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REVIEW 3 major objections 5 minor 52 references

Super-resolution of turbulent velocity fields in two-way coupled particle-laden flows

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A conditional GAN super-resolves turbulent velocity fields in two-way coupled particle-laden flows, matching DNS energy spectra, vorticity PDFs, and subgrid dissipation statistics.

desk verdict A credible incremental cGAN super-resolution study for particle-laden turbulence with solid in-distribution validation; the out-of-distribution generalization claim is thinner than the abstract suggests. read the letter →

arxiv 2507.03567 v1 pith:WPNDUO4D submitted 2025-07-04 physics.flu-dyn physics.comp-ph

Ali Shamooni , Ruyue Cheng , Thorsten Zirwes , Hesam Tofighian , Oliver T. Stein , Andreas Kronenburg This is my paper · ORCID
classification physics.flu-dynphysics.comp-ph
keywords super-resolutionparticle-ladenturbulencetwo-waycouplingconditionalGANsubgrid-scalemodelinglarge-eddysimulationmodulationdeeplearning
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 introduces a deep-learning super-resolution framework for two-way coupled particle-laden turbulent flows. The model, a conditional generative adversarial network, upsamples low-resolution velocity fields by a factor of four and is conditioned on subgrid kinetic energy and local particle mass density. The authors argue that these extra inputs let the network reconstruct high-frequency, particle-modulated vortical structures that a model trained only on particle-free data cannot capture. If correct, the approach offers a data-driven path to recovering subgrid-scale statistics—including dissipation and its backscatter—that are missed by classical closures like Smagorinsky in LES of particle-laden flows.

What carries the argument

The central object is the conditional GAN: a generator built from residual-in-residual dense blocks (RRDB) that maps a 4x-coarsened velocity field, along with subgrid kinetic energy $k_{sgs}$ and effective particle mass density $\rho_{p,eff}$, to a high-resolution velocity field; and a U-Net discriminator with spectral normalization that compares real and fake fields while also being conditioned on low-resolution input and on Haar stationary-wavelet detail coefficients (LH2, HL2, HH2). The particle conditioning is what carries the argument: it lets the network learn how two-way coupling modulates small-scale turbulence, which a particle-free-trained model misses.

What would settle it

Take a DNS velocity field, coarsen it with a Gaussian filter of width 4ΔDNS to create low-resolution inputs (instead of the implicit filter used in training), and apply the trained generator; if the reconstructed energy spectrum or subgrid dissipation no longer matches DNS, the claim that the model serves as a general LES subgrid surrogate is falsified for that filter.

Watch

Extended reading notes

Core claim

The central claim is that a cGAN-based super-resolution model, explicitly conditioned on physical parameters (subgrid kinetic energy and effective particle mass density), can reconstruct from 4x-coarsened velocity fields the full-resolution turbulent velocity in two-way coupled particle-laden flows. The discriminator is additionally conditioned on stationary-wavelet high-frequency details, which forces high-fidelity recovery of small scales. Across forced and decaying turbulence with Stokes numbers 0.6, 1, and 6 and mass loadings 0.49 and 0.75, the reconstructed fields reproduce DNS energy spectra, vorticity PDFs, and subgrid dissipation statistics, including backscatter; they also generalize to unseen Stokes numbers 3 and 10 with only mild high-wavenumber deviations. The authors further show that masking the particle channel degrades subgrid-scale reconstruction, demonstrating that particle information is actively used rather than ignored.

Load-bearing premise

The low-resolution training inputs are produced by an unspecified 4x filtering operation on DNS fields; if a practical LES filter or grid differs from that implicit coarsening, the reconstructed subgrid statistics are not guaranteed to match.

Editorial extensions

If this is right

  • If the central claim holds, SR-generated fields can be used as subgrid-scale surrogates in LES of particle-laden flows, recovering unresolved kinetic energy, dissipation, and backscatter that the Smagorinsky model cannot represent.
  • The model may reduce the error in computed drag forces in Euler-Lagrange simulations: velocity errors at particle positions are about ten times smaller than when using the filtered (LR) velocity.
  • The framework extends to decaying as well as forced turbulence regimes, suggesting applicability to unsteady or developing particle-laden flows.
  • The conditioning on effective particle mass density implies that the network learns a part of the turbulence-modulation physics, and removing that input causes subgrid reconstruction to degrade.
  • The model's generalization to Stokes numbers 3 and 10, which were outside the training range, indicates potential for interpolation and mild extrapolation in particle response time.

