数据驱动湍流模型的先验筛选
A priori screening of data-enabled turbulence models
AI总结：
本文提出一种基于数学定理的先验筛选方法，用于快速评估前馈神经网络湍流模型是否符合已知湍流物理规律，并验证其高雷诺数极限行为。
摘要：
评估白箱湍流模型是否符合已知的湍流知识是直接的。这使得用户能够筛选常规湍流模型并识别明显的不足，从而允许进行更有针对性和富有成效的验证与确认。然而，将黑箱机器学习模型与已知的经验标度进行比较并不直接。除非实现并测试模型，否则不清楚在有限雷诺数下训练的机器学习模型是否保留了已知的高雷诺数极限。这很不方便，特别是因为模型实现涉及重新训练和重新接口。本工作试图解决这一问题，允许对基于前馈神经网络（FNN）的机器学习模型进行快速的先验筛选。该方法利用了本文中提出的数学定理。这些定理即使在网络的确切权重和偏差未知的情况下，也能提供网络极限的估计。为演示目的，我们以先验方式筛选现有的机器学习壁面模型和RANS模型，检查它们是否符合对数层物理和粘性层物理。此外，这些定理为未来的机器学习模型提供了必要的指导方针。
英文摘要：
Assessing the compliance of a white-box turbulence model with known turbulent knowledge is straightforward. It enables users to screen conventional turbulence models and identify apparent inadequacies, thereby allowing for a more focused and fruitful validation and verification. However, comparing a black-box machine-learning model to known empirical scalings is not straightforward. Unless one implements and tests the model, it would not be clear if a machine-learning model, trained at finite Reynolds numbers preserves the known high Reynolds number limit. This is inconvenient, particularly because model implementation involves retraining and re-interfacing. This work attempts to address this issue, allowing fast a priori screening of machine-learning models that are based on feed-forward neural networks (FNN). The method leverages the mathematical theorems we present in the paper. These theorems offer estimates of a network's limits even when the exact weights and biases are unknown. For demonstration purposes, we screen existing machine-learning wall models and RANS models for their compliance with the log layer physics and the viscous layer physics in a priori manner. In addition, the theorems serve as essential guidelines for future machine-learning models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
