基于生成对抗网络（GAN）的强迫Burgers方程亚网格尺度参数化
Subgrid-scale parametrization of unresolved scales in forced Burgers equation using Generative Adversarial Networks (GAN)
摘要：
随机子网格尺度参数化的目的是将未解决的过程中的一个有效的模型，从一个分布采样通常描述的解决模式的影响。这是气候、天气和海洋科学中一个活跃的研究领域，其过程在广泛的空间和时间尺度上演变。在这项研究中，我们评估了条件生成对抗网络（GAN）在随机强迫Burgers方程的有限差分离散中参数化亚网格尺度效应的性能。我们将解析模式定义为局部空间平均值，与这些平均值的偏差是未解析的自由度。我们训练一个Wasserstein GAN（WGAN）的解决变量的条件下学习的亚网格通量趋势的分布，解决模式，因此，代表未解决的尺度的影响。由此产生的WGAN，然后在一个有效的模型中使用，以重现解析模式的统计特征。我们证明，各种平稳的统计量，如频谱，矩，自相关等，很好地近似这个有效的模型。
英文摘要：
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.
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