Reading between the lines

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

  • A natural testable extension is to vary the filter kernel used to generate low-resolution inputs (e.g., Gaussian vs. top-hat), since the paper does not specify the kernel that defines its LR data; if the model is sensitive to it, the approach would need filter-aware training to be a practical LES closure.
  • The current validation is on 2D slices of 3D fields; moving to fully 3D super-resolution would be a stronger test of whether the learned subgrid statistics are genuinely three-dimensional.
  • Because the model conditions on a single scalar (effective particle mass density), it may miss other particle statistics (e.g., local number density or size distribution) that also modulate small-scale turbulence; testing those inputs could extend the range of validity.
  • The success with backscatter statistics suggests that data-driven SR could complement or replace dynamic SGS models in flows where backscatter is significant, such as transitional or inhomogeneous turbulence.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript introduces a conditional generative adversarial network (cGAN) for 4x super-resolution of turbulent velocity fields in two-way coupled particle-laden flows. The generator is conditioned on subgrid kinetic energy and a local effective particle mass density, while the discriminator is conditioned on low-resolution data and stationary-wavelet high-frequency coefficients. Training and testing use in-house DNS of forced and decaying homogeneous isotropic turbulence covering a range of Stokes numbers and mass loadings, plus particle-free cases. Validation includes one-dimensional energy spectra, vorticity PDFs, subgrid-dissipation scatter and PDFs, an ablation that masks the particle input channel, and error metrics on a 16,000-plane test set. The out-of-distribution assessment uses two additional DNS cases with Stokes numbers St_eta = 3 and 10. The paper claims that the model accurately reconstructs both resolved and subgrid scales, recovers backscatter that Smagorinsky cannot, and generalizes to unseen Stokes numbers.

Significance. If the central claim holds, the framework is a useful a priori tool for LES-type deconvolution in particle-laden flows: it recovers subgrid energy and dissipation statistics, including backscatter, which classical eddy-viscosity closures cannot represent. The in-distribution validation is substantial: large test sets, multiple statistical targets (spectra, PDFs, subgrid dissipation), a particle-channel ablation with quantitative error reduction, and error metrics over the full test dataset. The explicit conditioning on physically motivated parameters is a strength. However, the out-of-distribution generalization claim currently rests on single-plane evidence, and the degradation operator used to create low-resolution inputs is not specified; both issues must be addressed before the predictive-capability claim is fully supported.

