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  • Open Access

Improving efficiency of the path optimization method for a gauge theory

Yusuke Namekawa1,2,3,*, Kouji Kashiwa4, Hidefumi Matsuda2,5, Akira Ohnishi3, and Hayato Takase

  • 1Education and Research Center for Artificial Intelligence and Data Innovation, Hiroshima University, Hiroshima 730-0053, Japan
  • 2Department of Physics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan
  • 3Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
  • 4Department of Computer Science and Engineering, Faculty of Information Engineering, Fukuoka Institute of Technology, Fukuoka 811-0295, Japan
  • 5Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China

  • *namekawa@hiroshima-u.ac.jp
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Phys. Rev. D 107, 034509 – Published 22 February, 2023

DOI: https://doi.org/10.1103/PhysRevD.107.034509

Abstract

We investigate efficiency of a gauge-covariant neural network and an approximation of the Jacobian in optimizing the complexified integration path toward evading the sign problem in lattice field theories. For the construction of the complexified integration path, we employ the path optimization method. The two-dimensional U(1) gauge theory with the complex gauge-coupling constant is used as a laboratory to evaluate the efficiency. It is found that the gauge-covariant neural network, which is composed of the Stout-like smearing, can enhance the average phase factor, as the gauge-invariant input does. For the approximation of the Jacobian, we test the most drastic case in which we perfectly drop the Jacobian during the learning process. It reduces the numerical cost of the Jacobian calculation from O(N3) to O(1), where N means the number of degrees of freedom of the theory. The path optimization using this Jacobian approximation still enhances the average phase factor at expense of a slight increase of the statistical error.

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Phys. Rev. D 107, 034509– Published 22 February, 2023
  • Received 15 October 2022
  • Accepted 1 February 2023
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