmstadt, Germany

  • *zhou@fias.uni-frankfurt.de

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Vol. 100, Iss. 1 — 1 July 2019

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