major comments (3)
  1. [IV.B.2, Figs. 13 and 14] The claim that the model generalizes to previously unseen Stokes numbers (St_eta = 3 and 10) is supported only by a single randomly sampled plane for each case. No mean, standard deviation, percentiles, NRMSE, or other aggregate statistics are reported over the 800 available test slices per case mentioned in Sec. III B. The apparent agreement in Fig. 13(a) and the 'minor deviations' in Fig. 13(b) could therefore be sample-specific. Since the abstract and conclusions describe the predictive capability as systematic, the authors should report aggregate spectral comparisons (e.g., mean and confidence bands), quantitative errors over the full OOD test subsets, and preferably additional statistics such as vorticity PDFs or subgrid dissipation for these cases.
  2. [II and III.B] The low-resolution training inputs are described as filtered DNS data, but the filter kernel is never specified. Equation (1) defines the mapping xi_hat = G(xi_LR, k_sgs, rho_p,eff), and Sec. III B describes how slices are sampled, but the operation that produces xi_LR from xi_GT is not stated. A top-hat filter of width 4*Delta_DNS appears only in the subgrid dissipation evaluation (Sec. IV.B), and it is not confirmed that this is the same filter used to generate training inputs. Without specifying the degradation operator, the learned inverse is not well defined, the method is not reproducible, and the model's applicability to LES with a different filter or numerical discretization is unsupported. This is load-bearing for the central claim and should be fixed.
  3. [IV.B.1, Eq. (16) and Fig. 11] The comparison with the Smagorinsky model is used to argue that the SR model is superior for subgrid dissipation prediction. However, the Smagorinsky constant Cs = 0.17 is a fixed, non-dynamic value, and no sensitivity to Cs or to the definition of |S| is reported. The conclusion that the SR model 'matches the DNS values better than the Smagorinsky model' may depend on this parameter choice. This does not invalidate the in-distribution SR validation, but it weakens the comparative claim unless a brief sensitivity check is added.
minor comments (5)
  1. [Table II] The case labels contain formatting artifacts (e.g., 'Case1 1', 'Case2 1', 'Case22'), and several numeric values run together; the table should be typeset carefully.
  2. [References] References 37 and 40 appear to refer to the same work (Real-ESRGAN) with overlapping author lists; please consolidate or disambiguate them.
  3. [Sec. III A 2] The phrase 'Pope's criteria' should be 'Pope's criterion' for consistency with the cited criterion kappa_max * eta >= 1.5.
  4. [Figs. 13 and 14] Please report the units and colorbar ranges explicitly for the wavelet coefficient panels, and state the plane index or time instant used for the 'randomly sampled plane' so the results are reproducible.
  5. [Data availability] The statement that code and datasets are 'available upon request' is a limitation for reproducibility; a persistent repository or DOI would strengthen the manuscript.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the super-resolution network is trained on DNS ground truth and evaluated on held-out and out-of-distribution samples; self-citations are architectural provenance, not load-bearing.

full rationale

The central mapping ξ̂ = G(ξ_LR, k_sgs, ρ_p,eff) is a trained neural operator whose optimization minimizes pixel, gradient, and adversarial losses against DNS ground truth. There is no fitted physical parameter later renamed as a prediction; the only learned parameters are CNN weights, optimized on 320,000 training samples and evaluated on 16,000 held-out slices plus two unseen Stokes-number cases. The low-resolution inputs are filtered DNS fields, but the SR output is not equal to the input by construction—the network must invert the filter and synthesize subgrid content, as shown by the energy-spectrum and vorticity validations. The ablation that masks the particle channel demonstrates that the conditioning genuinely changes the output, rather than the particle information being a passive relabeling of the target. Self-citations, including Ref. 25 by co-author Tofighian and Ref. 27 by co-authors Cheng et al., are invoked only for architectural choices such as k_sgs conditioning, LR/shuffled-HR discriminator conditioning, spectral losses, and wavelet-based discriminators; they are not used to justify the validation claims, which rest on the paper's own DNS statistics and error metrics. The main weakness—out-of-distribution generalization supported by one randomly sampled plane per case for Stη=3 and 10 without aggregate error bars—is a statistical robustness concern, not circularity. No derivation step reduces to its own input by construction, so the circularity score is 0.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a standard point-particle DNS database and a specific 4x filtering operation that defines the super-resolution task. The only hand-chosen parameters in the model are training loss weights; no physical constants are fitted. No new entities are postulated; the effective particle mass density is a conventional Eulerian cell average.

free parameters (1)
  • Generator loss weights (beta_p, beta_g, beta_a) = 1, 3.95, 1.24
    Chosen by hand in Sec. II to balance pixel, gradient, and adversarial losses after the first iteration so that all losses have comparable magnitudes.
assumptions (4)
  • domain assumption Point-particle drag-only model for particles (Stokes drag with a finite Reynolds number correction)
    Particle equation of motion (Eq. 13) includes only drag; gravity, collisions, and lift are neglected. This is standard for the low volume fractions considered here, and it defines the physics the SR model is trained to invert.
  • domain assumption DNS ground truth is fully resolved (kappa_max * eta >= 1.5)
    Stated in Sec. III A 2 via Pope's criterion. This justifies treating the DNS fields as the ground truth for training and validation.
  • domain assumption Low-resolution inputs are obtained by a fixed 4x filtering of DNS fields
    The exact filter kernel is not specified in Sec. III B. The model is trained to invert this particular filtering operation, and results may not transfer to other LES filters or numerical discretizations.
  • domain assumption Subgrid dissipation and stress validation assumes a top-hat filter with width 4*Delta_DNS
    Eqs. (14)-(16) evaluate SGS quantities using a top-hat filter of width 4*Delta_DNS, which is consistent with the implied LR generation but not explicitly linked to the LR data preparation.

