Unsupervised learning of phase transitions via modified anomaly detection with autoencoders

In this paper, a modified method of anomaly detection using convolutional autoencoders is employed to predict phase transitions in several statistical mechanical models on a square lattice. We show that, when the autoencoder is trained with input data of various phases, the mean-square-error loss function can serve as a measure of disorder, and its standard deviation becomes an excellent indicator of critical points. We find that various types of phase transition points, including first-order, second-order, and topological ones, can be faithfully detected by the peaks in the standard deviation of the loss function. Besides, the values of transition points can be accurately determined under the analysis of finite-size scaling. Our results demonstrate that the present approach has general application in identification/classification of phase transitions even without a priori knowledge of the systems in question.