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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Deep learning-based image segmentation for instantaneous flame front extraction
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“Recently, Machine Learning (ML) has been increasingly integrated into problem solving strategies in fluid dynamics (Brunton et al. 2020) and combustion (Zhou et al. 2022).”
Vibration-based multiphase flow identification by deep learning for the vertical section of subsea pipelines
Qiao, W., Guo, H., Huang, E., & Chen, H. (2024) · Applied Ocean Research · doi:10.1016/j.apor.2024.104167 · Cited by 19
Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint
Wang, H., Zhou, H., & Cheng, S. L. (2024) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2024.117339 · Cited by 17
“Furthermore, the lack of physics constraints in their approach may lead to ill-defined problems in sparse prediction scenarios, potentially resulting in infinitely many solutions [63].”
Background
Modeling two-phase flows with complicated interface evolution using parallel physics-informed neural networks
Qiu, R., Dong, H., Wang, J., Fan, C., & Wang, Y. (2024) · Physics of Fluids · doi:10.1063/5.0216609 · Cited by 17
Neural dynamical operator: Continuous spatial-temporal model with gradient-based and derivative-free optimization methods
Chen, C., & Wu, J. (2024) · Journal of Computational Physics · doi:10.1016/j.jcp.2024.113480 · Cited by 20
Integrated DNN and CFD model for real-time prediction of furnace waterwall slagging of coal-fired boiler
Yin, H., Liu, X., Li, M., Li, C., Li, X., & Wang, H. (2024) · Fuel · doi:10.1016/j.fuel.2024.133847 · Cited by 17
Multi-agent Reinforcement Learning for the Control of Three-Dimensional Rayleigh–Bénard Convection
Vasanth, J., Rabault, J., Alcántara-Ávila, F., Mortensen, M., & Vinuesa, R. (2024) · Flow Turbulence and Combustion · doi:10.1007/s10494-024-00619-2 · Cited by 17
“Even though there are a number of other techniques that aim at performing similar tasks as DRL (Brunton and Noack 2015; Brunton et al. 2020; Pino et al. 2023), DRL has been found to be particularly flexible and effective in the recent years.”
3D printing and artificial intelligence tools for droplet microfluidics: Advances in the generation and analysis of emulsions
Orsini, S., Lauricella, M., Montessori, A., Tiribocchi, A., Durve, M., Succi, S., Persano, L., Camposeo, A., & Pisignano, D. (2025) · Applied Physics Reviews · doi:10.1063/5.0228610 · Cited by 17
LESnets (large-eddy simulation nets): Physics-informed neural operator for large-eddy simulation of turbulence
Zhao, S., Li, Z., Fan, B., Wang, Y., Yang, H., & Wang, J. (2025) · Journal of Computational Physics · doi:10.1016/j.jcp.2025.114125 · Cited by 17
Machine Learning in Aircraft Design: A Comprehensive Review of Optimization, Aerodynamics, and Structural Applications
Mohaghegh, S., & Mohaghegh, A. (2025) · IEEE Access · doi:10.1109/access.2025.3580485 · Cited by 20
Learning hydrodynamic signatures through proprioceptive sensing by bioinspired swimmers
Pollard, B., & Tallapragada, P. (2020) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/abd044 · Cited by 17
Deep Learning of Conjugate Mappings
Bramburger, J. J., Brunton, S. L., & Kutz, J. N. (2021) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2021.133008 · Cited by 20
Self-citation
Deep Learning of Forced Convection Heat Transfer
Kang, M., & Kwon, B. (2021) · ASME Journal of Heat and Mass Transfer · doi:10.1115/1.4052893 · Cited by 17
Increasing efficiency and accuracy of magnetic interaction calculations in colloidal simulation through machine learning
Pan, C., Mahmoudabadbozchelou, M., Duan, X., Benneyan, J. C., Jamali, S., & Erb, R. M. (2021) · Journal of Colloid and Interface Science · doi:10.1016/j.jcis.2021.11.195 · Cited by 17
Coaxial-Injector Surrogate Modeling Based on Reynolds-Averaged Navier–Stokes Simulations Using Deep Learning
Krügener, M., Usandivaras, J. F. Z., Bauerheim, M., & Urbano, A. (2022) · Journal of Propulsion and Power · doi:10.2514/1.b38696 · Cited by 17
Semantic Terrain Segmentation in the Navigation Vision of Planetary Rovers—A Systematic Literature Review
Kuang, B., Gu, C., Rana, Z. A., Zhao, Y., Sun, S., & Nnabuife, S. G. (2022) · Sensors · doi:10.3390/s22218393 · Cited by 15
Active flow control for bluff body under high Reynolds number turbulent flow conditions using deep reinforcement learning
Chen, J., Ballini, E., & Micheletti, S. (2025) · Physics of Fluids · doi:10.1063/5.0253696 · Cited by 16
“Yunfei Li 33 and Steven L. Brunton 34 offer insightful overviews of recent advances in the field.”
