Cited by 3,063Model Reduction and Neural NetworksMachine Learning in Materials ScienceFluid Dynamics and Turbulent Flows

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Machine Learning for Fluid Mechanics

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Brunton, Steven L., Noack, Bernd R., Koumoutsakos, Petros·2020·Annual Review of Fluid Mechanics

DOI 10.1146/annurev-fluid-010719-060214

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Abstract

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from experiments, field measurements, and large-scale simulations at multiple spatiotemporal scales. Machine learning (ML) offers a wealth of techniques to extract information from data that can be translated into knowledge about the underlying fluid mechanics. Moreover, ML algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of ML for fluid mechanics. We outline fundamental ML methodologies and discuss their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experiments, and simulations. ML provides a powerful information-processing framework that can augment, and possibly even transform, current lines of fluid mechanics research and industrial applications.

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Zambrano, V., Mueller-Roemer, J., Sandberg, M., Talasila, P., Zanin, D., Larsen, P., Loeschner, E., Thronicke, W., Pietraroia, D., Landolfi, G., et al. (2022) · Array · doi:10.1016/j.array.2022.100176 · Cited by 48
“…runtime of simulation models must be close to real-time in a DT setting, so physics-based models are often supplemented with semantic (i.e., ML) [32] or Reduced Order Modeling (ROM) techniques [33,34] to bring down computation time, although the latter technique can be also used to build…”
Method
Explaining the physics of transfer learning in data-driven turbulence modeling
Subel, A., Guan, Y., Chattopadhyay, A., & Hassanzadeh, P. (2023) · PNAS Nexus · doi:10.1093/pnasnexus/pgad015 · Cited by 56
Predicting turbulent dynamics with the convolutional autoencoder echo state network
Racca, A., Doan, N. A. K., & Magri, L. (2023) · Journal of Fluid Mechanics · doi:10.1017/jfm.2023.716 · Cited by 57
Deep reinforcement learning for active flow control in a turbulent separation bubble
Font, B., Alcántara-Ávila, F., Rabault, J., Vinuesa, R., & Lehmkuhl, O. (2025) · Nature Communications · doi:10.1038/s41467-025-56408-6 · Cited by 58
Predicting the near-wall velocity of wall turbulence using a neural network for particle image velocimetry
Wang, H., Yang, Z., Li, B., & Wang, S. (2020) · Physics of Fluids · doi:10.1063/5.0023786 · Cited by 56
Application of Machine Learning to Investigation of Heat and Mass Transfer Over a Cylinder Surrounded by Porous Media—The Radial Basic Function Network
Alizadeh, R., Abad, J. M. N., Fattahi, A., Hajri, E. A., & Karimi, N. (2020) · Journal of Energy Resources Technology · doi:10.1115/1.4047402 · Cited by 55
“Making a comprehensive model from massive amount of data through taking conventional approaches is too complicated and ANN is a novel remedy [31].”
Background
A general Neural Particle Method for hydrodynamics modeling
Bai, J., Zhou, Y. L., Ma, Y., Jeong, H., Zhan, H., Rathnayaka, C., Sauret, E., & Gu, Y. (2022) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2022.114740 · Cited by 59
Deep reinforcement learning for computational fluid dynamics on HPC systems
Kurz, M., Offenhäuser, P., Viola, D., Shcherbakov, O. V., Resch, M., & Beck, A. (2022) · Journal of Computational Science · doi:10.1016/j.jocs.2022.101884 · Cited by 57
“In recent years, there have been increasing efforts to transfer advances in machine learning (ML) to the field of computational fluid dynamics (CFD) in order to enhance simulations for a myriad of different applications [1], which cover the fields of turbulence modeling [2, 3, 4, 5], shock detection [6, 7], the formul…”
Background
SVD perspectives for augmenting DeepONet flexibility and interpretability
Venturi, S., & Casey, T. A. (2022) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2022.115718 · Cited by 67
Super-resolution generative adversarial networks of randomly-seeded fields
Güemes, A., Vila, C. S., & Discetti, S. (2022) · Nature Machine Intelligence · doi:10.1038/s42256-022-00572-7 · Cited by 55
Ultrasound Microrobots with Reinforcement Learning
Schrage, M., Medany, M., & Ahmed, D. (2023) · Advanced Materials Technologies · doi:10.1002/admt.202201702 · Cited by 57
Machine learning in additive manufacturing & Microfluidics for smarter and safer drug delivery systems
Dedeloudi, A., Weaver, E., & Lamprou, D. A. (2023) · International Journal of Pharmaceutics · doi:10.1016/j.ijpharm.2023.122818 · Cited by 58
A Review of Application of Machine Learning in Storm Surge Problems
Qin, Y., Su, C., Chu, D., Zhang, J., & Song, J. (2023) · Journal of Marine Science and Engineering · doi:10.3390/jmse11091729 · Cited by 68
Physics-infused deep neural network for solution of non-associative Drucker–Prager elastoplastic constitutive model
Roy, A. M., Guha, S., Sundararaghavan, V., & Arróyave, R. (2024) · Journal of the Mechanics and Physics of Solids · doi:10.1016/j.jmps.2024.105570 · Cited by 60
Sensing the turbulent large-scale motions with their wall signature
Güemes, A., Discetti, S., & Ianiro, A. (2019) · Physics of Fluids · doi:10.1063/1.5128053 · Cited by 54
Methods in Raman spectroscopy for saliva studies – a review
Hardy, M., Kelleher, L., Gomes, P. D. C., Buchan, E., Chu, H. O., & Oppenheimer, P. G. (2021) · Applied Spectroscopy Reviews · doi:10.1080/05704928.2021.1969944 · Cited by 56
Mesh-Conv: Convolution operator with mesh resolution independence for flow field modeling
Hu, J., & Zhang, W. (2021) · Journal of Computational Physics · doi:10.1016/j.jcp.2021.110896 · Cited by 55
Deep reinforcement learning for large-eddy simulation modeling in wall-bounded turbulence
Kim, J., Kim, H., Kim, J., & Lee, C. (2022) · Physics of Fluids · doi:10.1063/5.0106940 · Cited by 54
“Recently, machine-learning-based models trained using high-fidelity data, mostly DNS, have emerged to address the above issues (see reviews (Kutz 2017; Brenner et al. 2019; Duraisamy et al. 2019; Brunton et al. 2020; Duraisamy 2021)).”
Method
Advancements and challenges of high-speed active flow control: Plasma actuators
Zhang, X., & Li, J. (2025) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2025.127481 · Cited by 54
Memory embedded non-intrusive reduced order modeling of non-ergodic flows
Ahmed, S. E., Rahman, S. M., San, O., Rasheed, A., & Navon, I. M. (2019) · Physics of Fluids · doi:10.1063/1.5128374 · Cited by 51
A Parametric Level Set Method for Topology Optimization Based on Deep Neural Network
Deng, H., & To, A. C. (2021) · Journal of Mechanical Design · doi:10.1115/1.4050105 · Cited by 54
“Based on this concept, several advanced machine learning-based method for solving PDEs [38-41] are proposed recently for forward and inverse PDE-based problems.”
Method
Conditioning and accurate solutions of Reynolds average Navier–Stokes equations with data-driven turbulence closures
Brener, B. P., Cruz, M. A., Thompson, R. L., & Anjos, R. P. (2021) · Journal of Fluid Mechanics · doi:10.1017/jfm.2021.148 · Cited by 54
Real-Time Simulation of Parameter-Dependent Fluid Flows through Deep Learning-Based Reduced Order Models
Fresca, S., & Manzoni, A. (2021) · Fluids · doi:10.3390/fluids6070259 · Cited by 54
“On the other hand, machine learning techniques – in particular, artificial neural networks (NNs) – in computational fluid dynamics have witnessed a dramatic blooming in the past ten years [22, 23].”
Machine Learning Aided Device Simulation of Work Function Fluctuation for Multichannel Gate-All-Around Silicon Nanosheet MOSFETs
Akbar, C., Li, Y., & Sung, W. L. (2021) · IEEE Transactions on Electron Devices · doi:10.1109/ted.2021.3084910 · Cited by 53
Model fusion with physics-guided machine learning: Projection-based reduced-order modeling
Pawar, S. A., San, O., Nair, A., Rasheed, A., & Kvamsdal, T. (2021) · Physics of Fluids · doi:10.1063/5.0053349 · Cited by 57
“Keywords Physics-guided machine learning, Reduced order modeling, Multi-fidelity modeling 1 Introduction Data-driven approaches are emerging as the new paradigm in computational modeling of various problems in different branches of science and engineering, including fluid dynamics [1, 2].”
Background

