Differentiable fluid simulators are increasingly demonstrating value as
useful tools for developing data-driven models in computational fluid dynamics
(CFD). Differentiable turbulence, or the end-to-end training of machine
learning (ML) models embedded in CFD solution algorithms, captures both the
generalization power and limited upfront cost of physics-based simulations, and
the flexibility and automated training of deep learning methods. We develop a
framework for integrating deep learning models into a generic finite element
numerical scheme for solving the Navier-Stokes equations, applying the
technique to learn a sub-grid scale closure using a multi-scale graph neural
network. We demonstrate the method on several realizations of flow over a
backwards-facing step, testing on both unseen Reynolds numbers and new
geometry. We show that the learned closure can achieve accuracy comparable to
traditional large eddy simulation on a finer grid that amounts to an equivalent
speedup of 10x. As the desire and need for cheaper CFD simulations grows, we
see hybrid physics-ML methods as a path forward to be exploited in the near
future.

利用可微流体模拟器和深度学习模型，开发了一种将深度学习模型整合到通用有限元数值方案中以求解 Naiver-Stokes 方程的框架，进而实现对子网尺度闭包的学习，该方法在流过倒角阶梯的多个实现中展示了与传统的大涡模拟相当的准确性，并且在相当于 10 倍速度提升的更细网格上进行测试。

可微湍流 II

Differentiable Turbulence II

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。