ANN-Based Prediction and RSM Optimization of Radiative Heat Transfer in Couple Stress Nanofluids with Thermodiffusion Effects
Alsemiry, R. D., Ahmed, S. E., Eid, M. R., & Elsaid, E. M. (2025) · Processes · doi:10.3390/pr13041055 · Cited by 16
Diff-FlowFSI: A GPU-optimized differentiable CFD platform for high-fidelity turbulence and FSI simulations
Fan, X., Liu, X., Wang, M., & Wang, J. (2025) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2025.118455 · Cited by 16
Data-driven model order reduction for granular media
Wallin, E., & Servin, M. (2021) · Computational Particle Mechanics · doi:10.1007/s40571-020-00387-6 · Cited by 16
Statistical-learning method for predicting hydrodynamic drag, lift, and pitching torque on spheroidal particles
Tajfirooz, S., Meijer, J. G., Kuerten, J. G. M., Hausmann, M., Fröhlich, J., & Zeegers, J. C. H. (2021) · Physical review. E · doi:10.1103/physreve.103.023304 · Cited by 16
Unsupervised modelling of a transitional boundary layer
Foroozan, F., Guerrero, V., Ianiro, A., & Discetti, S. (2021) · Journal of Fluid Mechanics · doi:10.1017/jfm.2021.829 · Cited by 16
“Unsupervised learning is a branch of ML aiming to identify relationships and hidden patterns in the data by specifying certain global criteria and without the need of a supervision or labelling to guide the search (Brunton et al. 2020).”
Background
A sparse optimal closure for a reduced-order model of wall-bounded turbulence
Khoo, Z. C., Chan, C. H., & Hwang, Y. (2022) · Journal of Fluid Mechanics · doi:10.1017/jfm.2022.161 · Cited by 16
Extending the Capabilities of Data-Driven Reduced-Order Models to Make Predictions for Unseen Scenarios: Applied to Flow Around Buildings
Heaney, C. E., Liu, X., Go, H., Wolffs, Z., Salinas, P., Navon, I. M., & Pain, C. C. (2022) · Frontiers in Physics · doi:10.3389/fphy.2022.910381 · Cited by 16
“This is a unique development and one which we hope paves the way to develop ML-based NIROMs that can make good predictions for unseen scenarios.”
BackgroundMethodInfluential
Application of machine learning in predicting blood flow and red cell distribution in capillary vessel networks
Ebrahimi, S., & Bagchi, P. (2022) · Journal of The Royal Society Interface · doi:10.1098/rsif.2022.0306 · Cited by 16
“It is being increasingly used in biomedical and fluid mechanical applications [47,48].”
Background
On the benefits and limitations of Echo State Networks for turbulent flow prediction
Ghazijahani, M. S., Heyder, F., Schumacher, J., & Cierpka, C. (2022) · Measurement Science and Technology · doi:10.1088/1361-6501/ac93a4 · Cited by 16
Prediction of Water Diffusion in Wide Varieties of Polymers with All-Atom Molecular Dynamics Simulations and Deep Generative Models
Kawada, R., Endo, K., Yasuoka, K., Kojima, H., & Matubayasi, N. (2022) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.2c01316 · Cited by 16
Differentiable physics-enabled closure modeling for Burgers’ turbulence
Shankar, V., Puri, V., Balakrishnan, R., Maulik, R., & Viswanathan, V. (2023) · Machine Learning Science and Technology · doi:10.1088/2632-2153/acb19c · Cited by 16
Hurricane-Induced Failure Mechanisms in Low-Rise Residential Buildings and Future Research Directions
Moeini, M., & Memari, A. M. (2023) · Natural Hazards Review · doi:10.1061/nhrefo.nheng-1544 · Cited by 16

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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