{"title":"数据驱动湍流模型的机器学习辅助混合","authors":"Mourad Oulghelou, Soufiane Cherroud, Xavier Merle, Paola Cinnella","doi":"10.1007/s10494-025-00661-8","DOIUrl":null,"url":null,"abstract":"<div><p>We present a machine learning–based framework for blending data-driven turbulent closures in the Reynolds-Averaged Navier–Stokes (RANS) equations, aimed at improving their generalizability across diverse flow regimes. Specialized models (hereafter referred to as “<i>experts</i>”) are trained via sparse Bayesian learning and symbolic regression for distinct flow classes, including turbulent channel flows, separated flows, and a near sonic axisymmetric jet. These experts are then combined <i>intrusively</i> within the RANS equations using weighting functions, initially derived via a Gaussian kernel on a dataset spanning equilibrium shear conditions to separated flows. Finally, a Random Forest Regressor is trained to map local physical features to these weighting functions, enabling deployment in previously unseen scenarios. We evaluate the resulting blended model on three representative test cases: a turbulent zero-pressure-gradient flat plate, a wall-mounted hump, and a NACA0012 airfoil at various angles of attack, ranging from fully attached to near-stall conditions. Results for these 2D flows show that the proposed strategy adapts to local flow characteristics, effectively leveraging the strengths of individual models and consistently selecting the most suitable expert in each region. Notably, the blended model also demonstrates robustness for flow configurations not included in the training set, underscoring its potential as a practical and generalizable framework for RANS turbulence modeling.</p></div>","PeriodicalId":559,"journal":{"name":"Flow, Turbulence and Combustion","volume":"115 :","pages":"1095 - 1132"},"PeriodicalIF":2.4000,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Machine-Learning-Assisted Blending of Data-Driven Turbulence Models\",\"authors\":\"Mourad Oulghelou, Soufiane Cherroud, Xavier Merle, Paola Cinnella\",\"doi\":\"10.1007/s10494-025-00661-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present a machine learning–based framework for blending data-driven turbulent closures in the Reynolds-Averaged Navier–Stokes (RANS) equations, aimed at improving their generalizability across diverse flow regimes. Specialized models (hereafter referred to as “<i>experts</i>”) are trained via sparse Bayesian learning and symbolic regression for distinct flow classes, including turbulent channel flows, separated flows, and a near sonic axisymmetric jet. These experts are then combined <i>intrusively</i> within the RANS equations using weighting functions, initially derived via a Gaussian kernel on a dataset spanning equilibrium shear conditions to separated flows. Finally, a Random Forest Regressor is trained to map local physical features to these weighting functions, enabling deployment in previously unseen scenarios. We evaluate the resulting blended model on three representative test cases: a turbulent zero-pressure-gradient flat plate, a wall-mounted hump, and a NACA0012 airfoil at various angles of attack, ranging from fully attached to near-stall conditions. Results for these 2D flows show that the proposed strategy adapts to local flow characteristics, effectively leveraging the strengths of individual models and consistently selecting the most suitable expert in each region. Notably, the blended model also demonstrates robustness for flow configurations not included in the training set, underscoring its potential as a practical and generalizable framework for RANS turbulence modeling.</p></div>\",\"PeriodicalId\":559,\"journal\":{\"name\":\"Flow, Turbulence and Combustion\",\"volume\":\"115 :\",\"pages\":\"1095 - 1132\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2025-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Flow, Turbulence and Combustion\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10494-025-00661-8\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Flow, Turbulence and Combustion","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10494-025-00661-8","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
摘要
我们提出了一个基于机器学习的框架,用于在reynolds - average Navier-Stokes (RANS)方程中混合数据驱动的湍流闭包,旨在提高它们在不同流动状态下的可泛化性。专门的模型(以下称为“专家”)通过稀疏贝叶斯学习和符号回归来训练不同的流动类别,包括湍流通道流动,分离流动和近音速轴对称射流。然后使用加权函数将这些专家组合到RANS方程中,这些权重函数最初是通过跨越平衡剪切条件到分离流的数据集上的高斯核得到的。最后,训练随机森林回归器将局部物理特征映射到这些加权函数,从而实现在以前未见过的场景中部署。我们在三个有代表性的测试案例上评估了混合模型:湍流零压力梯度平板,壁挂式驼峰和NACA0012翼型在不同攻角下,从完全附着到接近失速状态。二维流的结果表明,所提出的策略适应了局部流的特征,有效地利用了各个模型的优势,并始终在每个区域选择最合适的专家。值得注意的是,混合模型还展示了对未包含在训练集中的流动配置的鲁棒性,强调了其作为RANS湍流建模的实用和可推广框架的潜力。
Machine-Learning-Assisted Blending of Data-Driven Turbulence Models
We present a machine learning–based framework for blending data-driven turbulent closures in the Reynolds-Averaged Navier–Stokes (RANS) equations, aimed at improving their generalizability across diverse flow regimes. Specialized models (hereafter referred to as “experts”) are trained via sparse Bayesian learning and symbolic regression for distinct flow classes, including turbulent channel flows, separated flows, and a near sonic axisymmetric jet. These experts are then combined intrusively within the RANS equations using weighting functions, initially derived via a Gaussian kernel on a dataset spanning equilibrium shear conditions to separated flows. Finally, a Random Forest Regressor is trained to map local physical features to these weighting functions, enabling deployment in previously unseen scenarios. We evaluate the resulting blended model on three representative test cases: a turbulent zero-pressure-gradient flat plate, a wall-mounted hump, and a NACA0012 airfoil at various angles of attack, ranging from fully attached to near-stall conditions. Results for these 2D flows show that the proposed strategy adapts to local flow characteristics, effectively leveraging the strengths of individual models and consistently selecting the most suitable expert in each region. Notably, the blended model also demonstrates robustness for flow configurations not included in the training set, underscoring its potential as a practical and generalizable framework for RANS turbulence modeling.
期刊介绍:
Flow, Turbulence and Combustion provides a global forum for the publication of original and innovative research results that contribute to the solution of fundamental and applied problems encountered in single-phase, multi-phase and reacting flows, in both idealized and real systems. The scope of coverage encompasses topics in fluid dynamics, scalar transport, multi-physics interactions and flow control. From time to time the journal publishes Special or Theme Issues featuring invited articles.
Contributions may report research that falls within the broad spectrum of analytical, computational and experimental methods. This includes research conducted in academia, industry and a variety of environmental and geophysical sectors. Turbulence, transition and associated phenomena are expected to play a significant role in the majority of studies reported, although non-turbulent flows, typical of those in micro-devices, would be regarded as falling within the scope covered. The emphasis is on originality, timeliness, quality and thematic fit, as exemplified by the title of the journal and the qualifications described above. Relevance to real-world problems and industrial applications are regarded as strengths.