The DOI matches its Crossref record; 161 of the 161 references it cites were found in a registry or an index.
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“However, since Hinton proposed the deep belief networks (DBN) in 2006 [90], the deep network-based method has accomplished significant achievements in various sectors [91,92,93,94].”
From Semantic Terrain Segmentation in the Navigation Vision of Planetary Rovers—A Systematic Literature Review (2022) · cites this paper as [92]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Breiman, L. (2001) · Machine Learning · doi:10.1023/a:1010933404324 · Cited by 133,538
Hochreiter, S., & Schmidhuber, J. (1997) · Neural Computation · doi:10.1162/neco.1997.9.8.1735 · Cited by 102,318
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
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
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
Kohonen, T. (1995) · Springer series in information sciences · doi:10.1007/978-3-642-56927-2 · Cited by 16,032
Mastering the game of Go with deep neural networks and tree search
Silver, D., Huang, A., Maddison, C. J., Guez, A., Sifre, L., van den Driessche, G., Schrittwieser, J., Antonoglou, I., Panneershelvam, V., Lanctot, M., et al. (2016) · Nature · doi:10.1038/nature16961 · Cited by 15,612
The perceptron: A probabilistic model for information storage and organization in the brain.
Rosenblatt, F. (1958) · Psychological Review · doi:10.1037/h0042519 · Cited by 12,280
Schölkopf, B., & Smola, A. J. (2001) · The MIT Press eBooks · doi:10.7551/mitpress/4175.001.0001 · Cited by 11,934
Robust Face Recognition via Sparse Representation
Wright, J. N., Yang, A., Ganesh, A., Sastry, S., & Ma, Y. (2009) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2008.79 · Cited by 9,395
A dynamic subgrid–scale eddy viscosity model
Germano, M., Piomelli, U., Moin, P., & Cabot, W. H. (1991) · Physics of Fluids A: Fluid Dynamics · doi:10.1063/1.857955 · Cited by 7,305
Turbulence and the dynamics of coherent structures. I. Coherent structures
Sirovich, L. (1987) · Quarterly of Applied Mathematics · doi:10.1090/qam/910462 · Cited by 6,266
Dynamic mode decomposition of numerical and experimental data
Schmid, P. J. (2010) · Journal of Fluid Mechanics · doi:10.1017/s0022112010001217 · Cited by 6,189
Learning a Deep Convolutional Network for Image Super-Resolution
Dong, C., Loy, C. C., He, K., & Tang, X. (2014) · Lecture notes in computer science · doi:10.1007/978-3-319-10593-2_13 · Cited by 5,910
Image Super-Resolution Via Sparse Representation
Yang, J., Wright, J. N., Huang, T. S., & Ma, Y. (2010) · IEEE Transactions on Image Processing · doi:10.1109/tip.2010.2050625 · Cited by 5,241
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1517384113 · Cited by 4,796
Self-citationHalko, N., Martinsson, P., & Tropp, J. A. (2011) · SIAM Review · doi:10.1137/090771806 · Cited by 4,038
Particle-Imaging Techniques for Experimental Fluid Mechanics
Adrian, R. J. (1991) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fl.23.010191.001401 · Cited by 3,405 · cited 1×
“Experimental flow field measurements from particle image velocimetry (PIV) (Willert & Gharib 1991; Adrian 1991) provide a compelling application where there is a tension between local flow resolution and the size of the imaging domain.”
