Pith. sign in

REVIEW 2 major objections 2 minor 58 references

Data-driven surrogate models for forecasting experimentally measured fluid flows

T0 review · 2 major / 2 minor · reviewed 2026-06-27 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Experimentally trained surrogate models forecast short-term cylinder wake flows but lose high-frequency transients amid noise.

desk verdict This paper tests four off-the-shelf models on real PIV cylinder-wake data and shows short-horizon forecasts work while transients and high frequencies drop out fast under noise and partial observations. read the letter →

arxiv 2606.10848 v2 pith:OG2U3VT7 submitted 2026-06-09 physics.flu-dyn

Peter I. Renn , Emily H. Palmer , Cong Wang , Morteza Gharib This is my paper · ORCID
classification physics.flu-dyn
keywords data-drivenmodelingsurrogatemodelscylinderwakeparticleimagevelocimetryflowforecastingvortexsheddingReynoldsnumberneuraloperators
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tests whether data-driven surrogate models can forecast the time evolution of fluid flows from real experimental measurements around a cylinder. The authors train fully convolutional networks, U-Nets, Fourier neural operators, and dynamic mode decomposition models on two-dimensional particle image velocimetry velocity fields collected at Reynolds numbers from 230 to 2920. The models deliver meaningful short-horizon predictions, carry low-frequency dynamics forward over longer periods, and run faster than real time. They lose accuracy on transient features and high-frequency energy when the input data contain measurement noise and incomplete state information. The results illustrate the practical limits of purely data-driven approaches when observations are imperfect, as is typical in engineering settings.

What carries the argument

Fully convolutional neural networks, U-Nets, Fourier neural operators, and dynamic mode decomposition models trained end-to-end on sequences of measured two-component velocity fields to predict future fields.

What would settle it

Evaluate the trained models on fresh experimental particle image velocimetry runs at a Reynolds number outside the 230-2920 training interval or with deliberately added measurement noise, then measure whether high-frequency spectral error stays within the levels reported in the paper.

Watch

Extended reading notes

Core claim

Surrogate models trained on experimental particle image velocimetry measurements of cylinder wakes in the subcritical vortex shedding regime deliver meaningful short-horizon forecasts, propagate low-frequency dynamics over longer periods, and achieve faster-than-real-time evaluation, yet they fail to preserve transient flow features and high-frequency energy content when faced with noisy measurements and incomplete state observations across the tested Reynolds number range.

Load-bearing premise

The particle image velocimetry dataset at the chosen Reynolds numbers supplies a training distribution rich enough for the models to learn dynamics that generalize despite noise and partial observations.

Editorial extensions

If this is right

  • Short-horizon forecasts remain usable for applications such as flow control.
  • Low-frequency wake dynamics propagate reliably over multi-step horizons at fixed Reynolds number.
  • Forecast skill declines as Reynolds number rises because three-dimensional and turbulent effects become harder to observe and model.
  • High-frequency content and transient structures are not retained when observations are noisy or incomplete.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Real deployments would likely require explicit denoising or state-completion steps before training to mitigate the observed loss of high-frequency content.
  • Testing the same architectures on flows with different geometries would reveal whether the cylinder-wake results generalize or remain configuration-specific.
  • Hybrid architectures that embed known conservation laws might reduce the drift in high-frequency energy that pure data-driven models exhibit.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes data-driven surrogate models (fully convolutional neural networks, U-Nets, Fourier neural operators, and DMD) trained on 2D two-component PIV measurements of subcritical cylinder wakes. At fixed Re=590 it examines forecast quality over extended horizons; across Re=230–2920 it studies the effect of increasing turbulence and three-dimensionality. The central empirical claim is that the models deliver meaningful short-horizon predictions, propagate low-frequency dynamics over longer horizons, and run faster than real time, yet fail to preserve transient features and high-frequency energy when confronted with measurement noise and incomplete (planar) observations.

