Reconstruction of turbulent data from TURB-Rot database with deep generative models and Gappy POD*

We study the applicability of tools developed by the computer vision community for feature learning and semantic image inpainting to perform data reconstruction of fluid turbulence configurations. The aim is twofold. First, we explore on a quantitative basis, the capability of Convolutional Neural Networks embedded in a Deep Generative Adversarial Model (Deep-GAN) to generate missing data in turbulence, a paradigmatic high dimensional chaotic system. In particular, we investigate their use in reconstructing two-dimensional damaged snapshots extracted from a large database of numerical configurations of 3d turbulence in the presence of rotation and of turbulent channel flows. The generative model we present is based on a first Context Encoders network that infers the missing data via minimization of the $L_2$ pixel-wise reconstruction loss, plus an adversarial penalization given by a second network that aims to discriminate real from reconstructed data. Finally, we present a comparison with different and well-known data assimilation tools, such as Nudging,  an equation-informed unbiased protocol, or on Gappy POD, developed in the context of reconstruction of images. The TURB-Rot database, http://smart-turb.roma2.infn.it, of 300K 2d turbulent images is describeM. Buzzicotti$^1$, T. Li$^2$, F. Bonaccorso$^{1,3}$,  P. Clark Di Leoni$^4$, L. Biferale$^1$d and details on how to download it are given.