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 translate 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. The model learned based upon the wavy wall configuration is then validated against flow over a backward-facing step. This work demonstrates similar performance to that of modern NNs but with the added benefits of interpretability, increased ease of use and dissemination, and robustness to sparse and noisy training data sets.

中文翻译：

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使用稀疏回归和嵌入式形式不变性来制定湍流闭合

提供了一个数据驱动的框架，用于制定雷诺平均Navier-Stokes（RANS）方程的闭包。近年来，科学界已转向使用机器学习技术将数据转换为改进的RANS闭包。虽然该领域的工作主要是利用神经网络（NN），但我们也可以利用稀疏回归框架。该方法具有两个重要特性：（1）所得模型为封闭的代数形式，可以直接进行物理推论，并且可以将其幼稚地集成到现有的计算流体动力学求解器中；（2）通过周到的保证伽利略不变性特征空间的定制。我们的方法针对两类流进行了演示：均质的自由剪切湍流和波状壁上的湍流。然后，根据波浪形墙配置学习的模型是否经过后向步骤进行了验证。这项工作表现出与现代NN相似的性能，但具有可解释性，增​​加的易用性和分发性以及对稀疏和嘈杂的训练数据集的鲁棒性等附加好处。