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Cite this review

Pith. "Pith review of Super-resolution of turbulent velocity fields in two-way coupled particle-laden flows." pith.science (2026). https://pith.science/paper/WPNDUO4D

@misc{pith2026250703567,
  author       = {Pith},
  title        = {Pith review of: Super-resolution of turbulent velocity fields in two-way coupled particle-laden flows},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WPNDUO4D}},
  note         = {Machine review of arXiv:2507.03567}
}
read the original abstract

This paper introduces a deep learning-based super-resolution (SR) framework specifically developed for accurately reconstructing high-resolution velocity fields in two-way coupled particle-laden turbulent flows. Leveraging conditional generative adversarial networks (cGANs), the generator network architecture incorporates explicit conditioning on physical parameters, such as effective particle mass density and subgrid kinetic energy, while the discriminator network is conditioned on low-resolution data as well as high-frequency content of the input data. High-fidelity direct numerical simulation (DNS) datasets, covering a range of particle Stokes numbers, particle mass loadings, and carrier gas turbulence regimes, including forced- and decaying-turbulence, serve as training and testing datasets. Extensive validation studies, including detailed analyses of energy spectra, probability density functions (PDFs), vorticity distributions, and wavelet-based decomposition demonstrate the model's accuracy and generalization capabilities across different particle parameters. The results show that the network utilizes particle data, mainly in the reconstruction of high-frequency details modulated by particles. Additionally, systematic assessment of the model's performance in capturing previously unseen flow regimes further validates its predictive capabilities.

Figures

Figures reproduced from arXiv: 2507.03567 by the authors.

Figure 1
Figure 1. FIG. 1. The architecture of the generator ( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Temporal evolution of turbulent kinetic energy [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Turbulent statistics over time for ( [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Turbulent kinetic energy ( [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. One-dimensional kinetic energy spectra ( [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. One-dimensional kinetic energy spectra ( [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Three-dimensional kinetic energy ( [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Contours of the first velocity component ( [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. One-dimensional kinetic energy spectra: The model performance tested on cases with different [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Scatter plot of subgrid dissipation rate for 50,000 randomly selected points in the whole test [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. PDF of subgrid ( [PITH_FULL_IMAGE:figures/full_fig_p020_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Ablation study by masking input particle-related data: Contours of the [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. One-dimensional kinetic energy spectrum: The model performance tested on cases with different [PITH_FULL_IMAGE:figures/full_fig_p024_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Wavelet analysis on cases with different Stokes numbers not included in the training set. The first [PITH_FULL_IMAGE:figures/full_fig_p025_14.png]

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Works this paper leans on

52 extracted references · 27 canonical work pages

  1. [1]

    Sagaut ,\ 10.1007/b137536 title Large Eddy Simulation for Incompressible Flows ,\ edition 3rd \ ed.\ ( publisher Springer Berlin, Heidelberg ,\ year 2006 ) NoStop

    author author P. Sagaut ,\ 10.1007/b137536 title Large Eddy Simulation for Incompressible Flows ,\ edition 3rd \ ed.\ ( publisher Springer Berlin, Heidelberg ,\ year 2006 ) NoStop

    doi:10.1007/b137536 2006

  2. [2]

    Stolz \ and\ author N

    author author S. Stolz \ and\ author N. A. \ Adams ,\ title title An approximate deconvolution procedure for large-eddy simulation , \ 10.1063/1.869867 journal journal Phys. Fluids \ volume 11 ,\ pages 1699--1701 ( year 1999 ) NoStop

    doi:10.1063/1.869867 1999

  3. [3]

    Shotorban \ and\ author F

    author author B. Shotorban \ and\ author F. Mashayek ,\ title title Modeling subgrid-scale effects on particles by approximate deconvolution , \ 10.1063/1.2001691 journal journal Phys. Fluids \ volume 17 ,\ pages 1--4 ( year 2005 ) NoStop

    work page doi:10.1063/1.2001691

  4. [4]

