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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Random Forests
Breiman, L. (2001) · Machine Learning · doi:10.1023/a:1010933404324 · Cited by 133,538
Long Short-Term Memory
Hochreiter, S., & Schmidhuber, J. (1997) · Neural Computation · doi:10.1162/neco.1997.9.8.1735 · Cited by 102,318
Deep learning
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
Compressed sensing
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
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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

Show all 139 references

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

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Background
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“Machine learning has also shown potential in the fluid mechanics field for supporting the understanding and modeling of spatiotemporal complex behavior (Brunton et al 2020, Vinuesa et al 2023).”
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“For more machine learning applications on ﬂuid mechanics, we refer to the paper (Brunton, Noack, and Koumoutsakos 2020).”
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“There are two paradigms in ML based approaches, (i) data driven [22], and, (ii) physics informed [11, 25, 26, 27].”
BackgroundMethod
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“Recently, neural networks (NNs) have become increasingly popular in computational fluid dynamics (CFD) 21–23 .”
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“High-dimensional Partial Differential Equations (PDEs) provide the foundation for simulating complex phenomena such as climate [2], turbulence [38, 1, 25], material behavior [8] and epidemics [16].”
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Influential
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“16,17 For example, Rabault et al. 18 and Xu et al. 19 adopted DRL to realize the control and optimization of drag reduction flowing around a cylinder; Qiu et al. 20 studied the swimming strategy of settling elongated micro-swimmers by reinforcement learning; Gustavson et al. 21 used reinforcement…”
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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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