Unit:
Κατεύθυνση Πυρηνική Φυσική και Φυσική Στοιχειωδών ΣωματιδίωνLibrary of the School of Science
Author:
Doultsinos Georgios
Supervisors info:
Φώτιος Διάκονος, Αναπληρωτής Καθηγητής, Τμήμα Φυσικής ΕΚΠΑ
Original Title:
Μελέτη της κρίσιμης συμπεριφοράς σε μοντέλα spin με μηχανές Boltzmann
Translated title:
Studing the critical beahaviour of spin models using Boltzmann machines
Summary:
Last decades, machine learning and specifically neural networks, became a powerful tool for solving problems in many different scientific areas. Though their general success, only a few things are know according to their properties in a theoretical level. Their recent applications on the field of statistical mechanics and solid state physics reveled a connection between critical phenomena and the way machine learning works. In this work we focus exactly on this connection for the case of the Ising model, using a class of neural networks named Restricted Boltzmann Machines (RBM). For the first part of this work we study the thermodynamic properties of the Ising model using Monte Carlo simulations based on the Metropolis algorithm. Using the spin states created we calculated the critical exponents as well the critical temperature of the phase transition using finite size scaling techniques. For the second part, we trained Boltzmann machines with the spin configurations and used them to create the RBM flow by repetitively reconstructing states. Calculating thermodynamic properties such as the magnetization distribution we concluded that the RBM flow tends towards the critical region.
Main subject category:
Science
Keywords:
monte carlo simulations, Ising model, Metropolis, phase transition, critical behaviour, restricted boltzmann machines, unsupervised learning, rbm flow
