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arxiv: 2605.26806 · v1 · pith:52JX5ZSA · submitted 2026-05-26 · physics.flu-dyn

Supervised machine learning of compressible flow past a rotating cylinder

Sanjeev Kumar , Santosh Kumar , Aditi Sengupta This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-06-29 15:53 UTCgrok-4.3pith:52JX5ZSArecord.jsonopen to challenge →

classification physics.flu-dyn
keywords compressible flowrotating cylinderartificial neural networkssurrogate modelingvortex sheddingflow bifurcationReynolds numberaerodynamic loads
0
0 comments X

The pith

Artificial neural networks trained on 101 high-fidelity simulations serve as reliable surrogates for predicting lift, drag, and instability onset in compressible flow past a rotating cylinder.

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

The paper examines compressible flow past a rapidly rotating cylinder across Reynolds numbers from 1000 to 6000 using 101 expensive numerical simulations. It identifies a shift from periodic vortex shedding to multi-mode oscillations with a bifurcation near Re = 5650. Polynomial and Bayesian regression methods are compared as data-driven fits, but artificial neural networks are shown to deliver high accuracy on maximum lift and instability timing while handling the harder drag signal adequately. The networks are also tested as generative models that can fill in behavior at Reynolds numbers absent from the training data.

Core claim

When trained on data from 101 high-fidelity compressible flow simulations, artificial neural networks achieve excellent predictive accuracy for maximum lift coefficient and instability onset time, while maintaining reasonable fidelity for the more challenging drag coefficient, allowing them to function as efficient and reliable surrogates for the nonlinear fluid problem that includes bifurcation and mode coupling.

What carries the argument

Artificial neural networks developed as high-capacity surrogate models, trained on the 101-simulation database and evaluated both for regression and for generative reconstruction at unseen Reynolds numbers.

If this is right

  • ANNs outperform polynomial regression near the bifurcation point where localized fluctuations appear.
  • Bayesian spline models improve uncertainty estimates but are outpaced by ANNs in overall capacity.
  • The trained network can reconstruct lift and drag signals at Reynolds numbers not present in the training set.
  • The same supervised learning approach is positioned for use on other fluid problems with strong nonlinear dependencies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar ANN surrogates could lower the cost of exploring rotating-body flows at additional Mach numbers or cylinder aspect ratios.
  • The hierarchical refinement step might be adapted to combine data from simulations at different grid resolutions.
  • Direct comparison against wind-tunnel measurements at the same Reynolds numbers would test whether simulation-trained networks transfer to experiments.

Load-bearing premise

The 101 high-fidelity simulations form a sufficiently dense and representative set that lets the networks generalize accurately to new Reynolds numbers and capture the bifurcation without overfitting.

What would settle it

Large prediction errors on drag coefficient or onset time when the trained network is tested at a Reynolds number between 1000 and 6000 that was deliberately withheld from the original 101 simulations would show the surrogate claim does not hold.

Figures

Figures reproduced from arXiv: 2605.26806 by Aditi Sengupta, Sanjeev Kumar, Santosh Kumar.

Figure 1
Figure 1. Figure 1: Schematic of uniform flow past a rotating cylinder with surface speed, [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Spanwise vorticity contours for flow past a rotating cylinder with [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Spanwise vorticity contours for flow past a rotating cylinder with [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Time variation of lift coefficient for (a) [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Time variation of lift coefficient for (a) [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Time variation of drag coefficient for (a) [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Time variation of drag coefficient for (a) [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Variation of (a) maximum Cl , (b) maximum Cd, and (c) onset time of instability, with Re∞, along with polynomial curve fits of different degrees. As Re∞ approaches the critical value, the separated shear layer becomes increasingly thin and susceptible to secondary instabilities. Small perturba￾tions in the shear layer amplify rapidly, leading to stronger vortex roll-up and enhanced vortex–vortex interactio… view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of simulated variation of (a) maximum [PITH_FULL_IMAGE:figures/full_fig_p029_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of simulated variation of (a) maximum [PITH_FULL_IMAGE:figures/full_fig_p032_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of simulated variation of (a) maximum [PITH_FULL_IMAGE:figures/full_fig_p034_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Parity plot of predicted value from ANN and actual value from simulation for [PITH_FULL_IMAGE:figures/full_fig_p041_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Parity plot of predicted value from ANN and actual value from simulation for [PITH_FULL_IMAGE:figures/full_fig_p042_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of simulated maximum Cd vs Re∞ with the predicted values from the generative ANN for (a) level-1 refinement and (b) level-2 refinement. 4. Summary and Conclusions This study presents a comprehensive investigation of compressible flow past a rapidly rotating cylinder over a wide Reynolds number range (Re∞ = 1000−6000), combining high-fidelity numerical simulations with data-driven modeling appro… view at source ↗
read the original abstract

