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.

翻译：深度学习正逐渐成为提升大涡模拟（LES）中亚网格尺度（SGS）湍流闭合模型精度的有前景途径。我们利用可微分湍流的概念，将端到端可微分求解器与受物理启发的深度学习架构选择相结合，以学习高效且通用的二维湍流SGS模型。我们对所选架构中的归纳偏置进行了深入分析，发现纳入小尺度非局部特征对于有效的SGS建模最为关键，而大尺度特征则可提升后验解场的逐点精度。通过将输入和输出分解为各向同性、偏斜和反对称分量，滤波速度梯度张量可直接映射到SGS应力。我们观察到该模型能够泛化到多种流动构型，包括更高和更低雷诺数及不同强迫条件。研究证明，可微分物理范式比离线先验学习更为成功，而混合求解器在环深度学习方法则在计算效率、精度和泛化性之间实现了理想平衡。我们的实验为基于物理的深度学习SGS建模提供了建议，以实现可泛化的湍流闭合建模。