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We propose a new design of a neural network for solving a zero shot superresolution problem for turbulent flows. We embed Luenberger-type observer intothe network's architecture to inform the network of the physics of the process,and to provide error correction and stabilization mechanisms. In addition, tocompensate for decrease of observer's performance due to the presence ofunknown destabilizing forcing, the network is designed to estimate thecontribution of the unknown forcing implicitly from the data over the course oftraining. By running a set of numerical experiments, we demonstrate that theproposed network does recover unknown forcing from data and is capable ofpredicting turbulent flows in high resolution from low resolution noisyobservations.

Super Resolution for Turbulent Flows in 2D: Stabilized Physics Informed Neural Networks