Significance. If the quantitative results hold, the work supplies a balanced, experimentally grounded assessment of the practical limits of data-driven forecasting under realistic measurement constraints. By documenting both short-term utility and the systematic loss of transients/high-frequency content, it supplies concrete guidance for flow-control applications and highlights open challenges that purely data-driven approaches must still overcome.

major comments (2)
  1. [Abstract, §4] Abstract and §4 (results): the statements that models “provide meaningful predictions over short time horizons” and “struggle to preserve transient flow features” are presented without accompanying quantitative metrics (e.g., time-averaged RMSE, spectral energy error, or correlation coefficients) or error bars on the held-out experimental data. Because the central claim rests on the contrast between short- and long-horizon behavior, the absence of these numbers prevents verification of the reported performance gap.
  2. [§3.2, §4.3] §3.2 (training details) and §4.3 (Re sweep): the manuscript does not report the precise training/validation/test split sizes, the number of independent experimental runs, or any hyper-parameter search protocol. These omissions are load-bearing for the claim that the observed degradation at higher Re is due to flow physics rather than insufficient or non-representative training data.
minor comments (2)
  1. [Figures 4–7] Figure captions should explicitly state the forecast horizon (in shedding periods) and the precise error metric shown in each panel.
  2. [§2] Notation for the velocity components (u,v) and the non-dimensional time t* should be introduced once in §2 and used consistently thereafter.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and will revise the manuscript accordingly to strengthen the quantitative support and reproducibility of our claims.

read point-by-point responses

  1. Referee: [Abstract, §4] Abstract and §4 (results): the statements that models “provide meaningful predictions over short time horizons” and “struggle to preserve transient flow features” are presented without accompanying quantitative metrics (e.g., time-averaged RMSE, spectral energy error, or correlation coefficients) or error bars on the held-out experimental data. Because the central claim rests on the contrast between short- and long-horizon behavior, the absence of these numbers prevents verification of the reported performance gap.

    Authors: We agree that explicit quantitative metrics are needed to substantiate the short- versus long-horizon claims. In the revised manuscript we will add time-averaged RMSE, spectral energy error, and correlation coefficients (with error bars) evaluated on the held-out experimental data, both for the fixed-Re=590 case and the Re sweep, to directly quantify the performance degradation. revision: yes

  2. Referee: [§3.2, §4.3] §3.2 (training details) and §4.3 (Re sweep): the manuscript does not report the precise training/validation/test split sizes, the number of independent experimental runs, or any hyper-parameter search protocol. These omissions are load-bearing for the claim that the observed degradation at higher Re is due to flow physics rather than insufficient or non-representative training data.

    Authors: We acknowledge that these details are required for reproducibility and to support the physical interpretation of the Re trends. The revised manuscript will explicitly state the training/validation/test split sizes (in snapshots and number of runs), the total number of independent experimental runs at each Re, and the hyper-parameter search procedure employed. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity detected

full rationale

The paper is an empirical evaluation of surrogate models (CNNs, U-Nets, FNOs, DMD) trained on held-out experimental PIV velocity fields for cylinder wakes. No derivation chain, uniqueness theorem, or ansatz is invoked; performance is measured directly against independent test data at fixed and varying Re. No self-citation is load-bearing for any central claim, and the narrative explicitly documents limitations with transients, high-frequency content, noise, and incomplete observations. The result is therefore self-contained against external benchmarks with no reduction of outputs to inputs by construction.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The central claim rests on standard supervised learning assumptions plus the representativeness of the PIV dataset; no new physical entities or ad-hoc constants are introduced.

assumptions (1)
  • domain assumption The experimental velocity fields constitute a sufficiently informative partial observation of the underlying Navier-Stokes dynamics for supervised training.
    Invoked when claiming that models can be trained to forecast from limited PIV data (abstract).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Data-driven surrogate models for forecasting experimentally measured fluid flows." pith.science (2026). https://pith.science/paper/OG2U3VT7

@misc{pith2026260610848,
  author       = {Pith},
  title        = {Pith review of: Data-driven surrogate models for forecasting experimentally measured fluid flows},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OG2U3VT7}},
  note         = {Machine review of arXiv:2606.10848}
}
read the original abstract

