Abstract Stochastic subgrid-scale parametrizations aim to incorporate effects of unresolved processes in an effective model by sampling from a distribution usually described in terms of resolved modes. This is an active research area in fluid dynamics where processes evolve on a wide range of spatial and temporal scales. We propose a data-driven framework where resolved modes are defined as local spatial averages and deviations from these averages are the unresolved degrees of freedom. The proposed approach is applicable to a wide range of finite volume and finite difference numerical schemes commonly used to discretize many realistic problems in fluid dynamics. In this study, we evaluate the performance of conditional generative adversarial network (GAN) in parametrizing subgrid-scale effects in a finite difference discretization of stochastically forced Burgers equation. We train a Wasserstein GAN (WGAN) conditioned on the resolved variables to learn the distribution of the subgrid flux and, thus, represent the effect of unresolved scales. The resulting WGAN is then used in an effective model to reproduce the statistical features of resolved modes. We demonstrate that various stationary statistical quantities such as spectrum, moments and autocorrelation are well approximated by this effective model.
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