Inverse renormalization group based on image super-resolution using deep convolutional networks

The inverse renormalization group is studied based on the image super-resolution using the deep convolutional neural networks. We consider the improved correlation configuration instead of spin configuration for the spin models, such as the two-dimensional Ising and three-state Potts models. We propose a block-cluster transformation as an alternative to the block-spin transformation in dealing with the improved estimators. In the framework of the dual Monte Carlo algorithm, the block-cluster transformation is regarded as a transformation in the graph degrees of freedom, whereas the block-spin transformation is that in the spin degrees of freedom. We demonstrate that the renormalized improved correlation configuration successfully reproduces the original configuration at all the temperatures by the super-resolution scheme. Using the rule of enlargement, we repeatedly make inverse renormalization procedure to generate larger correlation configurations. To connect thermodynamics, an approximate temperature rescaling is discussed. The enlarged systems generated using the super-resolution satisfy the finite-size scaling.