论文标题
使用生成对抗网络（GAN）在强制汉堡方程中未分辨量表的亚网格尺度参数化
Subgrid-scale parametrization of unresolved scales in forced Burgers equation using Generative Adversarial Networks (GAN)
论文作者
论文摘要
随机亚网格尺度参数化旨在通过从通常用解决模式描述的分布中采样，将未解决过程的效果纳入有效模型中。这是气候，天气和海洋科学中的一个活跃研究领域，在该领域中，过程以各种空间和时间尺度进化。在这项研究中，我们评估了有条件的生成对抗网络（GAN）在参数化亚网格规模效应中的性能，以随机强制汉堡方程的有限差异化离散化。我们将解决的模式定义为局部空间平均值，与这些平均值的偏差是未解决的自由度。我们训练一个以分辨变量为条件的WASSERSTEIN GAN（WGAN），以了解解决模式的亚网格通量趋势的分布，因此代表了未解决的量表的效果。然后将所得的wgan用于有效模型中，以重现已解决模式的统计特征。我们证明，这种有效模型近似于光谱，矩，自相关等各种固定统计量。
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.
