Super-resolution of Finite Element spaces using Physics-informed Deep Learning Networks for Turbulent flows

High dimensional representation of turbulent flows present several challenges due to the wide range of spatial and temporal scales present in it. High Reynolds number simulations demand coarse-grained modeling, which requires an adequate representation of the impact of the unresolved scales. We present a deep learning (DL) based super-resolution technique to recover the fine scale information in the form of high-order Discontinuous Galerkin (DG) fields from a low-order DG solution. We train the DL models using coarse and fine scale data obtained by $L^2$-projection of the full order solution on low and high order DG sub-spaces respectively. The predictive and operational efficacy of the learning algorithms is then assessed. The performance of the model is improved by: (i) introducing non-dimensionalized physics-informed input and output features; and (ii) by weighting the loss with a prior obtained directly from the training data. The present approach is found to generalise to unseen data at different flow conditions as well.