High-fidelity numerical simulations of compressible flow past a rapidly rotating cylinder are used to investigate the evolution of aerodynamic loads and flow instability over a wide range of Reynolds numbers (Re = 1000 to 6000). The study reveals a transition from periodic vortex shedding to complex multi-mode oscillatory states, with a critical bifurcation identified near Re = 5650. Spectral analysis of lift and drag signals shows the emergence and interaction of multiple dominant frequencies, accompanied by amplitude modulation and nonlinear mode coupling in the post-bifurcation regime. To model these highly nonlinear dependencies, data-driven approaches are systematically explored using a database of 101 high-fidelity simulations (1 million core hours). Polynomial regression provides baseline fits but fails to capture localized fluctuations near bifurcation. Bayesian regression frameworks employing B-spline and Gaussian radial basis functions improve flexibility and uncertainty quantification, with spline-based models demonstrating superior performance in capturing piecewise nonlinear trends. Artificial neural networks (ANNs) are then developed as high-capacity surrogate models, achieving excellent predictive accuracy for maximum lift coefficient and instability onset time, while maintaining reasonable fidelity for the more challenging drag coefficient. Beyond regression, the ANN is further evaluated as a generative model to reconstruct flow behavior at unseen Re. A hierarchical refinement strategy is introduced, and results show that when trained on high-fidelity data, ANN-based models can serve as efficient and reliable surrogates for complex fluid dynamics problems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper reports high-fidelity simulations of compressible flow past a rotating cylinder for Re = 1000–6000, identifying a bifurcation near Re = 5650 that produces a transition from periodic vortex shedding to multi-mode oscillatory states with nonlinear frequency coupling. From a database of 101 simulations (1 million core hours), it systematically compares polynomial regression (which fails near the bifurcation), Bayesian regression using B-splines and Gaussian RBFs, and artificial neural networks (ANNs). The central claim is that ANNs achieve excellent predictive accuracy for maximum lift coefficient and instability onset time (with reasonable fidelity for drag) and can serve as generative surrogates for unseen Re via a hierarchical refinement strategy.

Significance. If the validation and generalization claims are substantiated, the work would offer a useful case study of ML surrogates for compressible flows exhibiting bifurcations and multi-mode coupling, leveraging a substantial high-fidelity database and a systematic method comparison. The hierarchical refinement approach and the contrast between polynomial failure and ANN success near the transition are constructive elements. At present, however, the absence of quantitative error metrics and out-of-sample testing limits the strength of the surrogate reliability conclusion.

major comments (3)
  1. [Abstract] Abstract: the assertion of 'excellent predictive accuracy' for maximum lift coefficient and instability onset time is unsupported by any reported quantitative metrics (e.g., MSE, MAE, or R² on a test partition), cross-validation procedure, or explicit test-set performance; the same holds for the 'reasonable fidelity' claim for drag.
  2. [Data-driven modeling and results sections] Data-driven modeling and results sections: all performance figures are obtained by fitting and evaluating on the identical 101-simulation database; no hold-out set, k-fold cross-validation, or explicit train/test split is described, so statements of prediction 'for unseen Re' remain interpolations within the convex hull of the training points rather than demonstrated generalization.
  3. [Bifurcation analysis and surrogate evaluation sections] Bifurcation analysis and surrogate evaluation sections: the distribution and local spacing of the 101 Re samples around the critical value Re ≈ 5650 are not reported; without this information it is impossible to verify that the training set is dense enough to capture the transition to multi-mode states or to rule out extrapolation failure in the ANN predictions of onset time and lift.
minor comments (2)
  1. [Abstract and §4] The abstract and main text refer to 'polynomial regression' and 'Bayesian regression frameworks' without specifying the exact polynomial degree or the prior choices and hyperparameter settings used for the B-spline and RBF models.
  2. [Figures 8–12] Figure captions and axis labels for the spectral analysis and ANN predictions should explicitly state the number of training points used and whether any points near Re = 5650 were held out.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive review. The comments correctly identify several areas where quantitative support and validation details are currently missing from the manuscript. We address each major comment below and will revise the paper to incorporate the requested information and analyses.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion of 'excellent predictive accuracy' for maximum lift coefficient and instability onset time is unsupported by any reported quantitative metrics (e.g., MSE, MAE, or R² on a test partition), cross-validation procedure, or explicit test-set performance; the same holds for the 'reasonable fidelity' claim for drag.

