The influence of adversarial training on turbulence closure modeling

Over the last years, fundamental advancements in deep learning frameworks combined with the availability of large highly-resolved datasets, as well as the exponential improvement in computer hardware performance have shown great promise to move beyond classical equation-based models for the turbulence closure. Deep convolutional neural networks (CNN) can be used to super-resolve low-resolution simulations, thus they become attractive for large eddy simulation subfilter-scale modeling. However, these models often lack generalization capabilities and cannot guarantee fields with high-wavenumber details. To tackle those problems, the use of generative adversarial networks (GAN), which are composed of two competing neural networks (a generator and a discriminator) has been proposed. Despite the remarkable performance of GAN in single-image super-reconstruction, its application in turbulence modeling applications is relatively unexplored. In this work, the contribution of adversarial training is assessed by comparing two types of deep neural networks: a supervised CNN-type model and a semi-supervised GAN-based model. This study demonstrates the ability of the GAN architecture to produce high-quality super-reconstructed fields compared to standard deep convolutional networks, enhancing subgrid physical structures. The prolonged adversarial training leads to extracting underlying small-dimensional features in a semi-supervised manner and, consequently, improved turbulence statistics. Finally, it is shown that the propensity of the GAN training to run into convergence oscillations can be limited by a proper selection of the learning rate for both generator and discriminator.