Weather research and forecasting model (WRF) is widely used all over the world for operational forecasting. However the model’s computational costs increase faster than O(h-3), where h is the grid spacing, and the transition to the resolutions of the city building scale seems completely impractical. Also the classical numerical model forecast quality has fundamental limits. These limits are determined by the initial and boundary conditions and intrinsic model uncertainties and cannot be lifted by going to finer resolutions. In this talk we introduce methods of physically informed super resolution for weather forecasts. We have tried to adapt well known models for image super resolution, such as SRFBN and ESRGAN, by finetuning them on WRF data and adding some physically informed parts. We will describe our experiments with spectral loss and reanalysis loss. Our work is still in progress, so this talk is more an invitation to an open discussion than a classical presentation of the results.