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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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Zhang, X., Ji, T., Xie, F., Zheng, C., & Zheng, Y. (2022) · Physics of Fluids · doi:10.1063/5.0090394 · Cited by 44
Prediction of wall-bounded turbulence from wall quantities using convolutional neural networks
Guastoni, L., Encinar, M. P., Schlatter, P., Azizpour, H., & Vinuesa, R. (2020) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1522/1/012022 · Cited by 42
A critical review of artificial intelligence in mineral concentration
Gomez-Flores, A., Ilyas, S., Heyes, G. W., & Kim, H. (2022) · Minerals Engineering · doi:10.1016/j.mineng.2022.107884 · Cited by 43
Geyer, P., Singh, M. M., & Chen, X. (2024) · Advanced Engineering Informatics · doi:10.1016/j.aei.2024.102843 · Cited by 56
“In fluid dynamics, data-driven modelling have been established for prediction of flows [9].”
MethodFan, D., Zhang, B., Zhou, Y., & Noack, B. R. (2020) · Physics of Fluids · doi:10.1063/5.0033156 · Cited by 43
Self-citationDeep learning enhanced dynamic mode decomposition
Alford-Lago, D. J., Curtis, C. W., Ihler, A., & Issan, O. (2022) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0073893 · Cited by 43
“While the need for such work was clear to researchers several decades ago [1], the ongoing shift occurring in the physical sciences away from first principles modeling to data-driven modeling [2, 3], coupled with the rise in computing power and algorithm design, has added impetus to the search for mathematically robus…”
BackgroundBracconi, M. (2022) · Chemical Engineering and Processing - Process Intensification · doi:10.1016/j.cep.2022.109148 · Cited by 42
Research Development on Fish Swimming
Liu, Y., & Jiang, H. (2022) · Chinese Journal of Mechanical Engineering · doi:10.1186/s10033-022-00791-4 · Cited by 44
“Petros’s team of ETH Zurich used RL to study fish school problem in 2014 and gave an overview of research development and promising opportunities of ML for fluid mechanics [254, 255].”
MethodBreather wave, lump type and interaction solutions for a high dimensional evolution model
Cao, N., Yin, X., Bai, S., & LiYangXu (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.113505 · Cited by 42
Bayesian conditional diffusion models for versatile spatiotemporal turbulence generation
Gao, H., Han, X., Fan, X., Sun, L., Liu, L., Duan, L., & Wang, J. (2024) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2024.117023 · Cited by 60
CF-DeepONet: Deep operator neural networks for solving compressible flows
Zheng, J., Hu, H., Huang, J., Zhao, B., & Huang, H. (2025) · Aerospace Science and Technology · doi:10.1016/j.ast.2025.110329 · Cited by 42
Tokarev, M. P., Palkin, E., & Mullyadzhanov, R. I. (2020) · Energies · doi:10.3390/en13225920 · Cited by 42
“An appealing way to design new closed-loop control strategies is to rely on the so-called data-driven and learning-based methods, which lately receive well-deserved attention [4].”
BackgroundMahmoudabadbozchelou, M., Kamani, K. M., Rogers, S. A., & Jamali, S. (2022) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2202234119 · Cited by 42
“These are referred to as supervised learning and unsupervised learning (24).”
BackgroundBayesian optimization for active flow control
Blanchard, A. B., Maceda, G. Y. C., Fan, D., Li, Y., Zhou, Y., Noack, B. R., & Sapsis, T. P. (2021) · Acta Mechanica Sinica · doi:10.1007/s10409-021-01149-0 · Cited by 41
Self-citationMilićević, A., Belosevic, S. V., Žarković, M., Tomanović, I., Crnomarković, N. Đ., Stojanović, A., Stupar, G., Deng, L., & Che, D. (2023) · Biomass and Bioenergy · doi:10.1016/j.biombioe.2023.106817 · Cited by 41
Fluid Simulation on Neural Flow Maps
Deng, Y., Yu, H.-X., Zhang, D., Wu, J., & Zhu, B. (2023) · ACM Transactions on Graphics · doi:10.1145/3618392 · Cited by 41
“Readers can refer to comprehensive surveys [Brunton et al. 2020; Chen et al. 2021; Majchrzak et al. 2023; Sharma et al. 2023] for in-depth discussions.”
BackgroundKasmaiee, S., Tadjfar, M., Kasmaiee, S., & Ahmadi, G. (2024) · Theoretical and Computational Fluid Dynamics · doi:10.1007/s00162-024-00685-2 · Cited by 41
Data-driven transient lift attenuation for extreme vortex gust–airfoil interactions
Fukami, K., Nakao, H., & Taira, K. (2024) · Journal of Fluid Mechanics · doi:10.1017/jfm.2024.592 · Cited by 41
“In such a case, nonlinear machine-learning-based techniques can be helpful [17, 18, 19].”
BackgroundPhysics-constrained deep learning for data assimilation of subsurface transport
Wu, H., & Qiao, R. (2020) · Energy and AI · doi:10.1016/j.egyai.2020.100044 · Cited by 41
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
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