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.

翻译：可微流体模拟器作为计算流体力学（CFD）中数据驱动模型开发的有用工具，其价值日益凸显。可微湍流，即将机器学习（ML）模型嵌入CFD求解算法中进行端到端训练，既保留了基于物理模拟的泛化能力和有限的初始成本，又兼顾了深度学习方法的灵活性和自动化训练特性。我们开发了一个将深度学习模型集成到求解Navier-Stokes方程的通用有限元数值方案中的框架，并应用该技术通过多尺度图神经网络学习亚网格尺度闭合模型。我们在多个后向台阶流动实现上验证了该方法，并在未见过的雷诺数和新几何结构上进行了测试。结果表明，与在更精细网格上进行的传统大涡模拟相比，所学到的闭合模型能够达到相当的精度，相当于实现了10倍的等效加速。随着对更廉价CFD模拟的需求日益增长，我们认为混合物理-ML方法是一条有望在不久的将来被利用的前进道路。