Regressive and generative neural networks for scalar field theory

Oct 30, 2018
7 pages
Published in:
  • Phys.Rev.D 100 (2019) 1, 011501
  • Published: Jul 10, 2019
e-Print:

Citations per year

201820202022202420250510152025
Abstract: (APS)
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.
Note:
  • 11 pages, 11 figures
  • field theory: scalar
  • dimension: 2
  • potential: chemical
  • field theory: scalar: complex
  • lattice field theory
  • neural network
  • network
  • critical phenomena
  • temperature
  • numerical calculations