BackgroundDistilling Free-Form Natural Laws from Experimental Data
Schmidt, M., & Lipson, H. (2009) · Science · doi:10.1126/science.1165893 · Cited by 3,327
Hansen, N., Müller, S. D., & Koumoutsakos, P. (2003) · Evolutionary Computation · doi:10.1162/106365603321828970 · Cited by 2,601
Self-citationExample-based super-resolution
Freeman, W. T., Jones, T. R., & Pasztor, E. C. (2002) · IEEE Computer Graphics and Applications · doi:10.1109/38.988747 · Cited by 2,497
Artificial neural networks for solving ordinary and partial differential equations
Lagaris, I. E., Likas, A., & Fotiadis, D. I. (1998) · IEEE Transactions on Neural Networks · doi:10.1109/72.712178 · Cited by 2,440
Spectral analysis of nonlinear flows
Rowley, C. W., Mezić, I., Bagheri, S., Schlatter, P., & Henningson, D. S. (2009) · Journal of Fluid Mechanics · doi:10.1017/s0022112009992059 · Cited by 2,332
Low-dimensional procedure for the characterization of human faces
Sirovich, L., & Kirby, M. J. L. (1987) · Journal of the Optical Society of America A · doi:10.1364/josaa.4.000519 · Cited by 2,329
Digital particle image velocimetry
Willert, C. E., & Gharib, M. (1991) · Experiments in Fluids · doi:10.1007/bf00190388 · Cited by 2,007
Playing for Data: Ground Truth from Computer Games
Richter, S. R., Vineet, V., Roth, S., & Koltun, V. (2016) · Lecture notes in computer science · doi:10.1007/978-3-319-46475-6_7 · Cited by 1,978
Modal Analysis of Fluid Flows: An Overview
Taira, K., Brunton, S. L., Dawson, S. T. M., Rowley, C. W., Colonius, T., McKeon, B., Schmidt, O. T., Gordeyev, S. V., Theofilis, V., & Ukeiley, L. (2017) · AIAA Journal · doi:10.2514/1.j056060 · Cited by 1,912
Self-citationGrossberg, S. (1976) · Biological Cybernetics · doi:10.1007/bf00344744 · Cited by 1,910
Kutz, J. N., Brunton, S. L., Brunton, B. W., & Proctor, J. L. (2016) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611974508 · Cited by 1,751
Self-citationBayesian Reasoning and Machine Learning
Barber, D. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9780511804779 · Cited by 1,663
Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
Ling, J., Kurzawski, A. J., & Templeton, J. A. (2016) · Journal of Fluid Mechanics · doi:10.1017/jfm.2016.615 · Cited by 1,655
Nonlinear neural networks: Principles, mechanisms, and architectures
Grossberg, S. (1988) · Neural Networks · doi:10.1016/0893-6080(88)90021-4 · Cited by 1,635
Deep learning for universal linear embeddings of nonlinear dynamics
Lusch, B., Kutz, J. N., & Brunton, S. L. (2018) · Nature Communications · doi:10.1038/s41467-018-07210-0 · Cited by 1,588
Self-citationData-driven discovery of partial differential equations
Rudy, S. H., Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2017) · Science Advances · doi:10.1126/sciadv.1602614 · Cited by 1,557
Self-citationTurbulence Modeling in the Age of Data
Duraisamy, K., Iaccarino, G., & Xiao, H. (2018) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-010518-040547 · Cited by 1,532
Scale-Invariance and Turbulence Models for Large-Eddy Simulation
Meneveau, C., & Katz, J. (2000) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fluid.32.1.1 · Cited by 1,396
Neural networks and principal component analysis: Learning from examples without local minima
Baldi, P., & Hornik, K. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90014-2 · Cited by 1,383
Pathak, J., Hunt, B. R., Girvan, M., Lu, Z., & Ott, E. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.024102 · Cited by 1,367
Hidden physics models: Machine learning of nonlinear partial differential equations
Raissi, M., & Karniadakis, G. E. (2017) · Journal of Computational Physics · doi:10.1016/j.jcp.2017.11.039 · Cited by 1,349
Data-Driven Science and Engineering
Brunton, S. L., & Kutz, J. N. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108380690 · Cited by 1,269
Self-citationThe space of interactions in neural network models
