Machine-Learning-Phases-of-Matter-with-Discriminative-Localization

This project reproduces results from the article "Machine Learning Phases of Matter" (https://arxiv.org/abs/1605.01735), in addition to exploring the application of discriminative localization (https://arxiv.org/pdf/1512.04150.pdf) to this area of study. The first article shows how neural networks, including fully connected networks (FCN) and convolutional neural networks (CNN), can be used to infer macroscopic information about a statistical mechanical system's state from its microstate. The focus here is on the particular case of the Ising model, and inferring the phase of the system from its underlying spin configuration. This project applies the results of the second article on discriminative localization to investigate the decision regions that determine the classification of Ising configuration by a CNN (including a global average pooling layer before the final dense/softmax layers) as being in the polarized or unpolarized phase.

The data of the Ising model is simulated for various temperatures around the critical temperature $T_c = 2.27$, at which the phase transition from disordered (unpolarized, spins pointing in random directions) to ordered (polarized, spins pointing in roughly the same direction). The simulation is performed using the Metropolis algorithm, a well-known form of Markov chain Monte Carlo (MCMC).