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Stochastic subgrid-scale parametrizations aim to incorporate effects ofunresolved processes in an effective model by sampling from a distributionusually described in terms of resolved modes. This is an active research areain climate, weather and ocean science where processes evolved in a wide rangeof spatial and temporal scales. In this study, we evaluate the performance ofconditional generative adversarial network (GAN) in parametrizing subgrid-scaleeffects in a finite-difference discretization of stochastically forced Burgersequation. We define resolved modes as local spatial averages and deviationsfrom these averages are the unresolved degrees of freedom. We train aWasserstein GAN (WGAN) conditioned on the resolved variables to learn thedistribution of subgrid flux tendencies for resolved modes and, thus, representthe effect of unresolved scales. The resulting WGAN is then used in aneffective model to reproduce the statistical features of resolved modes. Wedemonstrate that various stationary statistical quantities such as spectrum,moments, autocorrelation, etc. are well approximated by this effective model.

Subgrid-scale parametrization of unresolved scales in forced Burgers equation using Generative Adversarial Networks (GAN)