Subgrid-Scale Parametrization of Unresolved Scales using Generative Adversarial Networks (GAN)

Stochastic subgrid-scale parametrizations account for the bulk effects of unresolved processes in a reduced model by sampling from a distribution typically described in terms of resolved modes. Recently, potentials in developing effective parametrizations are seen in machine learning approaches. In this study, we evaluate the performance of conditional generative adversarial network (GAN) in parametrizing subgrid-scale effects in a finite-difference flux discretization of stochastically forced Burgers equation. In the model, the resolved modes are local averages while the unresolved variables are the deviations from these averages. We train a Wasserstain GAN to generate subgrid flux tendencies for the resolved modes. The optimized GAN generator is used in an effective model to emulate statistical features of the local averages. It was shown that stationary properties such as moments, autocorrelation, spectrum, etc. are well approximated by this model. Further analysis on the relation between the generated subgrid flux relates and some local properties of resolved modes is also is done.