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Evaluation of machine learning algorithms for predictive Reynolds stress transport modeling

预测雷诺应力输运模型的机器学习算法评估

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Abstract

The application of machine learning (ML) algorithms to turbulence modeling has shown promise over the last few years, but their application has been restricted to eddy viscosity based closure approaches. In this article, we discuss the rationale for the application of machine learning with high-fidelity turbulence data to develop models at the level of Reynolds stress transport modeling. Based on these rationales, we compare different machine learning algorithms to determine their efficacy and robustness at modeling the different transport processes in the Reynolds stress transport equations. Those data-driven algorithms include Random forests, gradient boosted trees, and neural networks. The direct numerical simulation (DNS) data for flow in channels are used both as training and testing of the ML models. The optimal hyper-parameters of the ML algorithms are determined using Bayesian optimization. The efficacy of the above-mentioned algorithms is assessed in the modeling and prediction of the terms in the Reynolds stress transport equations. It was observed that all three algorithms predict the turbulence parameters with an acceptable level of accuracy. These ML models are then applied for the prediction of the pressure strain correlation of flow cases that are different from the flows used for training, to assess their robustness and generalizability. This explores the assertion that ML-based data-driven turbulence models can overcome the modeling limitations associated with the traditional turbulence models and ML models trained with large amounts of data with different classes of flows can predict flow field with reasonable accuracy for unknown flows with similar flow physics. In addition to this verification, we carry out validation for the final ML models by assessing the importance of different input features for prediction.

摘要

近年来, 机器学习(ML)算法在湍流建模中的应用显示出了希望, 但它们的应用仅限于基于涡流黏度的封闭方法. 本文讨论了 应用机器学习与高保真湍流数据的基本原理, 以开发雷诺应力传输建模水平的模型. 基于这些理论, 本文比较了不同的机器学习算法, 以确定它们在雷诺应力输运方程中建模不同输运过程的有效性和鲁棒性. 这些数据驱动的算法包括随机森林、梯度增强树和神经网 络. 采用直接数值模拟(DNS)数据作为ML模型的训练和测试, 利用贝叶斯优化方法确定了ML算法的最优超参数. 在雷诺应力输运方程 的建模和预测中, 评估了上述算法的有效性. 观察到三种算法都以可接受的精度水平预测湍流参数. 再将这些模型应用在不同于训练 的流动情况的压力应变相关性的预测, 以评估其鲁棒性和通用性. 这探讨了基于ML的数据驱动湍流模型可以克服传统湍流模型的建 模局限性, 并且ML模型用大量不同类型的流数据训练, 可以对具有相似流物理的未知流以合理的精度预测流场. 除此之外, 本文通过 评估不同输入特征的重要性来验证最终的ML模型.

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Authors and Affiliations

  1. Department of Mechanical Engineering, DIT University, Dehradun, India

    Jyoti Prakash Panda

  2. Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology (IIT), Kharagpur, India

    Hari Vijayan Warrior

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  1. Jyoti Prakash Panda
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Correspondence to Jyoti Prakash Panda.

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Panda, J.P., Warrior, H.V. Evaluation of machine learning algorithms for predictive Reynolds stress transport modeling. Acta Mech. Sin. 38, 321544 (2022). https://doi.org/10.1007/s10409-022-09001-w

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  • DOI: https://doi.org/10.1007/s10409-022-09001-w

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