Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders

We employ unsupervised machine learning techniques to learn latent parameters which best describe states of the two-dimensional Ising model and the three-dimensional XY model. These methods range from principal component analysis to artificial neural network based variational autoencoders. The state...

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Podrobná bibliografie
Vydáno v:	arXiv.org
Hlavní autor:	Wetzel, Sebastian Johann
Médium:	Paper
Jazyk:	angličtina
Vydáno:	Ithaca Cornell University Library, arXiv.org 12.03.2017
Témata:	Artificial neural networks Computer simulation Critical temperature Ising model Machine learning Mathematical models Monte Carlo simulation Neural networks Order parameters Phase transitions Principal components analysis Three dimensional models Two dimensional models Unsupervised learning
ISSN:	2331-8422
On-line přístup:	Získat plný text
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Popis
Shrnutí:	We employ unsupervised machine learning techniques to learn latent parameters which best describe states of the two-dimensional Ising model and the three-dimensional XY model. These methods range from principal component analysis to artificial neural network based variational autoencoders. The states are sampled using a Monte-Carlo simulation above and below the critical temperature. We find that the predicted latent parameters correspond to the known order parameters. The latent representation of the states of the models in question are clustered, which makes it possible to identify phases without prior knowledge of their existence or the underlying Hamiltonian. Furthermore, we find that the reconstruction loss function can be used as a universal identifier for phase transitions.
Bibliografie:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1703.02435