Gardner, E. (1988) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/21/1/030 · Cited by 1,061
Evolution Strategies as a Scalable Alternative to Reinforcement Learning
Salimans, T., Ho, J., Chen, X., Sidor, S., & Sutskever, I. (2017) · arXiv · doi:10.48550/arxiv.1703.03864 · Cited by 1,027
On the theory of dynamic programming
Bellman, R. (1952) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.38.8.716 · Cited by 998
Analysis of Fluid Flows via Spectral Properties of the Koopman Operator
Mezić, I. (2012) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-011212-140652 · Cited by 982
Super-resolution reconstruction of turbulent flows with machine learning
Fukami, K., Fukagata, K., & Taira, K. (2019) · Journal of Fluid Mechanics · doi:10.1017/jfm.2019.238 · Cited by 873
Practical Issues in Temporal Difference Learning
Tesauro, G. J. (1992) · Machine Learning · doi:10.1007/bf00992697 · Cited by 818
Model Reduction for Flow Analysis and Control
Rowley, C. W., & Dawson, S. T. M. (2016) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-010816-060042 · Cited by 799
Numerische Optimierung von Computermodellen mittels der Evo-lutionsstrategie
Schwefel, H. (1977) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-5927-1 · Cited by 747
Wang, J.-X., Wu, J.-L., & Xiao, H. (2017) · Physical Review Fluids · doi:10.1103/physrevfluids.2.034603 · Cited by 737
Controlling the false discovery rate via knockoffs
Barber, R. F., & Candès, E. J. (2015) · The Annals of Statistics · doi:10.1214/15-aos1337 · Cited by 698
VAMPnets for deep learning of molecular kinetics
Mardt, A., Pasquali, L., Wu, H., & Noé, F. (2017) · Nature Communications · doi:10.1038/s41467-017-02388-1 · Cited by 678
A chronology of interpolation: from ancient astronomy to modern signal and image processing
Meijering, E. H. W. (2002) · Proceedings of the IEEE · doi:10.1109/5.993400 · Cited by 665
Neural‐network‐based approximations for solving partial differential equations
Dissanayake, G., & Phan-Thien, N. (1994) · Communications in Numerical Methods in Engineering · doi:10.1002/cnm.1640100303 · Cited by 663
Using Simulation and Domain Adaptation to Improve Efficiency of Deep Robotic Grasping
Bousmalis, K., Irpan, A., Wohlhart, P., Bai, Y., Kelcey, M., Kalakrishnan, M., Downs, L., Ibarz, J., Pastor, P., Konolige, K., et al. (2018) · 2018 IEEE International Conference on Robotics and Automation (ICRA) · doi:10.1109/icra.2018.8460875 · Cited by 636
Evolutionary algorithms in control systems engineering: a survey
Fleming, P. J., & Purshouse, R. C. (2002) · Control Engineering Practice · doi:10.1016/s0967-0661(02)00081-3 · Cited by 627
A paradigm for data-driven predictive modeling using field inversion and machine learning
Parish, E., & Duraisamy, K. (2015) · Journal of Computational Physics · doi:10.1016/j.jcp.2015.11.012 · Cited by 624
Closed-Loop Turbulence Control: Progress and Challenges
Brunton, S. L., & Noack, B. R. (2015) · Applied Mechanics Reviews · doi:10.1115/1.4031175 · Cited by 610
Self-citationRabault, J., Kuchta, M., Jensen, A., Réglade, U., & Cerardi, N. (2019) · Journal of Fluid Mechanics · doi:10.1017/jfm.2019.62 · Cited by 602
Manohar, K., Brunton, B. W., Kutz, J. N., & Brunton, S. L. (2018) · IEEE Control Systems · doi:10.1109/mcs.2018.2810460 · Cited by 583
Self-citationNeural Networks and Physical Systems with Emergent Collective Computational Abilities
Hopfield, J. J. (2018) · CRC Press eBooks · doi:10.1201/9780429500459-2 · Cited by 538
Nonlinear model order reduction based on local reduced‐order bases
Amsallem, D., Zahr, M. J., & Farhat, C. (2012) · International Journal for Numerical Methods in Engineering · doi:10.1002/nme.4371 · Cited by 504
Cherkassky, V., & Mulier, F. M. (2006) · Wiley eBooks · doi:10.1002/9780470140529 · Cited by 488
Li, Q., Dietrich, F., Bollt, E. M., & Kevrekidis, I. G. (2017) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4993854 · Cited by 482
A quantitative study of three-dimensional Lagrangian particle tracking algorithms
