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Reliably predictive simulation of complex flows requires a level of model sophistication and robustness exceeding the capabilities of current Reynolds-averaged Navier-Stokes (RANS) models. The necessary capability can often be provided by…

Fluid Dynamics · Physics 2022-01-20 Sigfried W. Haering , Todd A. Oliver , Robert D. Moser

Reynolds-Averaged Navier-Stokes(RANS) method will still play a vital role in the following several decade in aerospace engineering. Although RANS models are widely used, empiricism and large discrepancies between models reduce the…

Fluid Dynamics · Physics 2018-07-05 Weiwei Zhang , Linyang Zhu , Yilang Liu , Jiaqing Kou

The development of a reliable subgrid-scale (SGS) model for large-eddy simulation (LES) is of great importance for many scientific and engineering applications. Recently, deep learning approaches have been tested for this purpose using…

Fluid Dynamics · Physics 2022-11-09 Junhyuk Kim , Hyojin Kim , Jiyeon Kim , Changhoon Lee

Symbolic regression (SR) has emerged as a powerful method for uncovering interpretable mathematical relationships from data, offering a novel route to both scientific discovery and efficient empirical modelling. This article introduces the…

Machine Learning · Computer Science 2026-04-10 Deaglan J. Bartlett , Harry Desmond , Pedro G. Ferreira , Gabriel Kronberger

Reynolds-Averaged Navier-Stokes (RANS) models are widely used for turbulent flow simulations due to their computational efficiency, but their accuracy strongly depends on the selected turbulence closure and may vary across the flow domain.…

Numerical Analysis · Mathematics 2026-03-18 Piero Zappi , Anna Ivagnes , Niccolò Tonicello , Gianluigi Rozza

We introduce an Invertible Symbolic Regression (ISR) method. It is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps (or architectures). The proposed ISR…

Machine Learning · Computer Science 2024-05-14 Tony Tohme , Mohammad Javad Khojasteh , Mohsen Sadr , Florian Meyer , Kamal Youcef-Toumi

This work presents a review and perspectives on recent developments in the use of machine learning (ML) to augment Reynolds-averaged Navier--Stokes (RANS) and Large Eddy Simulation (LES) models of turbulent flows. Different approaches of…

Fluid Dynamics · Physics 2021-05-19 Karthik Duraisamy

This proposed work introduces a data-assimilation-assisted approach to train neural networks, aimed at effectively reducing epistemic uncertainty in state estimates of separated flows. This method, referred to as model-consistent training,…

Fluid Dynamics · Physics 2024-08-02 Minghan Chu

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…

Fluid Dynamics · Physics 2025-03-05 Mourad Oulghelou , Soufiane Cherroud , Xavier Merle , Paola Cinnella

Deep learning is increasingly becoming a promising pathway to improving the accuracy of sub-grid scale (SGS) turbulence closure models for large eddy simulations (LES). We leverage the concept of differentiable turbulence, whereby an…

A data-driven framework for formulation of closures of the Reynolds-Average Navier--Stokes (RANS) equations is presented. In recent years, the scientific community has turned to machine learning techniques to distill a wealth of highly…

Fluid Dynamics · Physics 2020-09-02 S. Beetham , J. Capecelatro

Accurately modeling wind turbine wakes is essential for optimizing wind farm performance but remains a persistent challenge. While the dynamic wake meandering (DWM) model captures unsteady wake behavior, it suffers from near-wake…

Fluid Dynamics · Physics 2025-06-18 Ding Wang , Dachuan Feng , Kangcheng Zhou , Yuntian Chen , Shijun Liao , Shiyi Chen

To develop a more convenient subgrid-scale (SGS) model that performs well even in coarse grid cases, we investigate the transport and modeling of SGS turbulent kinetic energy (hereafter SGS energy) in turbulent channel flows based on the…

Fluid Dynamics · Physics 2024-06-12 Kazuhiro Inagaki , Hiromichi Kobayashi

Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face…

Machine Learning · Computer Science 2024-07-11 Xieting Chu , Hongjue Zhao , Enze Xu , Hairong Qi , Minghan Chen , Huajie Shao

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…

Fluid Dynamics · Physics 2025-05-12 Chutian Wu , Xin-Lei Zhang , Duo Xu , Guowei He

Simulation of turbulent flows at high Reynolds number is a computationally challenging task relevant to a large number of engineering and scientific applications in diverse fields such as climate science, aerodynamics, and combustion.…

Computational Physics · Physics 2020-10-06 Jaideep Pathak , Mustafa Mustafa , Karthik Kashinath , Emmanuel Motheau , Thorsten Kurth , Marcus Day

The objective of this work is to investigate the challenges encountered in Scale-Resolving Simulations (SRS's) of turbulent wake flows driven by spatially-developing coherent structures. SRS's of practical interest are expressly intended…

Fluid Dynamics · Physics 2018-01-16 F. S. Pereira , L. Eca , G. Vaz , S. S. Girimaji

In recent years, machine learning methods represented by deep neural networks (DNN) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of…

Fluid Dynamics · Physics 2022-11-02 Z. Y. Wang , W. W. Zhang

This work proposes a novel methodology for turbulence modeling in Large Eddy Simulation (LES) based on Graph Neural Networks (GNNs), which embeds the discrete rotational, reflectional and translational symmetries of the Navier-Stokes…

Fluid Dynamics · Physics 2025-04-11 Marius Kurz , Andrea Beck , Benjamin Sanderse

In the realm of machine and deep learning regression tasks, the role of effective feature engineering (FE) is pivotal in enhancing model performance. Traditional approaches of FE often rely on domain expertise to manually design features…

Machine Learning · Computer Science 2024-06-18 Assaf Shmuel , Oren Glickman , Teddy Lazebnik