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.
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Since Hinton proposed the deep belief networks (DBN) in 2006, deep network-based methods have accomplished significant achievements in various sectors.
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“For example, we refer to recent surveys of ML in domainspecific areas of molecular and material science [326] and fluid mechanics [327].”
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“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.”
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“Several authors have surveyed the potential of machine learning to improve fluid mechanics [11, 12], including topics beyond the scope of CFD, such as experimental techniques, control applications, and related fields.”
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Self-citationPhysics-informed neural networks for solving Reynolds-averaged Navier–Stokes equations
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“At the same time it may offer a bridge to the physics community to appreciate and explore the importance of advanced ML algorithms for solving challenging physical problems (Brunton et al., 2020).”
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Krishnapriyan, A. S., Gholami, A., Zhe, S., Kirby, R. M., & Mahoney, M. W. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2109.01050 · Cited by 446 · see citing works
“In this vein, there have been a number of ML approaches to incorporate scientific knowledge into such problems while keeping the automatic, data-driven estimates of the solution [2, 17, 33, 39].”
BackgroundHaghighat, E., & Juanes, R. (2020) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2020.113552 · Cited by 430 · see citing works
“Even more recently, this data-driven framework has made inroads in engineering and scientific applications, such as earthquake detection [10–12], fluid mechanics and turbulence modeling [13,14], dynamical systems [15], and constitutive modeling [16,17].”
BackgroundPhysics-Informed Neural Operator for Learning Partial Differential Equations
Li, Z., Zheng, H., Kovachki, N., Jin, D., Chen, H., Liu, B., Azizzadenesheli, K., & Anandkumar, A. (2024) · ACM / IMS Journal of Data Science · doi:10.1145/3648506 · Cited by 408 · see citing works
“Machine learning methods have recently shown promise in solving partial differential equations ( PDEs ) [1–5].”
InfluentialMachine learning in aerodynamic shape optimization
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Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
Murata, T., Fukami, K., & Fukagata, K. (2019) · Journal of Fluid Mechanics · doi:10.1017/jfm.2019.822 · Cited by 364 · see citing works
Deep learning methods for super-resolution reconstruction of turbulent flows
Liu, B., Tang, J., Huang, H., & Lu, X. (2020) · Physics of Fluids · doi:10.1063/1.5140772 · Cited by 357 · see citing works
“16 The deep learning method was first used in the SR problem by Dong et al. 17 in 2014.”
MethodCai, S., Wang, Z., Fuest, F., Jeon, Y. J., Gray, C., & Karniadakis, G. E. (2021) · Journal of Fluid Mechanics · doi:10.1017/jfm.2021.135 · Cited by 351 · see citing works
“Recently, deep learning techniques have become increasingly popular in both computational and experimental fluid dynamics (Brunton et al. 2020; Duraisamy et al. 2019).”
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Fukami, K., Fukagata, K., & Taira, K. (2020) · Journal of Fluid Mechanics · doi:10.1017/jfm.2020.948 · Cited by 343 · see citing works
“In recent years, machine learning methods have been utilized to tackle various problems in fluid dynamics (Brunton et al. 2020; Fukami et al. 2020; Brenner et al. 2019).”
MethodNeural operators for accelerating scientific simulations and design
Azizzadenesheli, K., Kovachki, N., Li, Z., Liu-Schiaffini, M., Kossaifi, J., & Anandkumar, A. (2024) · Nature Reviews Physics · doi:10.1038/s42254-024-00712-5 · Cited by 351 · see citing works
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Machine learning for active matter
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Towards Physics-informed Deep Learning for Turbulent Flow Prediction
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“ccurately the properties of complex physical systems. Developing deep learning methods that can incorporate physical laws in a systematic manner is a key element in advancing AI for physical sciences [32]. Recently, several studies in data science and computational mathematics communities have attempted incorporating…”
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“The progress in machine learning that led to these advances has been mostly technological, and is well reviewed for fluid mechanics elsewhere [1].”
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“Over the past decade, with the availability of rich datasets from direct numerical simulations (DNS) and experiments, there has been a rapid growth in the use of machine learning methods in fluid mechanics [1].”
