中国物理B ›› 2023, Vol. 32 ›› Issue (6): 67401-067401.doi: 10.1088/1674-1056/ac989c

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Generalization properties of restricted Boltzmann machine for short-range order

M A Timirgazin and A K Arzhnikov   

  1. Udmurt Federal Research Center, Ural Branch of RAS, Izhevsk 426067, Russia
  • 收稿日期:2022-07-27 修回日期:2022-09-20 接受日期:2022-10-10 出版日期:2023-05-17 发布日期:2023-05-29
  • 通讯作者: M A Timirgazin E-mail:timirgazin@gmail.com

Generalization properties of restricted Boltzmann machine for short-range order

M A Timirgazin and A K Arzhnikov   

  1. Udmurt Federal Research Center, Ural Branch of RAS, Izhevsk 426067, Russia
  • Received:2022-07-27 Revised:2022-09-20 Accepted:2022-10-10 Online:2023-05-17 Published:2023-05-29
  • Contact: M A Timirgazin E-mail:timirgazin@gmail.com

摘要: A biased sampling algorithm for the restricted Boltzmann machine (RBM) is proposed, which allows generating configurations with a conserved quantity. To validate the method, a study of the short-range order in binary alloys with positive and negative exchange interactions is carried out. The network is trained on the data collected by Monte-Carlo simulations for a simple Ising-like binary alloy model and used to calculate the Warren-Cowley short-range order parameter and other thermodynamic properties. We demonstrate that the proposed method allows us not only to correctly reproduce the order parameters for the alloy concentration at which the network was trained, but can also predict them for any other concentrations.

关键词: machine learning, short-range order, Ising model, restricted Boltzmann machine

Abstract: A biased sampling algorithm for the restricted Boltzmann machine (RBM) is proposed, which allows generating configurations with a conserved quantity. To validate the method, a study of the short-range order in binary alloys with positive and negative exchange interactions is carried out. The network is trained on the data collected by Monte-Carlo simulations for a simple Ising-like binary alloy model and used to calculate the Warren-Cowley short-range order parameter and other thermodynamic properties. We demonstrate that the proposed method allows us not only to correctly reproduce the order parameters for the alloy concentration at which the network was trained, but can also predict them for any other concentrations.

Key words: machine learning, short-range order, Ising model, restricted Boltzmann machine

中图分类号:  (Metals; alloys and binary compounds)

  • 74.70.Ad
07.05.Mh (Neural networks, fuzzy logic, artificial intelligence) 64.60.De (Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.))