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. of isotropic turbulence in a periodic box and the coarse-grained data are obtained by the application of a Gaussian low-pass filter to the DNS data. We assessed the WCNN3d in terms of 3D visualization of vorticity, PDF of vorticity, and enstrophy spectra. We found that WCNN3d well reproduces vorticity statistics and the positions of the vortices from coarse-grained vorticity fields. For the vorticity-based approach, the use of wavelets enhances deep learning of turbulent flows considered here thanks to the sparsity of the wavelet representation which improves deep learning. For the velocity-based approach, we showed that weighting the wavelet coefficients of velocity, which yields velocity gradient information due to norm equivalence, improves the accuracy and yields results similar to the vorticity-based model. Furthermore, we assessed the divergence issue of the predicted fields and showed that its impact is negligible. We demonstrated the capability to predict a turbulent flow whose Reynolds number is higher than the flows used for the training.