In this repo I explore various deep learning algorithms as applied to the 2-dimensional Ising model. The Ising model can be viewed as a simplistic model of a magnet, in which a 2-d array of particles with "spin" can orient to point in one of two directions: "up" or "down". At low temperatures the spin of each particle tends to align with the spin of its neighbors, as this is the lower energy state. At high temperatures, the spin of each particle may be randomly up or down. This model is interesting in physics because it displays a well understood phase transition at a critical temperature. An interesting question in AI is whether models can be developed to learn the phases of physical materials. To explore this question, a good first step is to apply AI to this model, and see if the phase transition can be identified.
First, I generate and label a dataset of Ising model configurations by performing Monte Carlo simulations at various temperatures.
These simulations are performed in Ising_genData.ipynb. Further explanation of the Ising model configurations are included in this notebook.
In Ising_NN.ipynb, I explore how a neural net with a single hidden layer, and a convolutional neural net are able to classify the high and low temperature phases of the Ising model. I consider two different Ising system sizes (20x20 and 40x40) and examine how the performance of the models changes. These ideas are based off the paper: J. Carrasquilla, R. Melko, Nat. Phys. (2017).
Next, In Ising_GAN.ipynb I create a GAN that generates configurations of the Ising model. Training is performed over the full temperature range sampled in the simulations.
Given that the GAN may generate a configuration corresponding to any temperature, it is more interesting the explore a conditional GAN (cGAN).
In Ising_cGAN.ipynb I develop a conditional deep convolutional GAN (cDCGAN) that takes as input to the generator and discriminator a label of the temperature and creates an embedding of the temperature label. Therefore, the GAN can be used to generate configurations for specified temperatures. This model shows excellent results after some tuning of the discriminator (to prevent overpowering the generator). An upcoming step is to compare the statistical properties of the generated output with the output of the direct simulations. Quantities to explore are the spin-spin correlation function and the corresponding correlation length.
These notebooks and documentation are an active project and will be updated daily.