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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Portwood, G., Nadiga, B., Sáenz, J. A., & Livescu, D. (2020) · Journal of Fluid Mechanics · doi:10.1017/jfm.2020.861 · Cited by 34
An adaptive and energy-maximizing control optimization of wave energy converters using an extremum-seeking approach
Parrinello, L., Dafnakis, P., Pasta, E., Bracco, G., Naseradinmousavi, P., Mattiazzo, G., & Bhalla, A. P. S. (2020) · Physics of Fluids · doi:10.1063/5.0028500 · Cited by 34
“38,44 In contrast, model-free ES controllers rely mostly on perturbation signals, filters, and gradient estimation of the performance function; these operations have much lower computation overhead, which allows ES to be used as an “online” controller/optimizer.”
Method
Deep learning of the spanwise-averaged Navier–Stokes equations
Font, B., Weymouth, G. D., Nguyen, V.-T., & Tutty, O. R. (2021) · Journal of Computational Physics · doi:10.1016/j.jcp.2021.110199 · Cited by 34
Machine learning for multiphase flowrate estimation with time series sensing data
Wang, H., Zhang, M., & Yang, Y. (2020) · Measurement Sensors · doi:10.1016/j.measen.2020.100025 · Cited by 34
Data‐Driven Prediction of Turbulent Flow Statistics Past Bridge Piers in Large‐Scale Rivers Using Convolutional Neural Networks
Zhang, Z., Flora, K., Kang, S., Limaye, A. B. S., & Khosronejad, A. (2021) · Water Resources Research · doi:10.1029/2021wr030163 · Cited by 34
A Meta-Model to Predict the Drag Coefficient of a Particle Translating in Viscoelastic Fluids: A Machine Learning Approach
Faroughi, S. A., Roriz, A. I. A., & Fernandes, C. B. P. (2022) · Polymers · doi:10.3390/polym14030430 · Cited by 34
“, forward simulations) and the outer-loop (optimization and data assimilation) can be improved using the adaptivity and acceleration of ML- or DL-based models [12,13].”
BackgroundMethod
Data-driven methods for low-dimensional representation and state identification for the spatiotemporal structure of cavitation flow fields
Wang, Z., Zhang, G., Sun, T., Shi, C., & Zhou, B. (2023) · Physics of Fluids · doi:10.1063/5.0145453 · Cited by 33
Physically Interpretable Feature Learning of Supercritical Airfoils Based on Variational Autoencoders
Li, R., Zhang, Y., & Chen, H. (2022) · AIAA Journal · doi:10.2514/1.j061673 · Cited by 33
Towards multi-fidelity deep learning of wind turbine wakes
Pawar, S. A., Sharma, A., Vijayakumar, G., Bay, C. J., Yellapantula, S., & San, O. (2022) · Renewable Energy · doi:10.1016/j.renene.2022.10.013 · Cited by 33
Multi-fidelity model and reduced-order method for comprehensive hydrodynamic performance optimization and prediction of JBC ship
Liu, X., Wan, D., & Lei, L. (2022) · Ocean Engineering · doi:10.1016/j.oceaneng.2022.113321 · Cited by 33
“Machine learning (ML) or deep learning (DL) can provide many techniques to extract information from data that can be translated into knowledge about the underlying fluid mechanics, as long as outcomes are held to long-standing critical standards (Brunton et al., 2020).”
Background
On the accuracy of two-temperature models for hypersonic nonequilibrium flow
Wang, X., Hong, Q., Hu, Y., & Sun, Q. (2022) · Acta Mechanica Sinica · doi:10.1007/s10409-022-22193-x · Cited by 33
Reconstruction of three-dimensional turbulent flow structures using surface measurements for free-surface flows based on a convolutional neural network
Xuan, A., & Shen, L. (2023) · Journal of Fluid Mechanics · doi:10.1017/jfm.2023.154 · Cited by 36
“Various studies have discovered that the ability of NNs to process nonlinear dynamics often enables them to achieve better performance than linear methods when applied to turbulent flow problems (e.g. see Brunton et al. (2020) for a review).”
Background
A Framework on Fast Mapping of Urban Flood Based on a Multi-Objective Random Forest Model
Liao, Y., Wang, Z., Lai, C., & Xu, C. (2023) · International Journal of Disaster Risk Science · doi:10.1007/s13753-023-00481-2 · Cited by 33
“Furthermore, it can combine common feature data to form more abstract attributes, or higher-level feature representations, giving a more detailed description of hydrological and hydrodynamic phenomena (Lai et al. 2016; Brunton et al. 2019).”
