Statistical Physics Approach to Small Scale Artificial Neural Networks

Borisenok S.

5th International Online Conference on Mathematics "An Istanbul Meeting for World Mathematicians", İstanbul, Turkey, 1 - 03 December 2021, pp.572-579

  • Publication Type: Conference Paper / Full Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.572-579
  • Abdullah Gül University Affiliated: Yes

Abstract

We discuss the statistical physics approach to the application of small-scale artificial neural networks (ANNs) well-trained with data collected from the ‘Ab Initio’ principle, as it was proposed by Wang, Jiang, and Zhou in 2020 for mimicking the microscopic statistical states of a quantum system. Such networks could be used for efficient numerical modeling of different statistical systems: spin structures, phase transitions, and others related statistical systems. We investigate the alternative network configuration based on the Hodgkin – Huxley elements and demonstrate that the reproduction of the macroscopic states for the Ising quantum system can be done with a sufficiently smaller number of neurons, and with a lower computational cost.

Keywords: Ising ferromagnetic model, data collection, Hodgkin-Huxley neuron.