    Authors: We agree that the abstract claims lack supporting quantitative metrics and validation details. In the revised manuscript we will report explicit error metrics (MSE, MAE, R²) on a held-out test partition, describe the cross-validation procedure employed, and update the abstract to reflect these quantitative results. We will likewise provide corresponding metrics for the drag coefficient to substantiate the fidelity claim. revision: yes

  2. Referee: [Data-driven modeling and results sections] Data-driven modeling and results sections: all performance figures are obtained by fitting and evaluating on the identical 101-simulation database; no hold-out set, k-fold cross-validation, or explicit train/test split is described, so statements of prediction 'for unseen Re' remain interpolations within the convex hull of the training points rather than demonstrated generalization.

    Authors: The current manuscript indeed reports performance on the full database without an explicit train/test split. We will add k-fold cross-validation results, including metrics on held-out points, and revise the text to clarify that predictions for 'unseen Re' are within the sampled range. Claims of generalization will be adjusted accordingly to reflect the interpolation nature of the tests. revision: yes

  3. Referee: [Bifurcation analysis and surrogate evaluation sections] Bifurcation analysis and surrogate evaluation sections: the distribution and local spacing of the 101 Re samples around the critical value Re ≈ 5650 are not reported; without this information it is impossible to verify that the training set is dense enough to capture the transition to multi-mode states or to rule out extrapolation failure in the ANN predictions of onset time and lift.

    Authors: We will add a figure and accompanying text detailing the distribution and local spacing of the 101 Reynolds-number samples, with emphasis on the region around Re ≈ 5650. This will allow assessment of sampling density near the bifurcation and support evaluation of the ANN predictions in that regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard supervised ML validation on simulation database

full rationale

The paper trains ANNs and other regressors on a fixed database of 101 high-fidelity simulations and reports accuracy metrics (lift, drag, onset time) obtained by comparing model outputs to the same simulation data, including hold-out points labeled 'unseen Re'. This is ordinary empirical validation of a data-driven surrogate and does not reduce any claimed result to a self-definition, a fitted parameter renamed as prediction, or a self-citation chain. No load-bearing step equates the reported performance to its inputs by construction; the database serves as an external benchmark for the models. The absence of explicit sampling-density details around Re=5650 is a potential generalization limitation but is not a circularity issue under the defined patterns.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on the Navier-Stokes equations being solved accurately by the high-fidelity code, on the 101 runs being dense enough to train generalizable models, and on numerous hyperparameters in the regression and network architectures being chosen to fit the simulation outputs.

free parameters (3)
  • ANN architecture hyperparameters
    Number of layers, neurons per layer, learning rate, and regularization strength chosen to minimize error on the simulation database.
  • B-spline knot placement and order
    Knot locations and polynomial degree in the Bayesian spline model fitted during regression.
  • Gaussian RBF length scales
    Width parameters of the radial basis functions selected during Bayesian regression.
axioms (2)
  • domain assumption The compressible Navier-Stokes equations with appropriate boundary conditions govern the flow.
    Invoked to justify the high-fidelity simulation database.
  • domain assumption The chosen Reynolds-number sampling is dense enough to capture the bifurcation and post-bifurcation dynamics.
    Required for the claim that models trained on the database generalize to unseen Re.

pith-pipeline@v0.9.1-grok · 5781 in / 1644 out tokens · 35146 ms · 2026-06-29T15:53:51.189005+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

57 extracted references

  1. [1]

    magnus effect

    L. Prandtl, Application of the “magnus effect” to the wind propulsion of ships, Tech. rep. (1926)

    1926

  2. [2]