Authors: Brunton, S. L., Noack, B. R., & Koumoutsakos, P.
Affiliations: University of Washington (US)
Centre National de la Recherche Scientifique (FR)
ETH Zurich (CH)
ORCID: Brunton, Steven L.
Noack, Bernd R.
Koumoutsakos, Petros
Venue: Annual Review of Fluid Mechanics
Publisher: Annual Reviews
Published: 2020-01-05
Volume: 52
Issue: 1
Pages: 477-508
ISSN: 0066-4189 (ISSN-L)
1545-4479
DOI: 10.1146/annurev-fluid-010719-060214
OpenAlex: W2973119841
Semantic Scholar: 4087e84fc695bb6433d0104ee94f9d7e9f4b7da5
Cited by: 3,063
References: 139
Citations by year: 2026: 599 · 2025: 554 · 2024: 539 · 2023: 454 · 2022: 408 · 2021: 330 · 2020: 164
FWCI: 16.11
Type: journal article
Language: en
Open access: green
arxiv.org
Locations: Annual Review of Fluid Mechanics (publishedVersion)
arXiv (Cornell University) (submittedVersion)
HAL (submittedVersion)
arXiv (Cornell University)
Funders: Agence Nationale de la Recherche (ANR-11-IDEX-0003, ANR-17-ASTR-0022)
Centre National de la Recherche Scientifique
Air Force Office of Scientific Research (FA9550-, W911NF-17-1-0422, AFOSR FA9550-18-1-0200, FA9550-18-1-0200)
Army Research Office (W911NF-17-1-0422, W911NF-17-1-0306, W911NF, ARO W911NF-17-1-0306)
Topics: Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Turbulent Flows
Keywords: machine learning, fluid mechanics, data-driven modeling, flow control, flow optimization, large-scale simulation, spatial and temporal scales, scientific machine learning

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