Ouellette, N. T., Xu, H., & Bodenschatz, E. (2005) · Experiments in Fluids · doi:10.1007/s00348-005-0068-7 · Cited by 478
DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms
Bewley, T., Moin, P., & Témam, R. (2001) · Journal of Fluid Mechanics · doi:10.1017/s0022112001005821 · Cited by 453
Learning partial differential equations via data discovery and sparse optimization
Schaeffer, H. (2017) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2016.0446 · Cited by 436
Machine-Learning-Augmented Predictive Modeling of Turbulent Separated Flows over Airfoils
Singh, A. P., Medida, S., & Duraisamy, K. (2017) · AIAA Journal · doi:10.2514/1.j055595 · Cited by 435
Neural Network Modeling for Near Wall Turbulent Flow
Milano, M., & Koumoutsakos, P. (2002) · Journal of Computational Physics · doi:10.1006/jcph.2002.7146 · Cited by 431
Self-citationA direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow
Wu, X., & Moin, P. (2008) · Journal of Fluid Mechanics · doi:10.1017/s0022112008002085 · Cited by 426
A Randomized Algorithm for Principal Component Analysis
Rokhlin, V., Szlam, A. D., & Tygert, M. (2009) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/080736417 · Cited by 424
Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
Wehmeyer, C., & Noé, F. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5011399 · Cited by 421
Ling, J., & Templeton, J. A. (2015) · Physics of Fluids · doi:10.1063/1.4927765 · Cited by 415
Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks
Vlachas, P. R., Byeon, W., Wan, Z. Y., Sapsis, T. P., & Koumoutsakos, P. (2018) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2017.0844 · Cited by 404
Self-citationMachine learning strategies for systems with invariance properties
Ling, J., Jones, R. E., & Templeton, J. A. (2016) · Journal of Computational Physics · doi:10.1016/j.jcp.2016.05.003 · Cited by 398
Deep Fluids: A Generative Network for Parameterized Fluid Simulations
Kim, B., Azevedo, V. C., Thuerey, N., Kim, T., Gross, M., & Solenthaler, B. (2019) · Computer Graphics Forum · doi:10.1111/cgf.13619 · Cited by 372
Constrained sparse Galerkin regression
Loiseau, J.-C., & Brunton, S. L. (2018) · Journal of Fluid Mechanics · doi:10.1017/jfm.2017.823 · Cited by 346
Self-citationHansen, N., Niederberger, A. S. P., Guzzella, L., & Koumoutsakos, P. (2008) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2008.924423 · Cited by 327
Self-citationA Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems
Noé, F., & Nüske, F. (2013) · Multiscale Modeling & Simulation · doi:10.1137/110858616 · Cited by 327
A kernel-based method for data-driven koopman spectral analysis
Williams, M. O., Rowley, C. W., & Kevrekidis, I. G. (2015) · Journal of Computational Dynamics · doi:10.3934/jcd.2015005 · Cited by 325
Application of neural networks to turbulence control for drag reduction
Lee, C., Kim, J. J., Babcock, D., & Goodman, R. M. (1997) · Physics of Fluids · doi:10.1063/1.869290 · Cited by 321
Cluster-based reduced-order modelling of a mixing layer
Kaiser, E., Noack, B. R., Cordier, L., Spohn, A., Segond, M., Abel, M., Daviller, G., Östh, J., Krajnović, S., & Niven, R. K. (2014) · Journal of Fluid Mechanics · doi:10.1017/jfm.2014.355 · Cited by 320
Self-citationMachine Learning Control – Taming Nonlinear Dynamics and Turbulence
Duriez, T., Brunton, S. L., & Noack, B. R. (2016) · Fluid mechanics and its applications · doi:10.1007/978-3-319-40624-4 · Cited by 311
Self-citationXiao, H., Wu, J., Wang, J., Sun, R., & Roy, C. J. (2016) · Journal of Computational Physics · doi:10.1016/j.jcp.2016.07.038 · Cited by 306
Multi-dimensional Recurrent Neural Networks
Graves, A., Fernández, S., & Schmidhuber, J. (2007) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-74690-4_56 · Cited by 303
Subgrid modelling for two-dimensional turbulence using neural networks
Maulik, R., San, O., Rasheed, A., & Vedula, P. (2018) · Journal of Fluid Mechanics · doi:10.1017/jfm.2018.770 · Cited by 298
