Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
By Sebastian Johann Wetzel. Physical Review E, 2017
371 citations recorded by the source corpus.
We examine unsupervised machine learning techniques to learn features that best describe configurations of the two-dimensional Ising model and the three-dimensional XY model. The methods range from principal component analysis over manifold and clustering methods to artificial neural-network-based variational autoencoders. They are applied to Monte Carlo-sampled configurations and have, a priori, no knowledge about the Hamiltonian or the order parameter. We find that the most promising algorithms are principal component analysis and variational autoencoders. Their predicted latent parameters correspond to the known order parameters. The latent representations of the models in question are clustered, which makes it possible to identify phases without prior knowledge of their existence. Furthermore, we find that the reconstruction loss function can be used as a universal identifier for phase transitions.
Subfields: Condensed Matter Physics, Molecular Biology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/5941c982a43bd3388ae6ba6e5e0ccb5eb002247d
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In Condensed Matter Physics
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In Molecular Biology
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In Statistical and Nonlinear Physics
- Kyle Cranmer
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- Leslie Vogt-Maranto
- Laurent Daudet
- Naftali Tishby
- Yongmin Liu
- Xianzhe Zhang
- Yihao Xu
Citations in the corpus
- Interfacing photonics with artificial intelligence: an innovative design strategy for photonic structures and devices based on artificial neural networks (2021, methodology): “For the inverse design part, the authors incorporated a variational auto-encoder (VAE) structure [76,77], which is a probabilistic approach, in the model.”
- Machine learning and the physical sciences (2019, background): “For instance, in (Wetzel, 2017) for the Ising and XY model, in (Wang and Zhai, 2017, 2018) for frustrated spin systems.”