Sammendrag
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.