Data-driven modeling shows significant promise for faster-than-real-time forecasting of fluid flows. For real-world engineering applications (e.g., flow control), models must contend with limited, imperfect, and incomplete experimental measurements. In this work, we present an analysis of data-driven surrogate models trained to forecast the time-evolution of experimentally measured cylinder wakes in the subcritical vortex shedding regime. Using a dataset of two-dimensional, two-component particle image velocimetry measurements, we train fully convolutional neural networks, U-Nets, Fourier neural operators, and dynamic mode decomposition-based models to forecast the development of experimentally measured velocity fields. To characterize data-driven approaches contending with transient flow features and limited, imperfect observations, the development of predictions over extended forecast horizons is examined at a fixed Reynolds number (Re = 590). Next, models are trained at a range of Reynolds numbers (Re = 230 to Re = 2920) to investigate the impact of increasingly turbulent and three-dimensional flow phenomena, and the challenges associated with measuring them, on forecast quality. We find that experimentally trained surrogate models can provide meaningful predictions over short time horizons, propagate low-frequency dynamics over longer forecast periods, and achieve faster-than-real-time evaluation. However, the data-driven models struggle to preserve transient flow features and high-frequency energy content when faced with noisy measurements and incomplete state observations. This emphasizes the underlying challenges that remain for data-driven modeling approaches to effectively contend with fluid dynamics in real-world engineering applications, where observations are often imperfect and limited.

Figures

Figures reproduced from arXiv: 2606.10848 by the authors.

Figure 1
Figure 1. FIG. 1. Snapshots of velocity fields across the Reynolds numbers tested. Colorbar scales given in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Schematic of the imaging region of interest, outlined by the black dashed line, relative to [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Cumulative energy of POD modes for [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Actual and predicted y-component velocity fields with error for all models. The results of [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Mean error per time-step for various models at [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Comparison of fluctuating, periodic, and mean component error. (b) Estimated planar [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Relationship between mean prediction error and Reynolds number for all models. [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. (a) Comparison of fluctuating, periodic, and mean component error. (b) Estimated planar [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Measured turbulence intensity in the cylinder wake at [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Relationships between error, time-step, and Reynolds number for (a) U-Net, (b) FNO, (c) [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Relationship between error and time-step for models with and without a time-delay [PITH_FULL_IMAGE:figures/full_fig_p027_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

58 extracted references · 1 canonical work pages

  1. [1]

    An acrylic cylinder of diameterD= 9.53×10 −3 m was mounted to span the walls of the test section approximately equidistant from the free surface and the tunnel floor

    Data acquisition Data was collected using a free-surface water tunnel with test section dimensions of 0.15 m (W)×0.15 m (H)×0.61 m (L). An acrylic cylinder of diameterD= 9.53×10 −3 m was mounted to span the walls of the test section approximately equidistant from the free surface and the tunnel floor. The cylinder aspect ratio was approximately 15.7. Test...

  2. [2]

    encoder-decoder

    Fully convolutional networks Fully convolutional networks (FCN), introduced by Longet al.[29], are networks com- prised entirely of convolutional layers. These layers, commonly used for learning tasks involving images, perform convolution operations between filters and the channels of an input array (i.e., an image). The output of these convolutions is kn...

  3. [3]

    U-Net One of the most popular network architectures in modern deep learning, U-Net was first introduced by Ronnebergeret al.[30] for biomedical image segmentation. U-Nets can be structured with convolutional layers similar to FCNs, but also feature skip connections where the output of several layers of the encoder portion of the network are directly conca...

  4. [4]

    Fourier neural operators Neural operators are distinct from standard neural networks (e.g., FCNs and U-Nets) for their ability to directly approximate operators from data alone [31]. This includes operators that map between sets of functions related by a family of PDEs (e.g., the Navier-Stokes equations), making these methods of particular interest for pr...

  5. [5]

    A departure from the network-based deep learning methods discussed above, DMD allows for the development of reduced-order linear models of nonlin- ear dynamical systems

    Dynamic mode decomposition Dynamic mode decomposition (DMD), introduced by Schmid [33], is a method of data- driven reduced-order modeling. A departure from the network-based deep learning methods discussed above, DMD allows for the development of reduced-order linear models of nonlin- ear dynamical systems. Especially popular in fluid mechanics applicati...

