Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
This work addresses the challenge of phase transition detection in physics, offering a method that does not require prior knowledge of phases or Hamiltonians, though it is incremental as it applies existing ML techniques to known models.
The authors tackled the problem of identifying phase transitions in physical models without prior knowledge by applying unsupervised learning techniques, such as PCA and variational autoencoders, to the Ising and XY models, finding that latent parameters correspond to known order parameters and reconstruction loss serves as a universal identifier for transitions.
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.