Deep learning is increasingly becoming a promising pathway to improving the
accuracy of sub-grid scale (SGS) turbulence closure models for large eddy
simulations (LES). We leverage the concept of differentiable turbulence,
whereby an end-to-end differentiable solver is used in combination with
physics-inspired choices of deep learning architectures to learn highly
effective and versatile SGS models for two-dimensional turbulent flow. We
perform an in-depth analysis of the inductive biases in the chosen
architectures, finding that the inclusion of small-scale non-local features is
most critical to effective SGS modeling, while large-scale features can improve
pointwise accuracy of the a-posteriori solution field. The filtered velocity
gradient tensor can be mapped directly to the SGS stress via decomposition of
the inputs and outputs into isotropic, deviatoric, and anti-symmetric
components. We see that the model can generalize to a variety of flow
configurations, including higher and lower Reynolds numbers and different
forcing conditions. We show that the differentiable physics paradigm is more
successful than offline, a-priori learning, and that hybrid solver-in-the-loop
approaches to deep learning offer an ideal balance between computational
efficiency, accuracy, and generalization. Our experiments provide physics-based
recommendations for deep-learning based SGS modeling for generalizable closure
modeling of turbulence.

利用可微分湍流解算器与受物理启发的深度学习架构的组合，学习出极为有效且多功能的二维湍流流动的亚网尺度模型；通过研究所选择的架构的归纳偏差分析，发现包含小尺度非局部特征对于效果良好的亚网尺度建模至关重要，而大尺度特征可以提高后验解场的点位准确性；通过分解输入与输出为各向同性、去除偏差以及反对称分量，将滤波速度梯度张量直接映射到亚网尺度应力。同时，验证模型可应用于多种不同流动配置，包括更高和更低雷诺数以及不同的施加条件。实验证明可微分物理的范例比离线的先验学习更加成功，并且深度学习的混合解算器循环方法在计算效率、准确性和泛化性方面提供了理想的平衡。该研究为基于物理的湍流智能感知方法提供了推荐建议。