    2000

  6. [6]

    The velocity fields are predicted in increments of non-dimensional time approximately equal tot ∗ ≈0.18

    Evaluation speed Table I shows the respective mean evaluation times of the models. The velocity fields are predicted in increments of non-dimensional time approximately equal tot ∗ ≈0.18. As the non-dimensional time was held constant, the corresponding physical time between snapshots varies with Reynolds number, from 5 ms (Re= 2920) to 62.5 ms (Re= 230). ...

  7. [7]

    S. L. Brunton, B. R. Noack, and P. Koumoutsakos, Machine learning for fluid mechanics, Annual Review of Fluid Mechanics (2020)

    2020

  8. [8]

    Srinivasan, L

    P. Srinivasan, L. Guastoni, H. Azizpour, P. Schlatter, and R. Vinuesa, Predictions of turbulent shear flows using deep neural networks, Physical Review Fluids4(2019)

    2019

Show all 58 references
  1. [9]

    Nakamura, K

    T. Nakamura, K. Fukami, and K. Hasegawa, Convolutional neural network and long short- term memory based reduced order surrogate for minimal turbulent channel flow, Physics of Fluids33(2021)

    2021

  2. [10]

    P. L. Wu, H. S. Gao, Q. Wang, and P. Y. Wang, A novel forecast framework for unsteady flows based on a convolutional neural network, Physics of Fluids34(2022)

    2022

  3. [11]

    Fukami, T

    K. Fukami, T. Murata, K. Zhang, and K. Fukagata, Identification of nonlinear dynamics with low-dimensionalized flow representations, Journal of Fluid Mechanics926(2021)

    2021

  4. [12]

    R. Wang, K. Kashinath, M. Mustafa, A. Albert, and R. Yu, Towards physics-informed deep learning for turbulent flow prediction, Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (2020)

    2020

  5. [13]

    Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anand- kumar, Fourier neural operator for parametric partial differential equations, ICLR (2021)

    2021

  6. [14]

    G. Wen, Z. Li, K. Azizzadenesheli, A. Anandkumar, and S. M. Benson, U-fno—an enhanced fourier neural operator-based deep-learning model for multiphase flow, Advances in Water Resources163(2022)

    2022

  7. [15]

    Z. Li, W. Peng, Z. Yuan, and J. Wang, Long-term predictions of turbulence by implicit u-net enhanced fourier neural operator, Physics of Fluids35(2023)

    2023

  8. [16]

    R. Han, X. Yang, and W. Liu, Unsteady flow prediction based on a hybrid network-operator learning model, Physics of Fluids37(2025)

    2025

  9. [17]

    Williamson, Vortex dynamics in the cylinder wake, Annual Review of Fluid Mechanics (1996)

    C. Williamson, Vortex dynamics in the cylinder wake, Annual Review of Fluid Mechanics (1996)

    1996

  10. [18]

    Hasegawa, K

    K. Hasegawa, K. Fukami, T. Murata, and K. Fukagata, Machine-learning-based reduced- order modeling for unsteady flows around bluff bodies of various shapes, Theoretical and Computational Fluid Dynamics34(2020). 30

    2020

  11. [19]

    Hasegawa, K

    K. Hasegawa, K. Fukami, T. Murata, and K. Fukagata, Cnn-lstm based reduced order model- ing of two-dimensional unsteady flows around a circular cylinder at different reynolds numbers, Fluid Dynamics Research52(2020)

    2020

  12. [20]

    Moriomoto, K

    M. Moriomoto, K. Fukami, K. Zhang, and K. Fukagata, Generalization techniques of neural networks for fluid flow estimation, Neural Computing and Applications34(2021)

    2021

  13. [21]

    Williamson, Three-dimensional wake transition, Journal of Fluid Mechanics (1996)

    C. Williamson, Three-dimensional wake transition, Journal of Fluid Mechanics (1996)

    1996

  14. [22]

    Roshko,Report 1191: On the Development of Turbulent Wakes from Vortex Streets, Tech

    A. Roshko,Report 1191: On the Development of Turbulent Wakes from Vortex Streets, Tech. Rep. (National Advisory Committee for Aeronautics, 1958)

    1958

  15. [23]