    Modi, Moving surface boundary-layer control: a review, Journal of fluids and structures 11 (6) (1997) 627–663

    V. Modi, Moving surface boundary-layer control: a review, Journal of fluids and structures 11 (6) (1997) 627–663

    1997

  3. [3]

    Mittal, B

    S. Mittal, B. Kumar, Flow past a rotating cylinder, J. Fluid Mech. 476 (2003) 303–334. 49

    2003

  4. [4]

    J. O. Pralits, L. Brandt, F. Giannetti, Instability and sensitivity of the flow around a rotating circular cylinder, J. Fluid Mech. 650 (2010) 513– 536

    2010

  5. [5]

    T. K. Sengupta, A. Kasliwal, S. De, M. Nair, Temporal flow instability for magnus–robins effect at high rotation rates, J. Fluids Struct. 17 (7) (2003) 941–953

    2003

  6. [6]

    Stojković, M

    D. Stojković, M. Breuer, F. Durst, Effect of high rotation rates on the laminar flow around a circular cylinder, Phys. Fluids 14 (9) (2002) 3160– 3178

    2002

  7. [7]

    M. B. Glauert, The flow past a rapidly rotating circular cylinder, Proc. R. Soc. Lond. A Math. Phys. Sci. 242 (1228) (1957) 108–115

    1957

  8. [8]

    Nishioka, H

    M. Nishioka, H. Sato, Mechanism of determination of the shedding fre- quency of vortices behind a cylinder at low reynolds numbers, J. Fluid Mech. 89 (1) (1978) 49–60

    1978

  9. [9]

    J. O. Pralits, F. Giannetti, L. Brandt, Three-dimensional instability of the flow around a rotating circular cylinder, J. Fluid Mech. 730 (2013) 5–18

    2013

  10. [10]

    Sengupta, P

    A. Sengupta, P. Tucker, Effects of forced frequency oscillations and free stream turbulence on the separation-induced transition in pressure gra- dient dominated flows, Physics of Fluids 32 (10) (2020)

    2020

  11. [11]

    Sengupta, N

    A. Sengupta, N. Gupta, B. N. Ubald, Separation-induced transition on a t106a blade under low and elevated free stream turbulence, Physics of Fluids 36 (2) (2024)

    2024

  12. [12]

    Sengupta, N

    A. Sengupta, N. Shandilya, Thermal optimization of shock-induced sep- aration in a natural laminar airfoil operating at off-design conditions, Physics of Fluids 36 (4) (2024)

    2024

  13. [13]

    Salimipour, M

    E. Salimipour, M. Anbarsooz, Surface temperature effects on the com- pressible flow past a rotating cylinder, Phys. Fluids 31 (2) (2019)

    2019

  14. [14]

    Sundaram, T

    P. Sundaram, T. K. Sengupta, A. Sengupta, V. K. Suman, Multiscale instabilities of magnus–robins effect for compressible flow past rotating cylinder, Phys. Fluids 33 (3) (2021). 50

    2021

  15. [15]

    Sengupta, P

    A. Sengupta, P. Sundaram, Compressibility effects on the flow past a t106a low-pressure turbine cascade, Physics of Fluids 35 (10) (2023)

    2023

  16. [16]

    Kumar, C

    S. Kumar, C. Cantu, B. Gonzalez, Flow past a rotating cylinder at low and high rotation rates, J. Fluids Eng. 133 (4) (2011) 041201

    2011

  17. [17]

    V. K. Suman, P. Sundaram, J. K. Puttam, A. Sengupta, T. K. Sengupta, A novel compressible enstrophy transport equation-based analysis of instability during magnus–robins effects for high rotation rates, Phys. Fluids 34 (4) (2022)

    2022

  18. [18]

    A. R. Teymourtash, S. E. Salimipour, Compressibility effects on the flow past a rotating cylinder, Phys. Fluids 29 (1) (2017)

    2017

  19. [19]

    Sengupta, S

    A. Sengupta, S. Kumar, S. Kumar, Bifurcation analysis of compressible flow past a rotating cylinder for high rotation rate, Physics of Fluids 37 (12) (2025)

    2025

  20. [20]

    Fukami, K

    K. Fukami, K. Fukagata, K. Taira, Assessment of supervised machine learning methods for fluid flows: K. fukami et al., Theoretical and Com- putational Fluid Dynamics 34 (4) (2020) 497–519

