A wavelet-based three-dimensional Convolutional Neural Network for superresolution of turbulent vorticity

Abstract

We develop a wavelet-based three-dimensional convolutional neural network (WCNN3d) for superresolution of coarse-grained data of homogeneous isotropic turbulence. The turbulent flow data are computed by high resolution direct numerical simulation (DNS), while the coarse-grained data are obtained by applying a Gaussian filter to the DNS data. The CNNs are trained with the DNS data and the coarse-grained data. We compare vorticity- and velocity-based approaches and assess the proposed WCNN3d method in terms of flow visualization, enstrophy spectra and probability density functions. We show that orthogonal wavelets enhance the efficiency of the learning of CNN.