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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].”
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“Recent efforts on ML in the fluid dynamics community with its expected applications are well summarized in Brenner et al (2019) and Brunton et al (2020a), Brunton et al (2020b).”
MethodApplying machine learning to study fluid mechanics
Brunton, S. L. (2021) · Acta Mechanica Sinica · doi:10.1007/s10409-021-01143-6 · Cited by 160
Self-citationLiao, Y., Wang, Z., Chen, X., & Lai, C. (2023) · Journal of Hydrology · doi:10.1016/j.jhydrol.2023.129945 · Cited by 151
Lee, J., Park, D., Lee, M., Lee, H., Park, K., Lee, I., & Ryu, S. (2023) · Materials Horizons · doi:10.1039/d3mh00039g · Cited by 157
MaxwellNet: Physics-driven deep neural network training based on Maxwell’s equations
Lim, J., & Psaltis, D. (2022) · APL Photonics · doi:10.1063/5.0071616 · Cited by 167
Multiscale simulations of complex systems by learning their effective dynamics
Vlachas, P. R., Arampatzis, G., Uhler, C., & Koumoutsakos, P. (2022) · Nature Machine Intelligence · doi:10.1038/s42256-022-00464-w · Cited by 174
Self-citationBararnia, H., & Esmaeilpour, M. (2022) · International Communications in Heat and Mass Transfer · doi:10.1016/j.icheatmasstransfer.2022.105890 · Cited by 145
Roy, A. M., Bose, R., Sundararaghavan, V., & Arróyave, R. (2023) · Neural Networks · doi:10.1016/j.neunet.2023.03.014 · Cited by 159
Wessels, H., Weißenfels, C., & Wriggers, P. (2020) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2020.113127 · Cited by 152
An interpretable framework of data-driven turbulence modeling using deep neural networks
Jiang, C., Vinuesa, R., Chen, R., Mi, J., Laima, S., & Li, H. (2021) · Physics of Fluids · doi:10.1063/5.0048909 · Cited by 144
A perspective on machine learning methods in turbulence modeling
Beck, A., & Kurz, M. (2021) · GAMM-Mitteilungen · doi:10.1002/gamm.202100002 · Cited by 160
“With the recently exploding interest in machine learning (ML), artificial intelligence (AI), Big Data and generally data-driven methods for a wide range of applications, it is not surprising that these approaches have also found their way into the field of fluid mechanics [8], for example for optimization and control…”
BackgroundTowards extraction of orthogonal and parsimonious non-linear modes from turbulent flows
Eivazi, H., Clainche, S. L., Hoyas, S., & Vinuesa, R. (2022) · Expert Systems with Applications · doi:10.1016/j.eswa.2022.117038 · Cited by 152
Stergiou, K., Ntakolia, C., Varytis, P., Koumoulos, E., Karlsson, P., & Moustakidis, S. (2023) · Computational Materials Science · doi:10.1016/j.commatsci.2023.112031 · Cited by 161
Promising directions of machine learning for partial differential equations
Brunton, S., & Kutz, J. (2024) · Nature Computational Science · doi:10.1038/s43588-024-00643-2 · Cited by 196
“First, it is possible to dramatically improve the dimensionality reduction in equation (8) by replacing the linear subspace approximation with a nonlinear manifold approximation using a deep neural network autoencoder 15 , similar to the architecture shown in Fig.”
Self-citationPhysics-informed neural networks for phase-field method in two-phase flow
Qiu, R., Huang, R., Xiao, Y., Wang, J., Zhang, Z., Yue, J.-S., Zeng, Z., & Wang, Y. (2022) · Physics of Fluids · doi:10.1063/5.0091063 · Cited by 139
Mozaffar, M., Liao, S., Xie, X., Saha, S., Park, C., Cao, J., Liu, W. K., & Gan, Z. (2021) · Journal of Materials Processing Technology · doi:10.1016/j.jmatprotec.2021.117485 · Cited by 136
Constructing Neural Network Based Models for Simulating Dynamical Systems
Legaard, C. M., Schranz, T., Schweiger, G., Drgoňa, J., Falay, B., Gomes, C. Â. G., Iosifidis, A., Abkar, M., & Larsen, P. G. (2022) · ACM Computing Surveys · doi:10.1145/3567591 · Cited by 159
“The broader topic of using ML in scientific fields has received widespread attention within several application domains [11, 12, 19, 108].”
BackgroundFrom coarse wall measurements to turbulent velocity fields through deep learning
Güemes, A., Discetti, S., Ianiro, A., Sırmaçek, B., Azizpour, H., & Vinuesa, R. (2021) · Physics of Fluids · doi:10.1063/5.0058346 · Cited by 138
Recent progress of machine learning in flow modeling and active flow control
Li, Y., Chang, J., Kong, C., & Bao, W. B. (2021) · Chinese Journal of Aeronautics · doi:10.1016/j.cja.2021.07.027 · Cited by 133
nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling
Mahmoudabadbozchelou, M., Karniadakis, G. E., & Jamali, S. (2021) · Soft Matter · doi:10.1039/d1sm01298c · Cited by 133
Machine learning for polymer composites process simulation – a review
Cassola, S., Duhovic, M., Schmidt, T., & May, D. (2022) · Composites Part B Engineering · doi:10.1016/j.compositesb.2022.110208 · Cited by 134
Learning Nonlinear Reduced Models from Data with Operator Inference
Krämer, B., Peherstorfer, B., & Willcox, K. E. (2023) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-121021-025220 · Cited by 132
Jovanović, M. R. (2020) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-010719-060244 · Cited by 128
“Capitalizing on the availability of such data,machine and reinforcement learning have recently been used for flowmodeling, optimization, and control (Brunton et al. 2020) and this trend will continue.”
BackgroundAllal, Z., Noura, H. N., Salman, O., & Chahine, K. (2024) · Journal of Environmental Management · doi:10.1016/j.jenvman.2024.120392 · Cited by 130
Robust principal component analysis for modal decomposition of corrupt fluid flows
Scherl, I., Strom, B., Shang, J. K., Williams, O. J. H., Polagye, B. L., & Brunton, S. L. (2020) · Physical Review Fluids · doi:10.1103/physrevfluids.5.054401 · Cited by 126
“The majority of modal decompositions are linear [3,10], although emerging techniques in machine learning are providing improved nonlinear pattern extraction [1].”
BackgroundSelf-citationMachine Learning Force Fields: Recent Advances and Remaining Challenges
Poltavsky, I., & Tkatchenko, A. (2021) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.1c01204 · Cited by 130
de Wilde, P. (2023) · Energy and Buildings · doi:10.1016/j.enbuild.2023.113171 · Cited by 132
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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