    2020

  21. [21]

    Hasegawa, K

    K. Hasegawa, K. Fukami, T. Murata, K. Fukagata, Machine-learning- based reduced-order modeling for unsteady flows around bluff bodies of various shapes: K. hasegawa et al., Theoretical and Computational Fluid Dynamics 34 (4) (2020) 367–383

    2020

  22. [22]

    J. M. Pérez, Stability analysis of a uniform viscous transonic flow past a rotating circular cylinder, Results in Engineering 22 (2024) 102137

    2024

  23. [23]

    H. Xu, W. Zhang, J. Deng, J. Rabault, Active flow control with rotating cylinders by an artificial neural network trained by deep reinforcement learning, Journal of Hydrodynamics 32 (2) (2020) 254–258

    2020

  24. [24]

    S. Lee, D. You, Data-driven prediction of unsteady flow over a circular cylinder using deep learning, Journal of Fluid Mechanics 879 (2019) 217–254

    2019

  25. [25]

    Bairagi, M

    T. Bairagi, M. J. Hasan, M. Hudha, A. Azad, M. Rahman, Artificial neural network (ann) analysis on thermophysical properties of magne- tohydrodynamics flow with radiation in an arc-shaped enclosure with a rotating cylinder, Heliyon 10 (7) (2024). 51

    2024

  26. [26]

    J. Yu, J. S. Hesthaven, Flowfield reconstruction method using artificial neural network, Aiaa Journal 57 (2) (2019) 482–498

    2019

  27. [27]

    Sengupta, A

    A. Sengupta, A. Prakash, V. K. Suman, T. K. Sengupta, Benchmark study of unsteady flow inside a square lid driven cavity, Computers & Fluids (2025) 106812

    2025

  28. [28]

    Asghar, R

    A. Asghar, R. Mahmood, A. H. Majeed, H. Alotaibi, A. Refaie Ali, Predicting the passive control of fluid forces over circular cylinder in a time dependent flow using neuro-computing, AIP Advances 14 (12) (2024)

    2024

  29. [29]

    T. H. Pulliam, Implicit solution methods in computational fluid dynam- ics, Appl. Numer. Math. 2 (6) (1986) 441–474

    1986

  30. [30]

    K. A. Hoffmann, S. T. Chiang, Computational fluid dynamics volume i, Eng. Educ. Syst. (2000)

    2000

  31. [31]

    Sagaut, V

    P. Sagaut, V. K. Suman, P. Sundaram, M. K. Rajpoot, Y. G. Bhumkar, S. Sengupta, A. Sengupta, T. K. Sengupta, Global spectral analysis: Review of numerical methods, Comput. Fluids (2023) 105915

    2023

  32. [32]

    Jameson, Origins and further development of the jameson–schmidt– turkel scheme, AIAA J

    A. Jameson, Origins and further development of the jameson–schmidt– turkel scheme, AIAA J. 55 (5) (2017) 1487–1510

    2017

  33. [33]

    Y. Zhou, Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations, Physics of Plasmas 14 (8) (2007)

    2007

  34. [34]

    Sundaram, A

    P. Sundaram, A. Sengupta, V. K. Suman, T. K. Sengupta, Non- overlapping high-accuracy parallel closure for compact schemes: Ap- plication in multiphysics and complex geometry, ACM Trans. Parallel Comput. 10 (1) (2023) 1–28

    2023

  35. [35]

    Joshi, T

    B. Joshi, T. K. Sengupta, P. Sundaram, A. Sengupta, Highly resolved peta-scale direct numerical simulations: Onset of kelvin–helmholtz rayleigh–taylor instability via pressure pulses, Computers & Fluids 284 (2024) 106442. 52

    2024

  36. [36]

    Joshi, A

    B. Joshi, A. Sengupta, Y. Ajanif, L. Lestandi, Comparing the highly- resolved onset of rayleigh–taylor and kelvin–helmholtz rayleigh–taylor instabilities, European Journal of Mechanics-B/Fluids (2025) 204382

    2025

  37. [37]

    P. T. Tokumaru, P. E. Dimotakis, The lift of a cylinder executing rotary motions in a uniform flow, J. Fluid Mech. 255 (1993) 1–10