BackgroundDeep learning to replace, improve, or aid CFD analysis in built environment applications: A review
Calzolari, G., & Liu, W. (2021) · Building and Environment · doi:10.1016/j.buildenv.2021.108315 · Cited by 283 · see citing works
Reinforcement learning for bluff body active flow control in experiments and simulations
Fan, D., Yang, L., Wang, Z., Triantafyllou, M. S., & Karniadakis, G. E. (2020) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2004939117 · Cited by 272 · see citing works
“In recent years, machine learning has received increasing attention for fluid control problems (2) because it could provide a more efficient pathway to achieving effective solutions.”
BackgroundPhyCRNet: Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs
Ren, P., Rao, C., Liu, Y., Wang, J., & Sun, H. (2021) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2021.114399 · Cited by 272 · see citing works
Combustion machine learning: Principles, progress and prospects
Ihme, M., Chung, W. T., & Mishra, A. (2022) · Progress in Energy and Combustion Science · doi:10.1016/j.pecs.2022.101010 · Cited by 278 · see citing works
Machine learning for hydrologic sciences: An introductory overview
Xu, T., & Liang, F. (2021) · Wiley Interdisciplinary Reviews Water · doi:10.1002/wat2.1533 · Cited by 269 · see citing works
“…and industry, researchers from various scientific disciplines are eager to apply machine learning techniques to problems from their own fields (Brunton et al., 2020; Ching et al., 2018; Khan & Yairi, 2018; Mater & Coote, 2019; Radovic et al., 2018; Reichstein et al., 2019; Sengupta et al.,…”
Understanding Physics-Informed Neural Networks: Techniques, Applications, Trends, and Challenges
Farea, A., Yli-Harja, O. P., & Emmert‐Streib, F. (2024) · AI · doi:10.3390/ai5030074 · Cited by 270 · see citing works
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Data-Driven Aerospace Engineering: Reframing the Industry with Machine Learning
Brunton, S. L., Nathan Kutz, J., Manohar, K., Aravkin, A. Y., Morgansen, K., Klemisch, J., Goebel, N., Buttrick, J., Poskin, J., Blom-Schieber, A. W., et al. (2021) · AIAA Journal · doi:10.2514/1.j060131 · Cited by 270 · see citing works
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“…number of applications of machine learning has been witnessed in the field of computational mechanics and engineering, e.g. fluid mechanics [2, 3, 4], molecular dynamics [5, 6, 7, 8], learning constitutive laws [9, 10, 11, 12], solving fracture problems [13, 14], material property prediction…”
BackgroundGlobal field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning
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A Review of Physics-Informed Machine Learning in Fluid Mechanics
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Direct shape optimization through deep reinforcement learning
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Data-driven modeling for unsteady aerodynamics and aeroelasticity
Kou, J., & Zhang, W. (2021) · Progress in Aerospace Sciences · doi:10.1016/j.paerosci.2021.100725 · Cited by 249 · see citing works
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Donnelly, J., Daneshkhah, A., & Abolfathi, S. (2023) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2023.168814 · Cited by 240 · see citing works
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Assessment of supervised machine learning methods for fluid flows
Fukami, K., Fukagata, K., & Taira, K. (2020) · Theoretical and Computational Fluid Dynamics · doi:10.1007/s00162-020-00518-y · Cited by 235 · see citing works
“These applications have leveraged the powerful capability of supervised machine learning to serve as an universal approximator for the nonlinear relationship between input and output data [1,2,3,4,5, 6,7].”
BackgroundDeep neural networks for nonlinear model order reduction of unsteady flows
Eivazi, H., Veisi, H., Naderi, M. H., & Esfahanian, V. (2020) · Physics of Fluids · doi:10.1063/5.0020526 · Cited by 228 · see citing works
“Complementary information on the use of ML for fluid dynamics can be found in many recent reviews [18–23].”
