Statistical Physics Approach to Small Scale Artificial Neural Networks

Borisenok S.

5th International Online Conference on Mathematics "An Istanbul Meeting for World Mathematicians", İstanbul, Türkiye, 1 - 03 Aralık 2021, ss.572-579

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.572-579
  • Abdullah Gül Üniversitesi Adresli: Evet

Özet

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.