    Domingo \ and\ author L

    author author P. Domingo \ and\ author L. Vervisch ,\ title title Large Eddy Simulation of premixed turbulent combustion using approximate deconvolution and explicit flame filtering , \ 10.1016/j.proci.2014.05.146 journal journal Proc. Combust. Inst. \ volume 35 ,\ pages 1349--1357 ( year 2015 ) NoStop

    work page doi:10.1016/j.proci.2014.05.146 2014

  5. [5]

    Domingo \ and\ author L

    author author P. Domingo \ and\ author L. Vervisch ,\ title title DNS and approximate deconvolution as a tool to analyse one-dimensional filtered flame sub-grid scale modelling , \ 10.1016/j.combustflame.2016.12.008 journal journal Combust. Flame \ volume 177 ,\ pages 109--122 ( year 2017 ) NoStop

    work page doi:10.1016/j.combustflame.2016.12.008 2016

  6. [6]

    Bassenne , author M

    author author M. Bassenne , author M. Esmaily , author D. Livescu , author P. Moin , \ and\ author J. Urzay ,\ title title A dynamic spectrally enriched subgrid-scale model for preferential concentration in particle-laden turbulence , \ 10.1016/j.ijmultiphaseflow.2019.04.025 journal journal Int. J. Multiph. Flow \ volume 116 ,\ pages 270--280 ( year 2019 ) NoStop

    work page doi:10.1016/j.ijmultiphaseflow.2019.04.025

  7. [7]

    Oberle , author C

    author author D. Oberle , author C. D. \ Pruett , \ and\ author P. Jenny ,\ title title Temporal large-eddy simulation based on direct deconvolution , \ https://doi.org/10.1063/5.0006637 journal journal Phys. Fluids \ volume 32 ,\ pages 065112 ( year 2020 ) NoStop

    work page doi:10.1063/5.0006637

  8. [8]

    Wang \ and\ author M

    author author Q. Wang \ and\ author M. Ihme ,\ title title Regularized deconvolution method for turbulent combustion modeling , \ 10.1016/j.combustflame.2016.09.023 journal journal Combust. Flame \ volume 176 ,\ pages 125--142 ( year 2017 ) NoStop

    work page doi:10.1016/j.combustflame.2016.09.023 2016

Show all 52 references
  1. [9]

    Wang \ and\ author M

    author author Q. Wang \ and\ author M. Ihme ,\ title title A regularized deconvolution method for turbulent closure modeling in implicitly filtered large-eddy simulation , \ 10.1016/j.combustflame.2019.03.009 journal journal Combust. Flame \ volume 204 ,\ pages 341--355 ( year...

    2019 doi

  2. [10]

    Wang , author X

    author author Q. Wang , author X. Zhao , \ and\ author M. Ihme ,\ title title A regularized deconvolution model for sub-grid dispersion in large eddy simulation of turbulent spray flames , \ 10.1016/j.combustflame.2019.05.032 journal journal Combust. Flame \ volume 207 ,\ page...

    2019 doi

  3. [11]

    Bardina , author J

    author author J. Bardina , author J. Ferziger , \ and\ author W. Reynolds ,\ title title Improved subgrid-scale models for large-eddy simulation , \ in\ 10.2514/6.1980-1357 booktitle 13th Fluid and Plasma Dynamics Conference \ ( year 1980 ) NoStop

    1980 doi

  4. [12]

    author author P. E. \ DesJardin \ and\ author S. H. \ Frankel ,\ title title Large eddy simulation of a nonpremixed reacting jet: Application and assessment of subgrid-scale combustion models , \ 10.1063/1.869749 journal journal Phys. Fluids \ volume 10 ,\ pages 2298 ( year 19...

    doi

  5. [13]

    Shamooni , author A

    author author A. Shamooni , author A. Cuoci , author T. Faravelli , \ and\ author A. Sadiki ,\ title title New Dynamic Scale Similarity Based Finite-Rate Combustion Models for LES and a priori DNS Assessment in Non-premixed Jet Flames with High Level of Local Extinction , \ 10...

    doi

  6. [14]

