Data-driven deconvolution for the large eddy simulation of Kraichnan turbulence

In this study, we demonstrate the use of artificial neural networks as optimal maps which are utilized for the convolution and deconvolution of coarse-grained fields to account for sub-grid scale turbulence effects. We demonstrate that an effective eddy-viscosity is characterized by our purely data-driven large eddy simulation framework without the explicit utilization of phenomenological arguments. In addition, our data-driven framework does not require 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. Through this we seek to unite the 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 the Kraichnan turbulence case in addition to a detailed description of validation and testing. 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 theoretical kinetic-energy scaling trends in the wavenumber domain.