Xie, Y. X., Franz, A., Chu, M., & Thuerey, N. (2018) · ACM Transactions on Graphics · doi:10.1145/3197517.3201304 · Cited by 297
Randomized Algorithms for Matrices and Data
Mahoney, M. W. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000035 · Cited by 287
Data exploration of turbulence simulations using a database cluster
Perlman, E., Burns, R. C., Yi, L., & Meneveau, C. (2007) · ACM/IEEE Conference on Supercomputing (SC) · doi:10.1145/1362622.1362654 · Cited by 278
Learning probability distributions in continuous evolutionary algorithms – a comparative review
Kern, S., Müller, S. D., Hansen, N., Büche, D., Očenášek, J., & Koumoutsakos, P. (2004) · Natural Computing · doi:10.1023/b:naco.0000023416.59689.4e · Cited by 267
Self-citationState-of-the-art in aerodynamic shape optimisation methods
Skinner, S. N., & Zare‐Behtash, H. (2017) · Applied Soft Computing · doi:10.1016/j.asoc.2017.09.030 · Cited by 247
Identification of distributed parameter systems: A neural net based approach
González‐García, R., Rico-Martı́nez, R., & Kevrekidis, I. G. (1998) · Computers & Chemical Engineering · doi:10.1016/s0098-1354(98)00191-4 · Cited by 244
Optimal Approximation with Sparsely Connected Deep Neural Networks
Bölcskei, H., Grohs, P., Gitta Kutyniok, B., & Petersen, P. (2019) · SIAM Journal on Mathematics of Data Science · doi:10.1137/18m118709x · Cited by 244
Flow Navigation by Smart Microswimmers via Reinforcement Learning
Colabrese, S., Gustavsson, K., Celani, A., & Biferale, L. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.158004 · Cited by 238
Data-assisted reduced-order modeling of extreme events in complex dynamical systems
Wan, Z. Y., Vlachas, P. R., Koumoutsakos, P., & Sapsis, T. P. (2018) · PLoS ONE · doi:10.1371/journal.pone.0197704 · Cited by 222
Self-citationStep-size adaptation based on non-local use of selection information
Ostermeier, A., Gawelczyk, A., & Hansen, N. (1994) · Lecture notes in computer science · doi:10.1007/3-540-58484-6_263 · Cited by 198
Reduced-Order Nonlinear Unsteady Aerodynamic Modeling Using a Surrogate-Based Recurrence Framework
Glaz, B. J., Liu, L., & Friedmann, P. P. (2010) · AIAA Journal · doi:10.2514/1.j050471 · Cited by 197
Turbomachinery Blade Design Using a Navier–Stokes Solver and Artificial Neural Network
Pierret, S., & den Braembussche, R. A. V. (1999) · Journal of Turbomachinery · doi:10.1115/1.2841318 · Cited by 182
Bright, I., Lin, G., & Kutz, J. N. (2013) · Physics of Fluids · doi:10.1063/1.4836815 · Cited by 179
Glider soaring via reinforcement learning in the field
Reddy, G., Wong-Ng, J., Celani, A., B, T. J. S. A., & Vergassola, M. (2018) · Nature · doi:10.1038/s41586-018-0533-0 · Cited by 176
Learning to soar in turbulent environments
Reddy, G., Celani, A., B, T. J. S. A., & Vergassola, M. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1606075113 · Cited by 170
Evaluating convective heat transfer coefficients using neural networks
Jambunathan, K., Hartle, S. L., Ashforth-Frost, S. A., & Fontama, V. (1996) · International Journal of Heat and Mass Transfer · doi:10.1016/0017-9310(95)00332-0 · Cited by 163
Synchronisation through learning for two self-propelled swimmers
Novati, G., Verma, S., Alexeev, D., Rossinelli, D., van Rees, W. M., & Koumoutsakos, P. (2017) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/aa6311 · Cited by 157
Self-citationLearning to school in the presence of hydrodynamic interactions
Gazzola, M., Tchieu, A. A., Alexeev, D., Brauer, A. D., & Koumoutsakos, P. (2016) · Journal of Fluid Mechanics · doi:10.1017/jfm.2015.686 · Cited by 156
Self-citationC-start: optimal start of larval fish
Gazzola, M., van Rees, W. M., & Koumoutsakos, P. (2012) · Journal of Fluid Mechanics · doi:10.1017/jfm.2011.558 · Cited by 151
Self-citationPIV-DCNN: cascaded deep convolutional neural networks for particle image velocimetry
