Data-driven deconvolution for large eddy simulations of Kraichnan turbulence

In this article, we demonstrate the use of artificial neural networks as optimal maps which are utilized for convolution and deconvolution of coarse-grained fields to account for sub-grid scale turbulence effects. We demonstrate that an effective eddy-viscosity is predicted by our purely data-driven large eddy simulation framework without explicit utilization of phenomenological arguments. In addition, our data-driven framework precludes the knowledge of true sub-grid stress information during the training phase due to its focus on estimating an effective filter and its inverse so that grid-resolved variables may be related to direct numerical simulation data statistically. The proposed predictive framework is also combined with a statistical truncation mechanism for ensuring numerical realizability in an explicit formulation. Through this we seek to unite structural and functional modeling strategies for modeling non-linear partial differential equations using reduced degrees of freedom. Both a priori and a posteriori results are shown for a two-dimensional decaying turbulence case in addition to a detailed description of validation and testing. A hyperparameter sensitivity study also shows that the proposed dual network framework simplifies learning complexity and is viable with exceedingly simple network architectures. Our findings indicate that the proposed framework approximates a robust and stable sub-grid closure which compares favorably to the Smagorinsky and Leith hypotheses for capturing the theoretical $k^{-3}$ scaling in Kraichnan turbulence.