Nakamura, T., Fukami, K., Hasegawa, K., Nabae, Y., & Fukagata, K. (2021) · Physics of Fluids · doi:10.1063/5.0039845 · Cited by 226 · see citing works
Machine learning for combustion
Zhou, L., Song, Y., Ji, W., & Wei, H. (2021) · Energy and AI · doi:10.1016/j.egyai.2021.100128 · Cited by 232 · see citing works
Rabault, J., & Kuhnle, A. (2019) · Physics of Fluids · doi:10.1063/1.5116415 · Cited by 223 · see citing works
Gao, H., Sun, L., & Wang, J. (2021) · Physics of Fluids · doi:10.1063/5.0054312 · Cited by 217 · see citing works
“In past a few years, ML has been successfully applied in fluid dynamics [24, 25], for, e.”
MethodCai, S., Wang, Z., Lu, L., Zaki, T. A., & Karniadakis, G. E. (2021) · Journal of Computational Physics · doi:10.1016/j.jcp.2021.110296 · Cited by 217 · see citing works
“Recently, deep learning techniques have been introduced in modeling diverse fluid mechanics problems [1, 2, 3].”
BackgroundA review on flow-induced vibration of offshore circular cylinders
Wang, J., Fan, D., & Lin, K. (2020) · Journal of Hydrodynamics · doi:10.1007/s42241-020-0032-2 · Cited by 211 · see citing works
β-Variational autoencoders and transformers for reduced-order modelling of fluid flows
Solera-Rico, A., Vila, C. S., Gómez, M. A., Wang, Y., Almashjary, A., Dawson, S. T. M., & Vinuesa, R. (2024) · Nature Communications · doi:10.1038/s41467-024-45578-4 · Cited by 214 · see citing works
“One of the potential ML techniques adopted to create non-linear ROMs is the neural networks with convolutional autoencoder architectures 18,19 .”
MethodVariational Physics-informed Neural Operator (VINO) for solving partial differential equations
Eshaghi, M. S., Anitescu, C., Thombre, M., Wang, Y., Zhuang, X., & Rabczuk, T. (2025) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2025.117785 · Cited by 215 · see citing works
“Recent advancements in machine learning have shown potential in addressing Partial Differential Equations (PDEs) [1–8] with diverse applicability in wide applications such as mechanics [9, 10] fluid mechanics [11, 12], heat transfer [13], bio-engineering [14, 15], materials [16, 17], and finance…”
Hasegawa, K., Fukami, K., Murata, T., & Fukagata, K. (2020) · Theoretical and Computational Fluid Dynamics · doi:10.1007/s00162-020-00528-w · Cited by 213 · see citing works
Convolutional-network models to predict wall-bounded turbulence from wall quantities
Guastoni, L., Güemes, A., Ianiro, A., Discetti, S., Schlatter, P., Azizpour, H., & Vinuesa, R. (2021) · Journal of Fluid Mechanics · doi:10.1017/jfm.2021.812 · Cited by 210 · see citing works
“and flow control, DNNs have recently received extensive attention in the fluid-mechanics research community (Kutz 2017; Jiménez 2018; Duraisamy et al. 2019; Brunton et al. 2020).”
BackgroundStrategies towards a more sustainable aviation: A systematic review
Afonso, F., Sohst, M., Diogo, C. M. A., Rodrigues, S. S., Ferreira, A. F., Ribeiro, I., Marques, R., Rego, F., Sohouli, A., Portugal‐Pereira, J., et al. (2023) · Progress in Aerospace Sciences · doi:10.1016/j.paerosci.2022.100878 · Cited by 211 · see citing works
Fukami, K., Nakamura, T., & Fukagata, K. (2020) · Physics of Fluids · doi:10.1063/5.0020721 · Cited by 205 · see citing works
Parameter estimation and uncertainty analysis in hydrological modeling
Herrera, P. A., Marazuela, M. Á., & Hofmann, T. (2021) · Wiley Interdisciplinary Reviews Water · doi:10.1002/wat2.1569 · Cited by 222 · see citing works
“Such approach to generate information and/or extract information from available observations as part of supervised learning has been recently applied in other modeling disciplines such as computational fluid dynamics (Brunton et al., 2020; Novati et al., 2021).”