Lee, Y., Yang, H. S., & Yin, Z. (2017) · Experiments in Fluids · doi:10.1007/s00348-017-2456-1 · Cited by 150
Multiobjective evolutionary algorithm for the optimization of noisy combustion processes
Büche, D., Stoll, P., Dornberger, R., & Koumoutsakos, P. (2002) · IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews) · doi:10.1109/tsmcb.2002.804372 · Cited by 144
Self-citationDISCRETE- vs. CONTINUOUS-TIME NONLINEAR SIGNAL PROCESSING OF Cu ELECTRODISSOLUTION DATA
RICO-MARTÍNEZ, R., KRISCHER, K., KEVREKIDIS, I. G., KUBE, M. C., & HUDSON, J. L. (1992) · Chemical Engineering Communications · doi:10.1080/00986449208936084 · Cited by 144
Reinforcement Learning and Wavelet Adapted Vortex Methods for Simulations of Self-propelled Swimmers
Gazzola, M., Hejazialhosseini, B., & Koumoutsakos, P. (2014) · SIAM Journal on Scientific Computing · doi:10.1137/130943078 · Cited by 137
Self-citationMultifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets
Perdikaris, P. G., Venturi, D., & Karniadakis, G. E. (2016) · SIAM Journal on Scientific Computing · doi:10.1137/15m1055164 · Cited by 115
Analysis of multiphase flows using dual-energy gamma densitometry and neural networks
Bishop, C. M., & James, G. (1993) · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment · doi:10.1016/0168-9002(93)90728-z · Cited by 109
Low-Dimensional Approach for Reconstruction of Airfoil Data via Compressive Sensing
Bai, Z., Wimalajeewa, T., Berger, Z. P., Wang, G., Glauser, M., & Varshney, P. K. (2014) · AIAA Journal · doi:10.2514/1.j053287 · Cited by 98
Bénard, N., Pons‐Prats, J., Périaux, J., Bugeda, G., Braud, P., Bonnet, J.-P., & Moreau, É. (2016) · Experiments in Fluids · doi:10.1007/s00348-015-2107-3 · Cited by 96
Classifying vortex wakes using neural networks
Colvert, B., Alsalman, M., & Kanso, E. (2018) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/aaa787 · Cited by 95
Neural networks: Applications and opportunities in aeronautics
Faller, W. E., & Schreck, S. (1996) · Progress in Aerospace Sciences · doi:10.1016/0376-0421(95)00011-9 · Cited by 90
Aerodynamic shape design using evolutionary algorithms and new gradient-assisted metamodels
Giannakoglou, K. C., Papadimitriou, D., & Kampolis, I. C. (2006) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2005.12.008 · Cited by 84
Controlled gliding and perching through deep-reinforcement-learning
Novati, G., Mahadevan, L., & Koumoutsakos, P. (2019) · Physical Review Fluids · doi:10.1103/physrevfluids.4.093902 · Cited by 82
Self-citationTheodoridis, S. (2015) · Elsevier eBooks · doi:10.1016/b978-0-12-801522-3.00012-4 · Cited by 81
Network-theoretic approach to sparsified discrete vortex dynamics
Nair, A. G., & Taira, K. (2015) · Journal of Fluid Mechanics · doi:10.1017/jfm.2015.97 · Cited by 76
Variational tensor approach for approximating the rare-event kinetics of macromolecular systems
Nüske, F., Schneider, R., Vitalini, F., & Noé, F. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4940774 · Cited by 69
Intracycle angular velocity control of cross-flow turbines
Strom, B., Brunton, S. L., & Polagye, B. L. (2017) · Nature Energy · doi:10.1038/nenergy.2017.103 · Cited by 69
Self-citationEvolutionary Learning Algorithms for Neural Adaptive Control
Dracopoulos, D. C. (1997) · Perspectives in neural computing · doi:10.1007/978-1-4471-0903-7 · Cited by 61
Optimal morphokinematics for undulatory swimmers at intermediate Reynolds numbers
van Rees, W. M., Gazzola, M., & Koumoutsakos, P. (2015) · Journal of Fluid Mechanics · doi:10.1017/jfm.2015.283 · Cited by 61
Self-citationA new neural network for particle-tracking velocimetry
Labonté, G. (1999) · Experiments in Fluids · doi:10.1007/s003480050297 · Cited by 52
Cellular neural network to detect spurious vectors in PIV data
Liang, D., Jiang, C., & Li, Y. (2003) · Experiments in Fluids · doi:10.1007/s00348-002-0530-8 · Cited by 49
Grant, I., & Pan, X. (1995) · Experiments in Fluids · doi:10.1007/bf00189704 · Cited by 48
