The DOI matches its Crossref record; 161 of the 161 references it cites were found in a registry or an index.
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“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]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Breiman, L. (2001) · Machine Learning · doi:10.1023/a:1010933404324 · Cited by 133,538
Hochreiter, S., & Schmidhuber, J. (1997) · Neural Computation · doi:10.1162/neco.1997.9.8.1735 · Cited by 102,318
LeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126
Learning representations by back-propagating errors
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986) · Nature · doi:10.1038/323533a0 · Cited by 31,892
Human-level control through deep reinforcement learning
Mnih, V., Kavukcuoglu, K., Silver, D., Rusu, A. A., Veness, J., Bellemare, M. G., Graves, A., Riedmiller, M., Fidjeland, A. K., Ostrovski, G., et al. (2015) · Nature · doi:10.1038/nature14236 · Cited by 30,357
The Elements of Statistical Learning
Hastie, T., Tibshirani, R., & Friedman, J. (2009) · Springer Series in Statistics · doi:10.1007/978-0-387-84858-7 · Cited by 25,970
Donoho, D. L. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.871582 · Cited by 23,994
Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., & White, H. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90020-8 · Cited by 21,728
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019) · Journal of Computational Physics · doi:10.1016/j.jcp.2018.10.045 · Cited by 20,384
Neural networks and physical systems with emergent collective computational abilities.
Hopfield, J. J. (1982) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.79.8.2554 · Cited by 19,270
Research works printed but not linked: 23
- Chen TQ, 2018, Advances in Neural Information Processing Systems 31, 6571
- Goodfellow I, 2016, Deep Learning
- Goodfellow I, 2014, Advances in Neural Information Processing Systems 27, 2672
- Hinton GE, 1986, Parallel Distributed Processing: Explorations in the Microstructure of Cognition, 1, 282
- Holland JH, 1975, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence
- Kim HJ, 2004, Advances in Neural Information Processing Systems 17, 799
- Knaak M, 1997, IEEE Int. Conf. Neural Netw., 1, 48
- 10.1007/978-3-642-97610-0 · DOI
- Kolmogorov A, 1941, Cr. Acad. Sci. USSR, 30, 301
- Krizhevsky A, 2012, Advances in Neural Information Processing Systems 25, 1097
- Lumley J, 1970, Stochastic Tools in Turbulence
- Mahoney MW, 2011, Found. Trends Mach. Learn., 3, 123
- Mehta UB, 1984, Computational aerodynamics and artificial intelligence
- Minsky M, 1969, Perceptrons: An Introduction to Computational Geometry
- Noack BR, 2018, Fluid-Structure-Sound Interactions and Control: Proceedings of the 4th Symposium on Fluid-Structure-Sound Interactions and Control, 23
- Ollivier Y, 2017, J. Mach. Learn. Res., 18, 564
- Rechenberg I, 1964, Annual Conference of the WGLR at Berlin in September, 35, 33
- Rechenberg I, 1973, Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der Biologischen Evolution
- Schaul T, 2015, Proceedings of the 32nd International Conference on Machine Learning, 1312
- Sutton RS, 2018, Reinforcement Learning: An Introduction
- Takeishi N, 2017, Advances in Neural Information Processing Systems 30, 1130
- Tedrake R, 2009, Learning to fly like a bird
- Wu H, 2018, Adv. Neural Inf. Process. Syst., 31, 3975
Cited by
Sorted by citations
Digital twin: values, challenges and enablers from a modeling perspective
Rasheed, A., San, O., & Kvamsdal, T. (2020) · IEEE Access · doi:10.1109/access.2020.2970143 · Cited by 1,952
“For example, we refer to recent surveys of ML in domainspecific areas of molecular and material science [326] and fluid mechanics [327].”
A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
Haghighat, E., Raissi, M., Moure, A., Gómez, H., & Juanes, R. (2021) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2021.113741 · Cited by 1,556
“In engineering and science, ANNs have been applied to a arge number of areas, including geosciences [4–8], material science [9–12], fluid mechanics [13,14], genetics [15], nd infrastructure health monitoring [16,17], to name a few examples.”
MethodJin, X., Cai, S., Li, H., & Karniadakis, G. E. (2020) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.109951 · Cited by 1,218
“Comprehensive summaries of progress in fluid mechanics due to the introduction of various machine learning techniques can be found in [11, 12].”
BackgroundAlzubaidi, L., Bai, J., Al-Sabaawi, A., Santamaría, J., Albahri, A. S., Al-dabbagh, B. S. N., Fadhel, M. A., Manoufali, M., Zhang, J., Al-Timemy, A. H., et al. (2023) · Journal Of Big Data · doi:10.1186/s40537-023-00727-2 · Cited by 1,057
Gao, H., Sun, L., & Wang, J. (2020) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.110079 · Cited by 693
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