    Shamooni , author A

    author author A. Shamooni , author A. Cuoci , author T. Faravelli , \ and\ author A. Sadiki ,\ title title An a priori DNS analysis of scale similarity based combustion models for LES of non-premixed jet flames , \ 10.1007/s10494-019-00099-9 journal journal Flow, Turbul. Combu...

    doi

  7. [15]

    Ferrante \ and\ author S

    author author A. Ferrante \ and\ author S. Elghobashi ,\ title title On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence , \ 10.1063/1.1532731 journal journal Phys. Fluids \ volume 15 ,\ pages 315--329 ( year 2003 ) NoStop

    doi

  8. [16]

    author author A. H. \ Abdelsamie \ and\ author C. Lee ,\ title title Decaying versus stationary turbulence in particle-laden isotropic turbulence: Turbulence modulation mechanism , \ 10.1063/1.3678332 journal journal Phys. Fluids \ volume 24 ,\ pages 015106 ( year 2012 ) NoStop

    doi

  9. [17]

    Elghobashi ,\ title title Direct Numerical Simulation of Turbulent Flows Laden with Droplets or Bubbles , \ 10.1146/annurev-fluid-010518-040401 journal journal Annu

    author author S. Elghobashi ,\ title title Direct Numerical Simulation of Turbulent Flows Laden with Droplets or Bubbles , \ 10.1146/annurev-fluid-010518-040401 journal journal Annu. Rev. Fluid Mech. \ volume 51 ,\ pages 217--244 ( year 2019 ) NoStop

    doi

  10. [18]

    author author S. L. \ Brunton , author B. R. \ Noack , \ and\ author P. Koumoutsakos ,\ title title Machine Learning for Fluid Mechanics , \ 10.1146/annurev-fluid-010719-060214 journal journal Annu. Rev. Fluid Mech. \ volume 52 ,\ pages 477--508 ( year 2020 ) NoStop

    doi

  11. [19]

    Fukami , author K

    author author K. Fukami , author K. Fukagata , \ and\ author K. Taira ,\ title title Super-resolution reconstruction of turbulent flows with machine learning , \ 10.1017/jfm.2019.238 journal journal J. Fluid Mech. \ volume 870 ,\ pages 106--120 ( year 2019 ) NoStop

    2019 doi

  12. [20]

    author author K. Duraisamy ,\ title title Perspectives on machine learning-augmented Reynolds-averaged and large eddy simulation models of turbulence , \ 10.1103/PhysRevFluids.6.050504 journal journal Phys. Rev. Fluids \ volume 6 ,\ pages 050504 ( year 2021 ) NoStop

    doi

  13. [21]

    Kim , author J

    author author H. Kim , author J. Kim , author S. Won , \ and\ author C. Lee ,\ title title Unsupervised deep learning for super-resolution reconstruction of turbulence , \ 10.1017/jfm.2020.1028 journal journal J. Fluid Mech. \ volume 910 ,\ pages A29 ( year 2020 ) NoStop

    2020

  14. [22]

    Bode , author M

    author author M. Bode , author M. Gauding , author Z. Lian , author D. Denker , author M. Davidovic , author K. Kleinheinz , author J. Jitsev , \ and\ author H. Pitsch ,\ title title Using physics-informed enhanced super-resolution generative adversarial networks for subfilter...

    doi

  15. [23]

    Bode , author M

    author author M. Bode , author M. Gauding , author D. Goeb , author T. Falkenstein , \ and\ author H. Pitsch ,\ title title Applying physics-informed enhanced super-resolution generative adversarial networks to turbulent premixed combustion and engine-like flame kernel direct ...

    doi

  16. [24]

    Fukami , author K

    author author K. Fukami , author K. Fukagata , \ and\ author K. Taira ,\ title title Super-resolution analysis via machine learning: a survey for fluid flows , \ 10.1007/s00162-023-00663-0 journal journal Theor. Comput. Fluid Dyn. \ volume 37 ,\ pages 421--444 ( year 2023 ) NoStop

    doi

  17. [25]

    Tofighian , author J

    author author H. Tofighian , author J. A. \ Denev , \ and\ author N. Kornev ,\ title title A conditional deep learning model for super-resolution reconstruction of small-scale turbulent structures in particle-Laden flows , \ 10.1063/5.0235192 journal journal Phys. Fluids \ vol...

    doi

  18. [26]

    Nista , author C

    author author L. Nista , author C. D. \ Schumann , author P. Petkov , author V. Pavlov , author T. Grenga , author J. F. \ MacArt , author A. Attili , author S. Markov , \ and\ author H. Pitsch ,\ title title Parallel implementation and performance of super-resolution generati...

