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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Beheshtian, S., Roodbari, S. K., Ghorbani, H., Azodinia, M., & Mudabbir, M. (2024) · IEEE International Symposium on Applied Computational Intelligence and Informatics (SACI) · doi:10.1109/saci60582.2024.10619733 · Cited by 28
Differentiability in unrolled training of neural physics simulators on transient dynamics
List, B., Chen, L., Bali, K., & Thuerey, N. (2024) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2024.117441 · Cited by 53
Physics-informed machine learning for the structural health monitoring and early warning of a long highway viaduct with displacement transducers
Cianci, E., Civera, M., Biagi, V. D., & Chiaia, B. M. (2025) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2025.113659 · Cited by 32
“This inherent limitation restricts the effectiveness and reliability of purely data-driven ML models, which critically depend on the quality and representativeness of training datasets [23].”
Phase-based control of periodic flows
Nair, A., Taira, K., Brunton, B. W., & Brunton, S. L. (2021) · Journal of Fluid Mechanics · doi:10.1017/jfm.2021.735 · Cited by 28
“challenges of high-dimensionality, strong nonlinearity, and time-delays [10, 11].”
BackgroundSelf-citation
A survey of multiscale modeling: Foundations, historical milestones, current status, and future prospects
Radhakrishnan, R. (2020) · AIChE Journal · doi:10.1002/aic.17026 · Cited by 29
“This challenge can be addressed by subjecting the entire MSM model to contemporary data science and statistical methodologies, that is, 172 sensitivity,(1) evolvability,(2) robustness(173) analyses, uncertainty quantification,(174) multifidelity modeling,(4) and pattern discovery and model reduction.(175)”
Method
Deploying deep learning in OpenFOAM with TensorFlow
Maulik, R., Sharma, H., Patel, S., Lusch, B., & Jennings, E. (2021) · AIAA SciTech Forum · doi:10.2514/6.2021-1485 · Cited by 28
“[46] and Fukami et al.”
Methods for Panoramic Visualization and Digital Analysis of Thermophysical Flow Fields. A Review.
Znamenskaya, I. A. (2021) · Scientific Visualization · doi:10.26583/sv.13.3.13 · Cited by 28
“detailed review of research on this topic is given in [54].”
Background
Novel models for predicting the shape and motion of an ascending bubble in Newtonian liquids using machine learning
She, W., Zuo, Z.-Y., Zhao, H., Gao, Q., Zhang, L., & Shao, X. (2022) · Physics of Fluids · doi:10.1063/5.0088942 · Cited by 28
Physics-based statistical learning perspectives on droplet formation characteristics in microfluidic cross-junctions
Wang, J., Yu, W., Wu, Z., Liu, X., & Chen, Y. (2022) · Applied Physics Letters · doi:10.1063/5.0086933 · Cited by 28
Machine learning for flow-informed aerodynamic control in turbulent wind conditions
Renn, P. I., & Gharib, M. (2022) · Communications Engineering · doi:10.1038/s44172-022-00046-z · Cited by 28
Learning Neural-Network-Based Turbulence Models for External Transonic Flows Using Ensemble Kalman Method
Liu, Y., Zhang, X., & He, G. (2023) · AIAA Journal · doi:10.2514/1.j062664 · Cited by 28
Stabilizing the square cylinder wake using deep reinforcement learning for different jet locations
Yan, L., Li, Y., Hu, G., Chen, W., Zhong, W., & Noack, B. R. (2023) · Physics of Fluids · doi:10.1063/5.0171188 · Cited by 29
Self-citation
Physics-aware deep neural networks for surrogate modeling of turbulent natural convectionPreprint
Lucor, D., Agrawal, A. K., & Sergent, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.03565 · Cited by 38
“It seems to be somehow capable of producing realistic instantaneous flow fields with reasonable physically accurate spatio-temporal coherence, without solving the actual partial differential equations (PDEs) governing the system [1, 2].”
Background
A hybrid simulation method integrating CFD and deep learning for gas–liquid bubbly flow
Wen, K., Li, G., Xia, Z., Cheng, S. L., & Chen, J. (2024) · Chemical Engineering Journal · doi:10.1016/j.cej.2024.153515 · Cited by 27
Reconstruction of the turbulent flow field with sparse measurements using physics-informed neural network
Chaurasia, N. K., & Chakraborty, S. (2024) · Physics of Fluids · doi:10.1063/5.0218611 · Cited by 27
On data-driven induction of the low-frequency variability in a coarse-resolution ocean model
Ryzhov, E. A., Kondrashov, D., Agarwal, N., McWilliams, J. C., & Berloff, P. (2020) · Ocean Modelling · doi:10.1016/j.ocemod.2020.101664 · Cited by 27
“, 2020), as well as other machine-learning (deep learning) methods developed for fluid dynamics applications (Brunton et al., 2020; Bolton and Zanna, 2019).”
