Supervised learning of phase transitions in classical and quantum systems*

Supervised machine learning methods are used to identify transitions in physical systems using the classical solid-liquid transition of a Lennard-Jones system as well as the strong coupling-local moment quantum transition in the soft-gap Anderson model as examples. Monte Carlo sampling was used to achieve a uniform sampling of configurational data across a large range of the relevant transition parameter for each system. Hyperbolic feature scaling is applied to the features followed by training a 1-dimensional convolutional neural network with the samples corresponding to the extreme parameters of each phase as training data. The rest of the configurational data is assigned phase classification probabilities by the neural network, allowing for the prediction of the transition point with respect to the chosen varied parameter. This is done by fitting the mean classification probabilities for each set of configurational data with respect to the varied parameter with a logistic function and taking the transition to be at the value of the parameter corresponding to the midpoint of the sigmoid. The results obtained are comparable to results using contemporary methods for each system.