ИСТИНА

Nowadays machine learning is becoming more and more popular and powerful tool for scientific research. Carrasquilla and Melko have demonstrated how neural networks can be used for classifying phases in solids [1]. Restricted Boltzmann machine (RBM), a simple stochastic neural network, is shown to reproduce ferromagnetic Ising model results if trained on the dataset obtained by Monte-Carlo (MC) method [2]. The authors calculate observable physical properties with RBMs trained at different temperatures and find good agreement with MC results for corresponding temperatures. We show that RBM is able not only to reproduce observable physical properties calculated earlier, but also to predict them. First of all, we study short-range order in binary alloys. In the simplest case, this problem can be reduced to the Ising model with spins up and down corresponding to atoms of types A and B. The dataset of 106 samples of 10x10 square matrices is calculated using the Metropolis algorithm for the alloy concentration equal to one half. We propose an algorithm which allows RBM trained on this dataset to generate new samples for any alloy concentration. In Fig. 1 the Warren-Cowley short-range order parameter is presented. It can be seen that RBM trained at one concentration can correctly predict short-range order in the full concentration range. Moreover, long range magnetic order can also be successfully predicted. Fig. 2 shows the magnetization for the 2D ferromagnetic Ising model. RBM result is obtained by training the machine for T=2.5, which is close to the critical temperature, and then scaling the weights and biases to generate data for all other temperatures. We see that RBM, based on data for only one temperature, reproduces the thermodynamic properties for the entire temperature range and correctly predicts critical temperature.