BackgroundImproving aircraft performance using machine learning: A review
Clainche, S. L., Ferrer, E., Gibson, S., Cross, E. J., Parente, A., & Vinuesa, R. (2023) · Aerospace Science and Technology · doi:10.1016/j.ast.2023.108354 · Cited by 198 · see citing works
“Despite the significant progress, existing modelling approaches generally lack generality and predictivity [42].”
Applying deep reinforcement learning to active flow control in weakly turbulent conditions
Ren, F., Rabault, J., & Tang, H. (2021) · Physics of Fluids · doi:10.1063/5.0037371 · Cited by 189 · see citing works
3D Lagrangian Particle Tracking in Fluid Mechanics
Schröder, A., & Schanz, D. (2022) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-031822-041721 · Cited by 182 · see citing works
Super-resolution analysis via machine learning: a survey for fluid flows
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Machine learning for heat transfer correlations
Kwon, B., Ejaz, F., & Hwang, L. K. (2020) · International Communications in Heat and Mass Transfer · doi:10.1016/j.icheatmasstransfer.2020.104694 · Cited by 178 · see citing works
Taking the leap between analytical chemistry and artificial intelligence: A tutorial review
Ayres, L. B., Gómez, F. J. V., Linton, J. R., Silva, M. F., & García, C. D. (2021) · Analytica Chimica Acta · doi:10.1016/j.aca.2021.338403 · Cited by 178 · see citing works
Zhou, Z., He, G., Wang, S., & Jin, G. (2019) · Computers & Fluids · doi:10.1016/j.compfluid.2019.104319 · Cited by 173 · see citing works
Efficient Aerodynamic Shape Optimization with Deep-Learning-Based Geometric Filtering
Li, J., Zhang, M., Martins, J. R. R. A., & Shu, C. (2020) · AIAA Journal · doi:10.2514/1.j059254 · Cited by 172 · see citing works
Machine learning for microfluidic design and control
McIntyre, D., Lashkaripour, A., Fordyce, P. M., & Densmore, D. M. (2022) · Lab on a Chip · doi:10.1039/d2lc00254j · Cited by 170 · see citing works
Deep learning in computational mechanics: a review
Herrmann, L., & Kollmannsberger, S. (2024) · Computational Mechanics · doi:10.1007/s00466-023-02434-4 · Cited by 169 · see citing works
A concise guide to modelling the physics of embodied intelligence in soft robotics
Mengaldo, G., Renda, F., Brunton, S. L., Bächer, M., Calisti, M., Christian Duriez, A., Chirikjian, G. S., & Laschi, C. (2022) · Nature Reviews Physics · doi:10.1038/s42254-022-00481-z · Cited by 165 · see citing works
“All three main models for of internal and external interactions with fluid and solid media may benefit from advances in machine learning for modelling dynamical systems 60,62,63 .”
BackgroundSelf-citationRobust flow control and optimal sensor placement using deep reinforcement learning
Paris, R., Beneddine, S., & Dandois, J. (2021) · Journal of Fluid Mechanics · doi:10.1017/jfm.2020.1170 · Cited by 164 · see citing works
“In the context of the development of new and promising machine learning (ML) techniques, efficient nonlinear active flow control appears increasingly viable, as emphasised by Brunton & Noack (2015) and Brunton et al. (2020).”
BackgroundVignon, C., Rabault, J., & Vinuesa, R. (2023) · Physics of Fluids · doi:10.1063/5.0143913 · Cited by 161 · see citing works
Applications of Artificial Intelligence and Machine Learning Algorithms to Crystallization
Xiouras, C., Cameli, F., Quilló, G. L., Kavousanakis, M. E., Vlachos, D. G., & Stefanidis, G. D. (2022) · Chemical Reviews · doi:10.1021/acs.chemrev.2c00141 · Cited by 165 · see citing works
A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic
Cunha, B., Droz, C., Zine, A., Foulard, S., & Ichchou, M. (2022) · Mechanical systems and signal processing · doi:10.1016/j.ymssp.2023.110535 · Cited by 164 · see citing works
“ple spatiotemporal coherent modes from either linear or nonlinear dynamic systems based on data-driven regression [22, 177].”
