Title: A framework for learning symbolic turbulence models from indirect observation data via neural networks and feature importance analysis Show Chinese title

Title: 基于神经网络和特征重要性分析从间接观测数据学习符号湍流模型的框架

Abstract: Learning symbolic turbulence models from indirect observation data is of significant interest as it not only improves the accuracy of posterior prediction but also provides explicit model formulations with good interpretability. However, it typically resorts to gradient-free evolutionary algorithms, which can be relatively inefficient compared to gradient-based approaches, particularly when the Reynolds-averaged Navier-Stokes (RANS) simulations are involved in the training process. In view of this difficulty, we propose a framework that uses neural networks and the associated feature importance analysis to improve the efficiency of symbolic turbulence modeling. In doing so, the gradient-based method can be used to efficiently learn neural network-based representations of Reynolds stress from indirect data, which is further transformed into simplified mathematical expressions with symbolic regression. Moreover, feature importance analysis is introduced to accelerate the convergence of symbolic regression by excluding insignificant input features. The proposed training strategy is tested in the flow in a square duct, where it correctly learns underlying analytic models from indirect velocity data. Further, the method is applied in the flow over the periodic hills, demonstrating that the feature importance analysis can significantly improve the training efficiency and learn symbolic turbulence models with satisfactory generalizability. Show Chinese abstract

Abstract: 从间接观测数据学习符号湍流模型具有重要意义，因为它不仅能提高后验预测的准确性，还能提供具有良好可解释性的显式模型表达。 然而，它通常依赖于无梯度的进化算法，与基于梯度的方法相比，特别是在雷诺平均纳维-斯托克斯（RANS）仿真参与训练过程时，可能相对低效。 鉴于这一困难，我们提出了一种使用神经网络和相关特征重要性分析来提高符号湍流建模效率的框架。 通过这种方法，可以高效地使用基于梯度的方法从间接数据中学习基于神经网络的雷诺应力表示，然后将其进一步转化为简化后的数学表达式进行符号回归。 此外，引入特征重要性分析通过排除不显著的输入特征来加速符号回归的收敛。 所提出的训练策略在方形管道流动中进行了测试，在该流动中它能够正确地从间接速度数据中学习到潜在的解析模型。 进一步地，该方法被应用于周期丘陵上的流动，表明特征重要性分析可以显著提高训练效率，并学习到具有满意泛化能力的符号湍流模型。