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

TL;DR

This paper explores the use of Wasserstein GANs to model subgrid-scale effects in a forced Burgers equation, effectively capturing statistical properties of unresolved scales in a stochastic fluid dynamics setting.

Contribution

It introduces a novel application of conditional Wasserstein GANs for subgrid-scale parametrization in a stochastic Burgers equation, demonstrating accurate statistical reproduction.

Findings

WGAN effectively models subgrid flux tendencies.

Statistical features like spectrum and moments are well reproduced.

The approach improves subgrid-scale representation in simplified fluid models.

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 climate, weather and ocean science where processes evolved in a wide range of spatial and temporal scales. 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 define resolved modes as local spatial averages and deviations from these averages are the unresolved degrees of freedom. We train a Wasserstein GAN (WGAN) conditioned on the resolved variables to learn the distribution of subgrid flux tendencies for resolved modes 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, autocorrelation, etc. are well approximated by this effective model.