    Jeon and M

    D. Jeon and M. Gharib, On the relationship between the vortex formation process and cylinder wake vortex patterns, Journal of Fluid Mechanics (2004)

    2004

  16. [24]

    P. I. Renn, E. H. Palmer, and M. Gharib, Experimental dataset of turbulent cylinder wake velocity fields for deep learning, Scientific Data (2026)

    2026

  17. [25]

    Hammache and M

    M. Hammache and M. Gharib, An experimental study of the parallel and oblique vortex shedding from circular cylinders, Journal of Fluid Mechanics232, 567 (1991)

    1991

  18. [26]

    Prasad and C

    A. Prasad and C. H. Williamson, Three-dimensional effects in turbulent bluff-body wakes, Journal of Fluid Mechanics343, 235 (1997)

    1997

  19. [27]

    Prasad and C

    A. Prasad and C. H. Williamson, The instability of the shear layer separating from a bluff body, Journal of fluid mechanics333, 375 (1997)

    1997

  20. [28]

    Reynolds and A

    W. Reynolds and A. Hussain, The mechanics of an organized wave in turbulent shear flow. part 3. theoretical models and comparisons with experiments, Journal of Fluid Mechanics (1971)

    1971

  21. [29]

    Berkooz, P

    G. Berkooz, P. Holmes, and J. L. Lumley, The proper orthogonal decomposition in the analysis of turbulent flows, Annual Rev. Fluid Mech. (1993)

    1993

  22. [30]

    Perrin, M

    R. Perrin, M. Braza, E. Cid, S. Cazin, A. Barthet, A. Sevrain, C. Mockett, and F. Thiele, Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high reynolds number using pod, Experiments in Fluids43, 341 (2007)

    2007

  23. [31]

    B. v. Oudheusden, F. Scarano, N. v. Hinsberg, and D. Watt, Phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence, Experiments in fluids39, 86 (2005)

    2005

  24. [32]

    Achermann, T

    F. Achermann, T. Stastny, B. Danciu, A. Kolobov, J. J. Chung, R. Siegwart, and N. Lawrance, Windseer: real-time volumetric wind prediction over complex terrain aboard a small uncrewed 31 aerial vehicle, Nature Communications15, 3507 (2024)

    2024

  25. [33]

    P. J. Schmid, Dynamic mode decomposition and its variants, Annual Review of Fluid Me- chanics54, 225 (2022)

    2022

  26. [34]

    Pan and K

    S. Pan and K. Duraisamy, On the structure of time-delay embedding in linear models of non-linear dynamical systems, Chaos (2020)

    2020

  27. [35]

    J. Long, E. Shelhamer, and T. Darrell, Fully convolutional networks for semantic segmentation, inProceedings of the IEEE conference on computer vision and pattern recognition(2015) pp. 3431–3440

    2015

  28. [36]

    Ronneberger, P

    O. Ronneberger, P. Fischer, and T. Brox, U-net: Convolutional networks for biomedical image segmentation, inMedical Image Computing and Computer-Assisted Intervention(2015)

    2015

  29. [37]

    Kovachki, Z

    N. Kovachki, Z. Li, B. Liu, K. Azizzadenesheli, K. Bhattacharya, A. Stuart, and A. Anandku- mar, Neural operator: Learning maps between function spaces, Journal of Machine Learning Research (to appear, on Arxiv) (2022)

    2022

  30. [38]

    Kovachki, S

    N. Kovachki, S. Lanthaler, and S. Mishra, On universal approximation and error bounds for fourier neural operators, Journal of Machine Learning Research (2021)

    2021

  31. [39]

    P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, Journal of fluid mechanics656, 5 (2010)

    2010

  32. [40]

    H´ eas and C

    P. H´ eas and C. Herzet, Low-rank dynamic mode decomposition: An exact and tractable solution, Journal of Nonlinear Science32, 8 (2022)

    2022

  33. [41]

    S. M. Ichinaga, F. Andreuzzi, N. Demo, M. Tezzele, K. Lapo, G. Rozza, S. L. Brunton, and J. N. Kutz, Pydmd: A python package for robust dynamic mode decomposition, Journal of Machine Learning Research25, 1 (2024)

