Real-space renormalization group transformation from CNN and maximum likelihood estimation

We report a novel scheme to perform real-space renormalization group (RG) transformation based on supervised machine learning. The 2D Potts model on a square lattice is used as an example. System configurations generated by Monte Carlo simulations at selected temperatures below and above the transition temperature are fed into a convolutional neural network with the network weights optimized to produce the best match under a classifier. Effective model parameters that characterize the distribution of transformed configurations in one step are then extracted using maximum likelihood estimation. This allows us to construct the RG flow in the Hamiltonian space and obtain critical exponents for the transition. Results are presented for different q values.