BackgroundMethodInfluentialDPM: A deep learning PDE augmentation method with application to large-eddy simulation
Sirignano, J. A., MacArt, J. F., & Freund, J. B. (2020) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.109811 · Cited by 150 · see citing works
“The application of deep learning is an exciting direction in scientific computing [4–16].”
BackgroundOn closures for reduced order models—A spectrum of first-principle to machine-learned avenues
Ahmed, S. E., Pawar, S. A., San, O., Rasheed, A., Iliescu, T., & Noack, B. R. (2021) · Physics of Fluids · doi:10.1063/5.0061577 · Cited by 151 · see citing works
Self-citationProbabilistic neural networks for fluid flow surrogate modeling and data recovery
Maulik, R., Fukami, K., Ramachandra, N., Fukagata, K., & Taira, K. (2020) · Physical Review Fluids · doi:10.1103/physrevfluids.5.104401 · Cited by 148 · see citing works
“In particular, ML approaches hold great potential for extracting complex nonlinear relations embedded in fluid flow data [1, 2, 3, 4, 5].”
BackgroundHasegawa, K., Fukami, K., Murata, T., & Fukagata, K. (2020) · Fluid Dynamics Research · doi:10.1088/1873-7005/abb91d · Cited by 149 · see citing works
“Recent efforts on ML in the fluid dynamics community with its expected applications are well summarized in Brenner et al (2019) and Brunton et al (2020a), Brunton et al (2020b).”
MethodApplying machine learning to study fluid mechanics
Brunton, S. L. (2021) · Acta Mechanica Sinica · doi:10.1007/s10409-021-01143-6 · Cited by 149 · see citing works
Self-citationLiao, Y., Wang, Z., Chen, X., & Lai, C. (2023) · Journal of Hydrology · doi:10.1016/j.jhydrol.2023.129945 · Cited by 149 · see citing works
Lee, J., Park, D., Lee, M., Lee, H., Park, K., Lee, I., & Ryu, S. (2023) · Materials Horizons · doi:10.1039/d3mh00039g · Cited by 151 · see citing works
MaxwellNet: Physics-driven deep neural network training based on Maxwell's equationsPreprint
Lim, J., & Psaltis, D. (2021) · arXiv (Cornell University) · doi:10.1063/5.0071616 · Cited by 149 · see citing works
Multiscale simulations of complex systems by learning their effective dynamics
Vlachas, P. R., Arampatzis, G., Uhler, C., & Koumoutsakos, P. (2022) · Nature Machine Intelligence · doi:10.1038/s42256-022-00464-w · Cited by 155 · see citing works
Self-citationBararnia, H., & Esmaeilpour, M. (2022) · International Communications in Heat and Mass Transfer · doi:10.1016/j.icheatmasstransfer.2022.105890 · Cited by 145 · see citing works
Roy, A. M., Bose, R., Sundararaghavan, V., & Arróyave, R. (2023) · Neural Networks · doi:10.1016/j.neunet.2023.03.014 · Cited by 147 · see citing works
Wessels, H., Weißenfels, C., & Wriggers, P. (2020) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2020.113127 · Cited by 143 · see citing works
An interpretable framework of data-driven turbulence modeling using deep neural networks
Jiang, C., Vinuesa, R., Chen, R., Mi, J., Laima, S., & Li, H. (2021) · Physics of Fluids · doi:10.1063/5.0048909 · Cited by 140 · see citing works
A perspective on machine learning methods in turbulence modeling
Beck, A., & Kurz, M. (2021) · GAMM-Mitteilungen · doi:10.1002/gamm.202100002 · Cited by 140 · see citing works
“With the recently exploding interest in machine learning (ML), artificial intelligence (AI), Big Data and generally data-driven methods for a wide range of applications, it is not surprising that these approaches have also found their way into the field of fluid mechanics [8], for example for optimization and control…”
BackgroundTowards extraction of orthogonal and parsimonious non-linear modes from turbulent flows
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Stergiou, K., Ntakolia, C., Varytis, P., Koumoulos, E., Karlsson, P., & Moustakidis, S. (2023) · Computational Materials Science · doi:10.1016/j.commatsci.2023.112031 · Cited by 161 · see citing works
Promising directions of machine learning for partial differential equations
Brunton, S., & Kutz, J. (2024) · Nature Computational Science · doi:10.1038/s43588-024-00643-2 · Cited by 196 · see citing works
“First, it is possible to dramatically improve the dimensionality reduction in equation (8) by replacing the linear subspace approximation with a nonlinear manifold approximation using a deep neural network autoencoder 15 , similar to the architecture shown in Fig.”