  19. [27]

    Cheng , author A

    author author R. Cheng , author A. Shamooni , author T. Zirwes , \ and\ author A. Kronenburg ,\ title title Improved super-resolution reconstruction of turbulent flows with spectral loss function , \ 10.1063/5.0258090 journal journal Phys. Fluids \ volume 37 ,\ pages 035208 ( ...

    doi

  20. [28]

    Goodfellow , author J

    author author I. Goodfellow , author J. Pouget-Abadie , author M. Mirza , author B. Xu , author D. Warde-Farley , author S. Ozair , author A. Courville , \ and\ author Y. Bengio ,\ title title Generative adversarial networks , \ 10.1145/3422622 journal journal Commun. ACM \ vo...

    doi

  21. [29]

    Mirza \ and\ author S

    author author M. Mirza \ and\ author S. Osindero ,\ http://arxiv.org/abs/1411.1784 title Conditional Generative Adversarial Nets , \ ( year 2014 ) NoStop

    2014 arXiv

  22. [30]

    Wang , author K

    author author X. Wang , author K. Yu , author S. Wu , author J. Gu , author Y. Liu , author C. Dong , author Y. Qiao , \ and\ author C. C. \ Loy ,\ title title ESRGAN: Enhanced super-resolution generative adversarial networks , \ in\ 10.1007/978-3-030-11021-5_5 booktitle Lect....

    doi

  23. [31]

    author author W. T. \ Chung , author B. Akoush , author P. Sharma , author A. Tamkin , author K. S. \ Jung , author J. H. \ Chen , author J. Guo , author D. Brouzet , author M. Talei , author B. Savard , author A. Y. \ Poludnenko , \ and\ author M. Ihme ,\ title title Turbulen...

    doi arXiv

  24. [32]

    Nista , author C

    author author L. Nista , author C. Schumann , author T. Grenga , author A. Attili , \ and\ author H. Pitsch ,\ title title Investigation of the generalization capability of a generative adversarial network for large eddy simulation of turbulent premixed reacting flows , \ 10.1...

    doi

  25. [33]

    Sundararajan ,\ https://doi.org/10.1002/9781119113119 title Discrete Wavelet Transform: A Signal Processing Approach ,\ CourseSmart Series\ ( publisher Wiley ,\ year 2016 ) NoStop

    author author D. Sundararajan ,\ https://doi.org/10.1002/9781119113119 title Discrete Wavelet Transform: A Signal Processing Approach ,\ CourseSmart Series\ ( publisher Wiley ,\ year 2016 ) NoStop

    2016 doi

  26. [34]

    Cotter ,\ title Uses of Complex Wavelets in Deep Convolutional Neural Networks ,\ 10.17863/CAM.53748 Ph.D

    author author F. Cotter ,\ title Uses of Complex Wavelets in Deep Convolutional Neural Networks ,\ 10.17863/CAM.53748 Ph.D. thesis ,\ school Apollo - University of Cambridge Repository ( year 2019 ) NoStop

    2019 doi

  27. [35]

    Wang , author L

    author author Q. Wang , author L. Mahler , author J. Steiglechner , author F. Birk , author K. Scheffler , \ and\ author G. Lohmann ,\ title title DISGAN: Wavelet-informed Discriminator Guides GAN to MRI Super-resolution with Noise Cleaning , \ in\ 10.1109/ICCVW60793.2023.0025...

  28. [36]

    Xu , author Y

    author author Y. Xu , author Y. Zhou , author H. Ma , author H. Yang , author H. Wang , author S. Zhang , \ and\ author X. Li ,\ title title Wavelet-based dual discriminator GAN for image super-resolution , \ 10.1016/j.knosys.2025.113383 journal journal Knowledge-Based Syst. \...

