EAGER: Embedded Deep Neural Nets for Predicting Reynolds Stresses in Complex Flows

工程师依赖于在昂贵的实验测试之前对湍流进行计算模拟，以设计汽车、船舶、喷气发动机、风力涡轮机阵列和许多其他流动系统。从概念到解决方案的实际周转时间要求使用近似模型来表示设计过程中的湍流影响。对于实际的全尺寸系统来说，捕捉所有流动细节的直接数值模拟成本太高，而标准的湍流模型无法准确地预测工程系统中普遍存在的复杂的三维流动。当代机器学习算法正在创造一种范式转变，可以从数据中收集到的信息，以及可以有效处理的数据集的规模。该项目的目标是使用一种数据驱动的方法来改进湍流模型，这种方法利用了由流动的直接数值模拟产生的大量数据集。本研究的基本假设是，在雷诺平均的Navier-Stokes程序中实现的机器学习模型能够准确地预测给定平均流场的湍流应力，从而改善模拟结果。该项目将利用深度神经网络开发湍流动能传输方程中各向异性张量和项的改进模型。神经网络将只使用直接的数值模拟数据进行训练，并直接在计算流体动力学解算器中实现，因此预测与任何基线模型中的误差无关：这是对现有基于差异的方法的重大进步。可解释性方法的发展将把神经网络从黑盒工具提升到可靠的模型，在预测和潜在的流结构之间具有更清晰的联系。识别神经网络训练不佳的流动区域的技术将产生健壮的机器学习模型，这些模型不会使计算流体力学预测低于基线模型性能。我们的方法还在基本控制方程中引入了校正项。因此，所学到的经验教训将为任何基于力学的工程学科未来的建模工作提供一个框架。这些模型将使用一些与工业相关的流量的实验数据进行测试，这些流量给传统模型带来了困难。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Engineers rely on computational simulation of turbulent flows prior to costly experimental testing to design automobiles, ships, jet engines, wind turbine arrays, and many other flow systems. Realistic turn-around times from concept to solution requires using approximate models to represent the effects of turbulence in the design process. Direct numerical simulations capturing all details of the flow are too expensive for practical full-scale systems, and standard turbulence models are unable to accurately predict the complex, three-dimensional flows pervasive throughout engineering systems. Contemporary machine learning algorithms are creating a paradigm shift in the information that can be gleaned from data and the scale of the data sets that can be efficiently processed. The goal of this project is to improve turbulence models using a data-driven approach which leverages the massive data sets produced by direct numerical simulation of the flows. The fundamental hypothesis of this research is that a machine learning model which accurately predicts the turbulent stresses for a given mean flow field will improve simulation results when implemented in a Reynolds-Averaged Navier-Stokes code. This project will develop improved models for the anisotropy tensor and terms in the turbulent kinetic energy transport equation using deep neural networks. Neural networks will be trained using only direct numerical simulation data and implemented directly in a computational fluid dynamics solver so that the predictions are independent of errors in any baseline model: a substantial advancement over existing discrepancy-based methods. Development of interpretability methods will elevate neural networks from black box tools to trustable models with clearer links between predictions and the underlying flow structures. Techniques for identifying flow regions where the neural net is poorly trained will produce robust machine-learned models that do not degrade computational fluid dynamics predictions below baseline model performance. Our approach also introduces corrective terms into the basic governing equations. Therefore, the lessons learned will provide a framework for future modeling work in any mechanics-based engineering discipline. The models will be tested using experimental data for a number of industrially relevant flows that have caused difficulty for conventional models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.