Background
Applications of Physics-Informed Scientific Machine Learning in Subsurface Science: A Survey
Sun, A. Y., Yoon, H., Shih, C. Y., & Zhong, Z. (2022) · Chapman & Hall/CRC eBooks · doi:10.1201/9781003143376-5 · Cited by 32
Machine Learning and transcritical sprays: A demonstration study of their potential in ECN Spray-A
Koukouvinis, P. K., Rodríguez, C., Hwang, J., Karathanassis, I. K., Gavaises, M., & Pickett, L. M. (2021) · International Journal of Engine Research · doi:10.1177/14680874211020292 · Cited by 27
“A recent thorough review 37 discusses a variety of applications in fluid mechanics, involving flow feature extraction, turbulence modelling, optimisation and flow control.”
Background
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Jain, N., Moine, A. L., Chaussonnet, G., Flatau, A. B., Bravo, L. G., Ghoshal, A., Walock, M., Murugan, M., & Khare, P. (2021) · Applied Mechanics Reviews · doi:10.1115/1.4051503 · Cited by 27
Discovering equations that govern experimental materials stability under environmental stress using scientific machine learning
Naik, R. R., Tiihonen, A., Thapa, J., Batali, C., Liu, Z., Sun, S., & Buonassisi, T. (2022) · npj Computational Materials · doi:10.1038/s41524-022-00751-5 · Cited by 27
Performance and accuracy assessments of an incompressible fluid solver coupled with a deep convolutional neural network
Illarramendi, E. A., Bauerheim, M., & Cuenot, B. (2022) · Data-Centric Engineering · doi:10.1017/dce.2022.2 · Cited by 34
“[7]: either discovering unknown models, or improving existing models.”
Background
A CFD-ML augmented alternative to residence time for clarification basin scaling and design
Li, H., & Sansalone, J. J. (2021) · Water Research · doi:10.1016/j.watres.2021.117965 · Cited by 27
A new dynamic stall prediction framework based on symbiosis of experimental and simulation data
Wang, X., Kou, J., & Zhang, W. (2021) · Physics of Fluids · doi:10.1063/5.0075083 · Cited by 28
A Direct-Forcing Immersed Boundary Method for Incompressible Flows Based on Physics-Informed Neural Network
Huang, Y., Zhang, Z., & Zhang, X. (2022) · Fluids · doi:10.3390/fluids7020056 · Cited by 27
“Over the past few years, machine learning (ML) has permeated into various research areas of fluid mechanics [1], e.”
Background
Machine-Learning-Based Reconstruction of Turbulent Vortices From Sparse Pressure Sensors in a Pump Sump
Fukami, K., An, B., Nohmi, M., Obuchi, M., & Taira, K. (2022) · Journal of Fluids Engineering · doi:10.1115/1.4055178 · Cited by 28
Applications of machine learning to the analysis of engine in-cylinder flow and thermal process: A review and outlook
Zhao, F., & Hung, D. L. S. (2022) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2022.119633 · Cited by 28
Data-driven turbulence model for unsteady cavitating flow
Zhang, Z., Wang, J., Huang, R., Qiu, R., Chu, X., Ye, S., Wang, Y., & Liu, Q. (2022) · Physics of Fluids · doi:10.1063/5.0134992 · Cited by 27
Data-Driven Control: Theory and Applications
Soudbakhsh, D., Annaswamy, A. M., Wang, Y., Brunton, S. L., Gaudio, J. E., Hussain, H. S., Vrabie, D., Drgoňa, J., & Filev, D. (2023) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc55779.2023.10156081 · Cited by 27
“However, the field of fluid dynamics poses several challenges for control [115], [116].”
BackgroundSelf-citation
A flexible and lightweight deep learning weather forecasting model
Zenkner, G., & Navarro-Martinez, S. (2023) · Applied Intelligence · doi:10.1007/s10489-023-04824-w · Cited by 37
“Machine Learning (ML) is showing large potential in fluid mechanics [6, 7], where it can be used to model sub-grid stress [8, 9] or extract turbulent structures [10].”
Background

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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