Data reconstruction of rotating turbulent flows with Gappy POD and Generative Adversarial Networks*

Two methods are used to reconstruct two-dimensional instantaneous velocity module fields in a turbulent flow under rotation. The first method is Gappy POD, in which we use proper orthogonal decomposition (POD) to complete flow fields from gappy data, while the second one reconstructs the flow fields using convolutional neural networks embedded in a Generative Adversarial Network (GAN). We first show that there is always an optimal number of POD modes for Gappy POD reconstruction regarding a specific gap. In order to systematically compare the applicability of the two tools, we consider one square gap at the center with different gap sizes. Results show that compared with Gappy POD, GAN reconstruction not only has a smaller L2 error, but also better turbulent statistics of both the velocity module and the velocity module gradient. This can be attributed to the ability of nonlinearity expression of the network and the presence of adversarial loss during the GAN training. We also investigate effects of the adversarial ratio, which controls the compromising between the L2 error and the statistical properties. Finally, we access the reconstruction on random gappiness. Both methods perform well for small and medium gappiness, while GAN works better when the gappiness is large.