    1993

  38. [38]

    P. Pal, A. Guha, A. Sengupta, Direct numerical simulations of separation-induced transition in a low-pressure turbine under varying compressibility, Physics of Fluids 38 (3) (2026)

    2026

  39. [39]

    Munir, M

    A. Munir, M. Zhao, H. Wu, F. Tong, Flow-induced vibration of a rotat- ing circular cylinder at high reduced velocities and high rotation rates, Ocean Engineering 238 (2021) 109562

    2021

  40. [40]

    Y. Chew, M. Cheng, S. Luo, A numerical study of flow past a rotating circular cylinder using a hybrid vortex scheme, Journal of fluid mechan- ics 299 (1995) 35–71

    1995

  41. [41]

    Sengupta, P

    A. Sengupta, P. Tucker, Effects of forced frequency oscillations and un- steady wakes on the separation-induced transition in pressure gradient dominated flows, Physics of Fluids 32 (9) (2020)

    2020

  42. [42]

    Richter, G

    D. Richter, G. Iaccarino, E. S. Shaqfeh, Effects of viscoelasticity in the high reynolds number cylinder wake, Journal of fluid mechanics 693 (2012) 297–318

    2012

  43. [43]

    A. Sengupta, Compressible enstrophy transport for flow in a low- pressure turbine with unsteady wakes impinging at the inflow, in: Com- putational Fluid Dynamics: Novel Numerical and Computational Ap- proaches: Methodology and Numerics, Springer, 2025, pp. 59–85

    2025

  44. [44]

    P. K. Kundu, I. M. Cohen, D. R. Dowling, Fluid mechanics, 5th version, Academic, Berlin (2012)

    2012

  45. [45]

    Barkley, R

    D. Barkley, R. D. Henderson, Three-dimensional floquet stability anal- ysis of the wake of a circular cylinder, Journal of Fluid Mechanics 322 (1996) 215–241

    1996

  46. [46]

    F. M. White, Fluid mechanics, McGraw-Hill, New York (1994). 53

    1994

  47. [47]

    Zhou, Hydrodynamic Instabilities and Turbulence: Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz Mixing, Cambridge Univer- sity Press, 2024

    Y. Zhou, Hydrodynamic Instabilities and Turbulence: Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz Mixing, Cambridge Univer- sity Press, 2024

    2024

  48. [48]

    A. Gond, A. Sengupta, Data-driven optimal design of premixed hydrogen-air combustion in a microcombustor, AI Thermal Fluids 1 (2025) 100007

    2025

  49. [49]

    Theofilis, Advances in global linear instability analysis of nonparallel and three-dimensional flows, Prog

    V. Theofilis, Advances in global linear instability analysis of nonparallel and three-dimensional flows, Prog. Aerosp. Sci. 39 (4) (2003) 249–315

    2003

  50. [50]

    Hastie, R

    T. Hastie, R. Tibshirani, J. H. Friedman, J. H. Friedman, The elements of statistical learning: data mining, inference, and prediction, Vol. 2, Springer, 2009

    2009

  51. [51]

    R. L. Burden, J. D. Faires, Numerical analysis. 9th. brooks (2011)

    2011

  52. [52]

    S. L. Brunton, B. R. Noack, P. Koumoutsakos, Machine learning for fluid mechanics, Annual review of fluid mechanics 52 (1) (2020) 477–508

    2020

  53. [53]

    C. M. Bishop, Pattern recognition and machine learning by Christopher M. Bishop, Vol. 350, Springer Science+ Business Media, LLC Berlin, Germany:, 2006

    2006

  54. [54]

    K. P. Murphy, Machine learning: a probabilistic perspective, MIT press, 2012

    2012

  55. [55]

    M. D. Buhmann, Radial basis functions, Acta numerica 9 (2000) 1–38

    2000

  56. [56]

    I.Goodfellow, Y.Bengio, A.Courville, Deepfeedforwardnetworks, Deep learning 1 (2016) 161–217

    2016

  57. [57]

    Joshi, A

    B. Joshi, A. Sengupta, P. Sundaram, Exploring role of aspect ratio for compressible flow in a rectangular lid-driven cavity with a vertical tem- perature gradient, Physics of Fluids 35 (6) (2023). 54

    2023