  29. [37]

    Wang , author L

    author author X. Wang , author L. Xie , author C. Dong , \ and\ author Y. Shan ,\ title title Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data , \ in\ http://arxiv.org/abs/2107.10833 booktitle Proc. IEEE Int. Conf. Comput. Vis. ,\ Vol.\ volume 2...

    2021 arXiv

  30. [38]

    Miyato , author T

    author author T. Miyato , author T. Kataoka , author M. Koyama , \ and\ author Y. Yoshida ,\ title title Spectral Normalization for Generative Adversarial Networks , \ http://arxiv.org/abs/1802.05957 journal journal 6th Int. Conf. Learn. Represent. ICLR 2018 - Conf. Track Proc...

    2018 arXiv

  31. [39]

    Nista , author C

    author author L. Nista , author C. Schumann , author G. Scialabba , author T. Grenga , author H. Pitsch , \ and\ author A. Attili ,\ title title The influence of adversarial training on turbulence closure modeling , \ 10.2514/6.2022-0185 journal journal AIAA Sci. Technol. Foru...

    doi

  32. [40]

    Wang , author L

    author author X. Wang , author L. Xie , author C. Dong , \ and\ author Y. Shan ,\ title title Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data , \ 10.1109/ICCVW54120.2021.00217 journal journal Proc. IEEE Int. Conf. Comput. Vis. \ volume 2021-Oct...

    2021

  33. [41]

    author author P. L. \ Carroll \ and\ author G. Blanquart ,\ title title A proposed modification to Lundgren's physical space velocity forcing method for isotropic turbulence , \ 10.1063/1.4826315 journal journal Phys. Fluids \ volume 25 ,\ pages 105114 ( year 2013 ) NoStop

    doi

  34. [42]

    author author M. R. \ Maxey \ and\ author J. J. \ Riley ,\ title title Equation of motion for a small rigid sphere in a nonuniform flow , \ 10.1063/1.864230 journal journal Phys. Fluids \ volume 26 ,\ pages 883--889 ( year 1983 ) NoStop

    doi

  35. [43]

    Bailly \ and\ author D

    author author C. Bailly \ and\ author D. Juve ,\ title title A stochastic approach to compute subsonic noise using linearized Euler's equations , \ in\ 10.2514/6.1999-1872 booktitle 5th AIAA/CEAS Aeroacoustics Conf. Exhib. ,\ series and number number c \ ( publisher American I...

    1999 doi

  36. [44]

    Saad , author D

    author author T. Saad , author D. Cline , author R. Stoll , \ and\ author J. C. \ Sutherland ,\ title title Scalable Tools for Generating Synthetic Isotropic Turbulence with Arbitrary Spectra , \ 10.2514/1.J055230 journal journal AIAA J. \ volume 55 ,\ pages 327--331 ( year 20...

    doi

  37. [45]

    author author S. B. \ Pope ,\ @noop title Turbulent Flows ,\ edition 1st \ ed.\ ( publisher Cambridge University Press ,\ year 2000 ) NoStop

    2000

  38. [46]

    author author J. R. \ Ristorcelli ,\ title title The self-preserving decay of isotropic turbulence: Analytic solutions for energy and dissipation , \ 10.1063/1.1604780 journal journal Phys. Fluids \ volume 15 ,\ pages 3248--3250 ( year 2003 ) NoStop

    doi

  39. [47]

    Piomelli , author W

    author author U. Piomelli , author W. H. \ Cabot , author P. Moin , \ and\ author S. Lee ,\ title title Subgrid-scale backscatter in turbulent and transitional flows , \ 10.1063/1.857956 journal journal Phys. Fluids A \ volume 3 ,\ pages 1766--1771 ( year 1991 ) NoStop

    doi

  40. [48]

    merlin.mbs aapmrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aapmrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number org...

    2010

  41. [49]

    merlin.mbs aipauth4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aipauth4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number org...

    2010

  42. [50]

    merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number orga...

    2010

  43. [51]

    merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number orga...

    2010

  44. [52]

    merlin.mbs apsrmp4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs apsrmp4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number orga...

    2010

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.