Background
Review: Machine learning for advancing low-temperature plasma modeling and simulation
Trieschmann, J., Vialetto, L., & Gergs, T. (2023) · Journal of Micro/Nanopatterning Materials and Metrology · doi:10.1117/1.jmm.22.4.041504 · Cited by 54
“The reader is referred to corresponding comprehensive surveys by Brunton and Vinuesa et al. 191,192 Concerning data-driven process control and MPC, it should be noted that the plasma information based VM methodology for LTP etching processes previously introduced may be adapted based on physical or data-driven model d…”
Method
A deep learning‒genetic algorithm approach for aerodynamic inverse design via optimization of pressure distribution
Shirvani, A., Nili‐Ahmadabadi, M., & Ha, M. Y. (2024) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2024.117187 · Cited by 33
Renewable wind energy resources in offshore low wind speeds regions near the equator: A review
Nizamani, Z., Muhammad, A. K., Ali, M. O. A., Wahab, M. A., Nakayama, A., & Ahmed, M. M. (2024) · Ocean Engineering · doi:10.1016/j.oceaneng.2024.118834 · Cited by 33
GSA for machine learning problems: A comprehensive overview
Ávalos, O. (2020) · Applied Mathematical Modelling · doi:10.1016/j.apm.2020.11.013 · Cited by 33
Black-box real-time identification of sub-regime of gas-liquid flow using Ultrasound Doppler Velocimetry with deep learning
Mao, N., Azman, A. N., Ding, G., Jin, Y., Kang, C., & Kim, H.-B. (2021) · Energy · doi:10.1016/j.energy.2021.122319 · Cited by 33
Fast estimation of internal flowfields in scramjet intakes via reduced-order modeling and machine learning
Brahmachary, S., Bhagyarajan, A., & Ogawa, H. (2021) · Physics of Fluids · doi:10.1063/5.0064724 · Cited by 33
Learning emergent partial differential equations in a learned emergent space
Kemeth, F. P., Bertalan, T., Thiem, T. N., Dietrich, F., Moon, S. J., Laing, C. R., & Kevrekidis, I. G. (2022) · Nature Communications · doi:10.1038/s41467-022-30628-6 · Cited by 33
Solving Time Dependent Fokker-Planck Equations Via Temporal Normalizing Flow
Feng, X., Zeng, L., & Zhou, T. Z. T. (2022) · Communications in Computational Physics · doi:10.4208/cicp.oa-2022-0090 · Cited by 33
“These approaches have been widely applied to many realistic problems, such as fluid mechanics [29, 2], high dimensional PDEs (with applications in computational finance) [11, 41], uncertainty quantification [39, 27, 42, 14, 22], to name just a few.”
Fill in the Blank: Transferrable Deep Learning Approaches to Recover Missing Physical Field Information
Yang, Z., & Buehler, M. J. (2023) · Advanced Materials · doi:10.1002/adma.202301449 · Cited by 34
Enhancing heat transfer from a circular cylinder undergoing vortex induced vibration based on reinforcement learning
Ren, F., Zhang, F., Zhu, Y., Wang, Z., & Zhao, F. (2023) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2023.121919 · Cited by 34
Comparison of dimensionality reduction techniques for multi-variable spatiotemporal flow fields
Wang, Z., Zhang, G., Xing, X., Xu, X., & Sun, T. (2023) · Ocean Engineering · doi:10.1016/j.oceaneng.2023.116421 · Cited by 32
Deep learning probability flows and entropy production rates in active matter
Boffi, N. M., & Vanden‐Eijnden, E. (2024) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2318106121 · Cited by 42
RF-PINNs: Reactive flow physics-informed neural networks for field reconstruction of laminar and turbulent flames using sparse data
Yadav, V. K., Casel, M., & Ghani, A. (2024) · Journal of Computational Physics · doi:10.1016/j.jcp.2024.113698 · Cited by 32
A novel deep learning approach for investigating liquid fuel injection in combustion system
Inam, S. A., Khan, A. A., Ahmed, N., Mazhar, T., Shahzad, T., Khan, S., Saeed, M. M. A., & Hamam, H. (2025) · Discover Artificial Intelligence · doi:10.1007/s44163-025-00248-2 · Cited by 32
“Currently, several techniques have been developed, ranging from algorithms to databases, fueling the interest of the researchers of fluid dynamics to use machines and deep learning to extract valuable insights from the data [13, 16].”
Influential

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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