Self-citationPhysics-informed neural networks for phase-field method in two-phase flow
Qiu, R., Huang, R., Xiao, Y., Wang, J., Zhang, Z., Yue, J.-S., Zeng, Z., & Wang, Y. (2022) · Physics of Fluids · doi:10.1063/5.0091063 · Cited by 139 · see citing works
Mozaffar, M., Liao, S., Xie, X., Saha, S., Park, C., Cao, J., Liu, W. K., & Gan, Z. (2021) · Journal of Materials Processing Technology · doi:10.1016/j.jmatprotec.2021.117485 · Cited by 136 · see citing works
Constructing Neural Network Based Models for Simulating Dynamical Systems
Legaard, C. M., Schranz, T., Schweiger, G., Drgoňa, J., Falay, B., Gomes, C. Â. G., Iosifidis, A., Abkar, M., & Larsen, P. G. (2022) · ACM Computing Surveys · doi:10.1145/3567591 · Cited by 137 · see citing works
“The broader topic of using ML in scientific fields has received widespread attention within several application domains [11, 12, 19, 108].”
BackgroundFrom coarse wall measurements to turbulent velocity fields through deep learning
Güemes, A., Discetti, S., Ianiro, A., Sırmaçek, B., Azizpour, H., & Vinuesa, R. (2021) · Physics of Fluids · doi:10.1063/5.0058346 · Cited by 133 · see citing works
Recent progress of machine learning in flow modeling and active flow control
Li, Y., Chang, J., Kong, C., & Bao, W. B. (2021) · Chinese Journal of Aeronautics · doi:10.1016/j.cja.2021.07.027 · Cited by 133 · see citing works
nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling
Mahmoudabadbozchelou, M., Karniadakis, G. E., & Jamali, S. (2021) · Soft Matter · doi:10.1039/d1sm01298c · Cited by 133 · see citing works
Machine learning for polymer composites process simulation – a review
Cassola, S., Duhovic, M., Schmidt, T., & May, D. (2022) · Composites Part B Engineering · doi:10.1016/j.compositesb.2022.110208 · Cited by 134 · see citing works
Learning Nonlinear Reduced Models from Data with Operator Inference
Krämer, B., Peherstorfer, B., & Willcox, K. E. (2023) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-121021-025220 · Cited by 130 · see citing works
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“Capitalizing on the availability of such data,machine and reinforcement learning have recently been used for flowmodeling, optimization, and control (Brunton et al. 2020) and this trend will continue.”
BackgroundAllal, Z., Noura, H. N., Salman, O., & Chahine, K. (2024) · Journal of Environmental Management · doi:10.1016/j.jenvman.2024.120392 · Cited by 130 · see citing works
Robust principal component analysis for modal decomposition of corrupt fluid flows
Scherl, I., Strom, B., Shang, J. K., Williams, O. J. H., Polagye, B. L., & Brunton, S. L. (2020) · Physical Review Fluids · doi:10.1103/physrevfluids.5.054401 · Cited by 126 · see citing works
“The majority of modal decompositions are linear [3,10], although emerging techniques in machine learning are providing improved nonlinear pattern extraction [1].”
BackgroundSelf-citationMachine Learning Force Fields: Recent Advances and Remaining Challenges
Poltavsky, I., & Tkatchenko, A. (2021) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.1c01204 · Cited by 125 · see citing works
de Wilde, P. (2023) · Energy and Buildings · doi:10.1016/j.enbuild.2023.113171 · Cited by 132 · see citing works
- 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 · 2019: 15
- 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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