论文标题
使用嵌入式形式不变性的稀疏回归制定湍流封闭
Formulating turbulence closures using sparse regression with embedded form invariance
论文作者
论文摘要
提出了一个数据驱动的框架，用于介绍雷诺平均Navier（RANS）方程的封闭框架。近年来，科学界已转向机器学习技术，以将大量高度解决的数据提炼成改进的收入。虽然该领域的工作主体主要利用神经网络（NNS），但我们交替利用稀疏的回归框架。该方法具有两个重要属性：（1）所得模型以封闭的代数形式为封闭的代数形式，可以绘制直接的物理推断，并将其幼稚地集成到现有的计算流体动力学求解器中，并且（2）Galilean不变性可以通过对特征空间进行周到的量身定制来保证。我们的两类流量展示了我们的方法：均匀的自由剪切湍流和波浪壁上的湍流。这项工作证明了与现代NN的相同性能，但具有可解释性的额外好处，提高的易用性和传播以及对稀疏培训数据集的鲁棒性。
A data-driven framework for formulation of closures of the Reynolds-Average Navier--Stokes (RANS) equations is presented. In recent years, the scientific community has turned to machine learning techniques to distill a wealth of highly resolved data into improved RANS closures. While the body of work in this area has primarily leveraged Neural Networks (NNs), we alternately leverage a sparse regression framework. This methodology has two important properties: (1) The resultant model is in a closed, algebraic form, allowing for direct physical inferences to be drawn and naive integration into existing computational fluid dynamics solvers, and (2) Galilean invariance can be guaranteed by thoughtful tailoring of the feature space. Our approach is demonstrated for two classes of flows: homogeneous free shear turbulence and turbulent flow over a wavy wall. This work demonstrates equivalent performance to that of modern NNs but with the added benefits of interpretability, increased ease-of-use and dissemination, and robustness to sparse training datasets.
