We develop a novel data-driven approach to modeling the atmospheric boundary layer. This approach leads to a nonlocal, anisotropic synthetic turbulence model which we refer to as the deep rapid distortion (DRD) model. Our approach relies on an operator regression problem which characterizes the best fitting candidate in a general family of nonlocal covariance kernels parameterized in part by a neural network. This family of covariance kernels is expressed in Fourier space and is obtained from approximate solutions to the Navier--Stokes equations at very high Reynolds numbers. Each member of the family incorporates important physical properties such as mass conservation and a realistic energy cascade. The DRD model can be calibrated with noisy data from field experiments. After calibration, the model can be used to generate synthetic turbulent velocity fields. To this end, we provide a new numerical method based on domain decomposition which delivers scalable, memory-efficient turbulence generation with the DRD model as well as others. We demonstrate the robustness of our approach with both filtered and noisy data coming from the 1968 Air Force Cambridge Research Laboratory Kansas experiments. Using this data, we witness exceptional accuracy with the DRD model, especially when compared to the International Electrotechnical Commission standard.

翻译：我们开发了一种新型的数据驱动方法来模拟大气边界层。 这种方法导致一种非本地的、 异常的合成合成气流模型, 我们称之为深度快速扭曲( DRD) 模型。 我们的方法依赖于操作者回归问题, 它将非本地共变内核整体中最合适的候选者定性为由神经网络部分参数化的非本地共变内核。 这个共变内核的组合在 Fourier 空间中表现, 是从对导航- Stokes 方程式的近似解决方案中获得的, 以非常高的 Reynolds 数字表示。 每个家庭成员都包含重要的物理特性, 如质量保护和现实的能源级等。 DRD 模型可以用来自实地实验的噪音数据校准。 校准后, 该模型可用于生成合成的动荡速度字段。 为此, 我们提供了一个基于域分解定位的新的数字方法, 通过DRD模型和其他模型产生可缩缩放、记忆高效的波动。 我们用1968年空军剑桥研究实验室实验室的过滤和紧凑数据展示了我们的方法的稳健健性, 将这一数据与特殊的D- 技术实验室实验室实验室的精确性加以比较。