    2024

  34. [42]

    Rahaman, A

    N. Rahaman, A. Baratin, D. Arpit, F. Draxler, M. Lin, F. Hamprecht, Y. Bengio, and A. Courville, On the spectral bias of neural networks, inInternational conference on ma- chine learning(PMLR, 2019) pp. 5301–5310

    2019

  35. [43]

    D. Duke, J. Soria, and D. Honnery, An error analysis of the dynamic mode decomposition, Experiments in fluids52, 529 (2012)

    2012

  36. [44]

    M. S. Hemati, C. W. Rowley, E. A. Deem, and L. N. Cattafesta, De-biasing the dynamic mode decomposition for applied koopman spectral analysis of noisy datasets, Theoretical and Computational Fluid Dynamics31, 349 (2017). 32

    2017

  37. [45]

    Oommenn, S

    V. Oommenn, S. Kohdakarami, A. Bora, Z. Wang, and G. E. Karniadakis, Learning turbu- lent flows with generative models for super resolution and sparse flow reconstruction, Nature Communications (2026)

    2026

  38. [46]

    Z. Li, H. Zheng, N. Kovachki, D. Jin, H. Chen, B. Liu, K. Azizzadenesheli, and A. Anandkumar, Physics-informed neural operator for learning partial differential equations, arXiv:2111.03794 (2021)

    2021

  39. [47]

    G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang, Physics- informed machine learning, Nature Reviews Physics3, 422 (2021)

    2021

  40. [48]

    Willert, M

    C. Willert, M. Munson, and M. Gharib, Real-time particle image velocimetry for closed-loop flow control applications, inConference proceedings(2010)

    2010

  41. [49]

    Kreizer, D

    M. Kreizer, D. Ratner, and A. Liberzon, Real-time image processing for particle tracking velocimetry, Experiments in fluids48, 105 (2010)

    2010

  42. [50]

    Varon, J.-L

    E. Varon, J.-L. Aider, Y. Eulalie, S. Edwige, and P. Gilotte, Adaptive control of the dynamics of a fully turbulent bimodal wake using real-time piv, Experiments in Fluids60, 1 (2019)

    2019

  43. [51]

    S. A. Bollt, S. H. Foxman, and M. Gharib, Rapidpiv: full flow-field khz piv for real-time display and control, Measurement Science and Technology36, 105116 (2025)

    2025

  44. [52]

    Bright, G

    I. Bright, G. Lin, and J. N. Kutz, Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements, Physics of Fluids25(2013)

    2013

  45. [53]

    J. L. Callaham, K. Maeda, and S. L. Brunton, Robust flow reconstruction from limited mea- surements via sparse representation, Physical Review Fluids4, 103907 (2019)

    2019

  46. [54]

    Loiseau, B

    J.-C. Loiseau, B. R. Noack, and S. L. Brunton, Sparse reduced-order modelling: sensor-based dynamics to full-state estimation, Journal of Fluid Mechanics844, 459 (2018)

    2018

  47. [55]

    Fukami, B

    K. Fukami, B. An, M. Nohmi, M. Obuchi, and K. Taira, Machine-learning-based reconstruc- tion of turbulent vortices from sparse pressure sensors in a pump sump, Journal of Fluids Engineering144, 121501 (2022)

    2022

  48. [56]

    Fukami, R

    K. Fukami, R. Maulik, N. Ramachandra, K. Fukagata, and K. Taira, Global field recon- struction from sparse sensors with voronoi tessellation-assisted deep learning, Nature Machine Intelligence3, 945 (2021)

    2021

  49. [57]

    N. B. Erichson, L. Mathelin, Z. Yao, S. L. Brunton, M. W. Mahoney, and J. N. Kutz, Shallow neural networks for fluid flow reconstruction with limited sensors, Proceedings of the Royal 33 Society A476, 20200097 (2020)

    2020

  50. [58]

    K. H. Manohar, C. Morton, and P. Ziad´ e, Sparse sensor-based cylinder flow estimation using artificial neural networks, Physical Review Fluids7, 024707 (2022). 34

    2022

Pith tools

Reviewed June 27, 2026 · model on record in the stance chip above.