论文标题
深层结构化神经网络，用于湍流闭合建模
Deep Structured Neural Networks for Turbulence Closure Modelling
论文作者
论文摘要
尽管由于计算效率，尽管雷诺（Reynolds）平均的Navier-Stokes（RANS）模拟存在众所周知的局限性，但由于计算效率，该方法仍然是预测许多湍流的工具。机器学习是提高命令模拟准确性的一种有前途的方法。改进的一个主要领域是使用机器学习模型来代表平均流场梯度与雷诺强调张量之间的复杂关系。在目前的工作中，提出并评估了改善先前最佳涡流粘度方法的稳定性的修改和评估。最佳的涡流粘度通过非负约束重新制定，从而促进数值稳定性。我们证明，最佳涡流粘度的新配方可改善对周期性山丘测试案例的RANS方程的调节。 To demonstrate the suitability of this proportional/orthogonal tensor decomposition for use in a physics-informed data-driven turbulence closure, we use two neural networks (structured on this specific tensor decomposition which is incorporated as an inductive bias into the network design) to predict the newly reformulated linear and non-linear parts of the Reynolds stress tensor.将这些网络模型的预测注入雷诺，即使与基于物理物理的湍流闭合模型相比，即使相比，即使相比，即使在速度场中，也会改善对速度场的预测。最后，我们应用Shap（Shapley添加说明）值，以从学习的表示形式中获取有关神经网络的内部功能的见解，该神经网络用于预测输入特征数据的最佳涡流粘度。
Despite well-known limitations of Reynolds-averaged Navier-Stokes (RANS) simulations, this methodology remains the most widely used tool for predicting many turbulent flows, due to computational efficiency. Machine learning is a promising approach to improve the accuracy of RANS simulations. One major area of improvement is using machine learning models to represent the complex relationship between the mean flow field gradients and the Reynolds stress tensor. In the present work, modifications to improve the stability of previous optimal eddy viscosity approaches for RANS simulations are presented and evaluated. The optimal eddy viscosity is reformulated with a non-negativity constraint, which promotes numerical stability. We demonstrate that the new formulation of the optimal eddy viscosity improves the conditioning of the RANS equations for a periodic hills test case. To demonstrate the suitability of this proportional/orthogonal tensor decomposition for use in a physics-informed data-driven turbulence closure, we use two neural networks (structured on this specific tensor decomposition which is incorporated as an inductive bias into the network design) to predict the newly reformulated linear and non-linear parts of the Reynolds stress tensor. Injecting these network model predictions for the Reynolds stresses into a RANS simulation improves predictions of the velocity field, even when compared to a sophisticated (state of the art) physics-based turbulence closure model. Finally, we apply SHAP (SHapley Additive exPlanations) values to obtain insights from the learned representation for the inner workings of the neural network used to predict the optimal eddy viscosity from the input feature data.
