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Machine Learning for Fluid Mechanics
Open accessAbstract
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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“However, since Hinton proposed the deep belief networks (DBN) in 2006 [90], the deep network-based method has accomplished significant achievements in various sectors [91,92,93,94].”
From Semantic Terrain Segmentation in the Navigation Vision of Planetary Rovers—A Systematic Literature Review (2022) · cites this paper as [92]
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“…unit (GPU) capability, accompanied by the enormous amounts of high-fidelity data generated from experimental and numerical simulations, encourage exploring new data-driven approaches that can efficiently tackle various fluid-flow problems (Brunton et al. 2020; Kutz 2017; Vinuesa & Brunton 2021).”
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BackgroundMethodCluster-based network modeling—From snapshots to complex dynamical systems
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BackgroundMethodYu, L., Yousif, M. Z., Zhang, M., Hoyas, S., Vinuesa, R., & Lim, H.-C. (2022) · Physics of Fluids · doi:10.1063/5.0129203 · Cited by 81
A review of graph neural network applications in mechanics-related domains
Zhao, Y., Li, H., Zhou, H., Attar, H. R., Pfaff, T., & Li, N. (2024) · Artificial Intelligence Review · doi:10.1007/s10462-024-10931-y · Cited by 91
“Over the past several decades, artificial neural network (ANN) models have seen widespread adoption across various mechanics-related domains, including solid mechanics (Kumar and Kochmann 2022), fluid mechanics (Brunton et al. 2020), and interdisciplinary domains (Guo et al. 2022).”
Exploration and prediction of fluid dynamical systems using auto-encoder technology
Agostini, L. M. (2020) · Physics of Fluids · doi:10.1063/5.0012906 · Cited by 88
Airfoil design and surrogate modeling for performance prediction based on deep learning method
Du, Q., Liu, T., Yang, L., Li, L., Zhang, D., & Xie, Y. (2022) · Physics of Fluids · doi:10.1063/5.0075784 · Cited by 80
Applications of Machine Learning to Wind Engineering
Wu, T., & Snaiki, R. (2022) · Frontiers in Built Environment · doi:10.3389/fbuil.2022.811460 · Cited by 84
“There is a long and signi fi cant history for machine learning (ML) applications in several sub fi elds involved in wind engineering, such as fl uid mechanics (Brunton et al., 2020), meteorology (Chen et al., 2020) and mechanics of structures (Salehi and Burgueño 2018).”
BackgroundEmbedding data analytics and CFD into the digital twin concept
Molinaro, R., Singh, J.-S., Catsoulis, S., Narayanan, C., & Lakehal, D. (2020) · Computers & Fluids · doi:10.1016/j.compfluid.2020.104759 · Cited by 79
Learning hydrodynamic equations for active matter from particle simulations and experiments
Supekar, R., Song, B., Hastewell, A., Choi, G. P. T., Mietke, A., & Dunkel, J. (2023) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2206994120 · Cited by 88
Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics
Racca, A., & Magri, L. (2021) · Neural Networks · doi:10.1016/j.neunet.2021.05.004 · Cited by 78
“Examples of successful applications span from speech recognition [16], through language translation [17], fluids [18, 19, 20, 21, 22], to thermo-acoustic oscillations [23], among many others.”
BackgroundWall model based on neural networks for LES of turbulent flows over periodic hills
Zhou, Z., He, G., & Yang, X. (2021) · Physical Review Fluids · doi:10.1103/physrevfluids.6.054610 · Cited by 79
Zhu, Y. F., Tian, F.-B., Young, J., Liao, J. C., & Lai, J. C. S. (2021) · Scientific Reports · doi:10.1038/s41598-021-81124-8 · Cited by 78
Physics-guided deep learning for generating turbulent inflow conditions
Yousif, M. Z., Yu, L., & Lim, H.-C. (2022) · Journal of Fluid Mechanics · doi:10.1017/jfm.2022.61 · Cited by 84
A deep learning framework for solution and discovery in solid mechanicsPreprint
Haghighat, E., Raissi, M., Moure, A., Gómez, H., & Juanes, R. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2003.02751 · Cited by 76
“In engineering and science, ANNs have been applied to an increasing number of areas, including geosciences [4, 5, 6, 7, 8], material science [9, 10, 11, 12], fluid mechanics [13, 14], genetics [15], and infrastructure health monitoring [16, 17], to name a few examples.”
BackgroundSingle-step deep reinforcement learning for open-loop control of laminar and turbulent flows
Ghraieb, H., Viquerat, J., Larcher, A., Méliga, P., & Hachem, E. (2021) · Physical Review Fluids · doi:10.1103/physrevfluids.6.053902 · Cited by 82
Borah, S., Sarma, B., Kewming, M. J., Milburn, G. J., & Twamley, J. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.190403 · Cited by 85
Information-theoretic formulation of dynamical systems: Causality, modeling, and control
Lozano-Durán, A., & Arranz, G. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023195 · Cited by 77
“Machine learning also provides a modular and agile framework that can be tailored to address reduced-order modeling (Duraisamy et al., 2019; Brunton et al., 2020).”
Subel, A., Chattopadhyay, A., Guan, Y., & Hassanzadeh, P. (2021) · Physics of Fluids · doi:10.1063/5.0040286 · Cited by 76
Buzzicotti, M., Bonaccorso, F., Leoni, P. C. D., & Biferale, L. (2021) · Physical Review Fluids · doi:10.1103/physrevfluids.6.050503 · Cited by 78
“[32] Steven L Brunton, Bernd R Noack, and Petros Koumoutsakos.”
BackgroundData-driven cardiovascular flow modelling: examples and opportunities
Arzani, A., & Dawson, S. T. M. (2021) · Journal of The Royal Society Interface · doi:10.1098/rsif.2020.0802 · Cited by 76
“Additionally, lack of interpretability is a shortcoming of current deep learning techniques, which is an important issue in fluid mechanics where we are often interested in the flow physics [14].”
BackgroundA generative deep learning framework for airfoil flow field prediction with sparse data
Wu, H., Liu, X., An, W., & Lyu, H. (2021) · Chinese Journal of Aeronautics · doi:10.1016/j.cja.2021.02.012 · Cited by 75
Li, K., Kou, J., & Zhang, W. (2022) · AIAA Journal · doi:10.2514/1.j061330 · Cited by 75
“Moreover, ML algorithms also provide a critical tool in the fluid mechanics research [41].”
BackgroundMethodFourier neural operator approach to large eddy simulation of three-dimensional turbulence
Li, Z., Peng, W., Yuan, Z., & Wang, J. (2022) · Theoretical and Applied Mechanics Letters · doi:10.1016/j.taml.2022.100389 · Cited by 75
Long-term predictions of turbulence by implicit U-Net enhanced Fourier neural operator
Li, Z., Peng, W., Yuan, Z., & Wang, J. (2023) · Physics of Fluids · doi:10.1063/5.0158830 · Cited by 85
Cheng, C.-D., Tian, B., Ma, Y.-X., Zhou, T.-Y., & Shen, Y. (2022) · Physics of Fluids · doi:10.1063/5.0119516 · Cited by 74
Metadata
- Authors
- Brunton, S. L., Noack, B. R., & Koumoutsakos, P.
- Affiliations
- University of Washington (US)
- Centre National de la Recherche Scientifique (FR)
- ETH Zurich (CH)
- 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
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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