Using image Super-Resolution techniques as a coarse-graining method for physical systems*

One of the most generic probelms in theoretical physics is that of coarse graining - how to represent the behavior of a physical theory at long wave lengths and slow frequencies, by "integrating out" the irrelevant degrees of freedom which change rapidly in time and space. This is usually done by writing effective long-wavelength governing equations which take into account the small scale physics (a few examples: renormalization approaches, eddy viscosity, geometrical optics, the lubrication approximation and Taylor dispersion). The problem of single image Super-Resolution -- upscaling a given image to sub-pixel resolution -- is of similar nature, but in the opposite direction: the goal is to infer the short-wavelength behaviour from the long-wavelength data. Recently, machine learning approaches has been used to solve the upscaling problem in a data-driven manner, by learning the coarse-to-fine mapping from natural images (e.g. RAISR). Inspired by these techniques, we use similar data-driven approaches to write effective coarse-grained equations to dynamic PDEs, extracting effective equations and physical constants. Possible applications of these results will be discussed.