A statistical learning strategy for closed-loop control of fluid flows
Guéniat, F., Mathelin, L., & Hussaini, M. Y. (2016) · Theoretical and Computational Fluid Dynamics · doi:10.1007/s00162-016-0392-y · Cited by 48
Colabrese, S., Gustavsson, K., Celani, A., & Biferale, L. (2018) · Physical Review Fluids · doi:10.1103/physrevfluids.3.084301 · Cited by 48
Network community-based model reduction for vortical flows
Meena, M. G., Nair, A., & Taira, K. (2018) · Physical review. E · doi:10.1103/physreve.97.063103 · Cited by 45
Practical Issues in Temporal Difference Learning
Tesauro, G. J. (1992) · Machine Learning · doi:10.1023/a:1022624705476 · Cited by 41
Toward an Algorithmic Control Theory
Panagiotis Tsiotras, B., & Mesbahi, M. (2017) · Journal of Guidance Control and Dynamics · doi:10.2514/1.g002754 · Cited by 40
Qualitative dynamics of wave packets in turbulent jets
Semeraro, O., Lusseyran, F., Pastur, L. R., & Jordan, P. (2017) · Physical Review Fluids · doi:10.1103/physrevfluids.2.094605 · Cited by 38
Training bioinspired sensors to classify flows
Alsalman, M., Colvert, B., & Kanso, E. A. (2018) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/aaef1d · Cited by 33
Turbomachinery Blade Design Using a Navier-Stokes Solver and Artificial Neural Network
Pierret, S., & den Braembussche, R. A. V. (1998) · Volume 1: Turbomachinery · doi:10.1115/98-gt-004 · Cited by 33
Compact representation of wall-bounded turbulence using compressive sampling
Bourguignon, J.-L., Tropp, J. A., Sharma, A., & McKeon, B. (2014) · Physics of Fluids · doi:10.1063/1.4862303 · Cited by 27
A neural net approach in analyzing photograph in PIV
Teo, C. L., Lim, K. B., Hong, G. S., & Yeo, M. H. T. (2002) · Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics · doi:10.1109/icsmc.1991.169906 · Cited by 24
Computational Complexity and Simulation of Rare Events of Ising Spin Glasses
Pelikán, M., Očenášek, J., Trebst, S., Troyer, M., & Alet, F. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-24855-2_4 · Cited by 23
OPTIMAL SENSOR PLACEMENT FOR THE ESTIMATION OF TURBULENCE MODEL PARAMETERS IN CFD
Papadimitriou, D. I., & Papadimitriou, C. (2015) · International Journal for Uncertainty Quantification · doi:10.1615/int.j.uncertaintyquantification.2015015239 · Cited by 20
Experimental trajectory optimization of a flapping fin propulsor using an evolutionary strategy
Martin, N., & Gharib, M. (2018) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/aaefa5 · Cited by 17
ON NEURAL NETWORKS IN IDENTIFICATION AND CONTROL OF DYNAMIC SYSTEMS
Phan, M. Q., Juang, J.-N., & Hyland, D. C. (1995) · Series on stability, vibration and control of systems - Series B · doi:10.1142/9789812796455_0007 · Cited by 14
Machine Learning Based Detection of Flow Disturbances Using Surface Pressure Measurements
Hou, W., Darakananda, D., & Eldredge, J. D. (2019) · AIAA SciTech Forum · doi:10.2514/6.2019-1148 · Cited by 14
Efficient collective swimming by harnessing vortices through deep reinforcement learning
Verma, S., Novati, G., & Koumoutsakos, P. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1800923115 · Cited by 10
Self-citationHamdaouı, M., Chaskalovic, J., Doncieux, S., & Sagaut, P. (2010) · Journal of Aircraft · doi:10.2514/1.45046 · Cited by 7
Wang, J.-X., Wu, J.-L., & Xiao, H. (2016) · arXiv · doi:10.48550/arxiv.1606.07987 · Cited by 1
Toward Automated Design of Industrial-Strength Analog Circuits by Means of Genetic Programming
Koza, J. R., Jones, L. W., Keane, M. A., Streeter, M. J., & Al-Sakran, S. H. (n.d.) · Genetic Programming · doi:10.1007/0-387-23254-0_8
Decision support systems for drought management
Loucks, D. (2005) · Drought Management and Planning for Water Resources · doi:10.1201/9780203486368.ch5
Whither Turbulence and Big Data for the Twenty-First Century
Pollard, A. (2016) · Whither Turbulence and Big Data in the 21st Century? · doi:10.1007/978-3-319-41217-7_30
Cybernetics and psychopathology.
Wiener, N. (n.d.) · Cybernetics, or control and communication in the animal and the machine (2nd ed.). · doi:10.1037/13140-007
Detecting exotic wakes with hydrodynamic sensors
Wang, M., & Hemati, M. S. (2017) · arXiv · doi:10.48550/arxiv.1711.10576
Super-resolution reconstruction of turbulent flows with machine learning
Fukami, K., Fukagata, K., & Taira, K. (2018) · arXiv · doi:10.48550/arxiv.1811.11328
Deep Fluids: A Generative Network for Parameterized Fluid Simulations
Kim, B., Azevedo, V. C., Thuerey, N., Kim, T., Gross, M., & Solenthaler, B. (2018) · arXiv · doi:10.48550/arxiv.1806.02071
Qualitative dynamics of wavepackets in turbulent jets
Semeraro, O., Lusseyran, F., Pastur, L., & Jordan, P. (2016) · arXiv · doi:10.48550/arxiv.1608.06750
Using Simulation and Domain Adaptation to Improve Efficiency of Deep Robotic Grasping
Bousmalis, K., Irpan, A., Wohlhart, P., Bai, Y., Kelcey, M., Kalakrishnan, M., Downs, L., Ibarz, J., Pastor, P., Konolige, K., et al. (2017) · arXiv · doi:10.48550/arxiv.1709.07857
Turbulence and the dynamics of coherent structures. III. Dynamics and scaling
Sirovich, L. (1987) · Quarterly of Applied Mathematics · doi:10.1090/qam/910464
Meijering, E., & Falk, H. (2002) · Proceedings of the IEEE · doi:10.1109/jproc.2002.993399
Demo: Robust face recognition via sparse representation
Wright, J., Ganesh, A., Zhou, Z., Wagner, A., & Ma, Y. (2008) · 2008 8th IEEE International Conference on Automatic Face & Gesture Recognition · doi:10.1109/afgr.2008.4813404
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
Cited by
Sorted by citations
Digital twin: values, challenges and enablers from a modeling perspective
Rasheed, A., San, O., & Kvamsdal, T. (2020) · IEEE Access · doi:10.1109/access.2020.2970143 · Cited by 1,952
“For example, we refer to recent surveys of ML in domainspecific areas of molecular and material science [326] and fluid mechanics [327].”
A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
Haghighat, E., Raissi, M., Moure, A., Gómez, H., & Juanes, R. (2021) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2021.113741 · Cited by 1,556
“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.”
MethodJin, X., Cai, S., Li, H., & Karniadakis, G. E. (2020) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.109951 · Cited by 1,218
“Comprehensive summaries of progress in fluid mechanics due to the introduction of various machine learning techniques can be found in [11, 12].”
BackgroundAlzubaidi, L., Bai, J., Al-Sabaawi, A., Santamaría, J., Albahri, A. S., Al-dabbagh, B. S. N., Fadhel, M. A., Manoufali, M., Zhang, J., Al-Timemy, A. H., et al. (2023) · Journal Of Big Data · doi:10.1186/s40537-023-00727-2 · Cited by 1,057
Gao, H., Sun, L., & Wang, J. (2020) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.110079 · Cited by 693
Metadata
- 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
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review