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REVIEW 3 major objections 5 minor 60 references

Assessment of non-intrusive sensing in wall-bounded turbulence through explainable deep learning

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

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Pith's one-line read Wall pressure, not shear stress, is the input a CNN relies on to reconstruct near-wall velocity fluctuations.

desk verdict Solid explainable-DL application with a plausible but unverified pressure-dominance ranking; the independence assumption is the load-bearing soft spot. read the letter →

arxiv 2502.07610 v1 pith:SGCGJS74 submitted 2025-02-11 physics.flu-dyn

A. Cremades , R. Freibergs , S. Hoyas , A. Ianiro , S. Discetti , R. Vinuesa This is my paper · ORCID
classification physics.flu-dyn
keywords wall-boundedturbulencedeeplearningexplainableSHAPvaluesnon-intrusivesensingwallpressureshearstressturbulentchannelflow
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 asks which wall measurements a convolutional neural network truly depends on when it reconstructs velocity fluctuations at y+ = 15 inside a turbulent open channel at Re_tau = 180. Using deep-SHAP, an additive feature-attribution method, the authors assign an importance score to every wall grid point of the pressure and shear-stress input fields. They report that wall pressure is the most influential input for all three velocity components, ahead of streamwise and spanwise wall shear stress, and that the high-importance wall regions form streak-like clusters with a typical size of about 80 by 40 wall units and a range of 20 to 120 wall units. If correct, this gives a concrete design rule for non-intrusive sensing: pressure accuracy should be prioritized, and sensor arrays must resolve structures of this scale, which for commercial-aircraft conditions translates to roughly 100 to 600 microns.

What carries the argument

The argument is carried by deep-SHAP, a Shapley-value-based attribution method that assigns each input feature a numerical importance for a given prediction. Here the features are the 192 x 192 grid points of wall pressure and streamwise/spanwise wall shear stress, and the output is the predicted velocity fluctuation at y+ = 15; the importance fields are thresholded, segmented into deciles, filtered by a minimum area of S+ = $30^{2}$, and clustered to define coherent high-importance structures. The CNN itself has a receptive field of 15 x 15 grid points, which explains how a small set of important input pixels can influence a larger output region.

What would settle it

A decisive test would be a causal ablation experiment on the same trained CNN: corrupt the wall-pressure field while leaving shear stress intact, and independently corrupt shear stress while leaving pressure intact, then compare the rise in reconstruction error; the paper's claim predicts pressure corruption is markedly more damaging. A second check would recompute the importance ranking with a correlation-aware attribution method and see whether the 20-to-120-wall-unit cluster sizes survive.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a CNN trained to estimate near-wall velocity fluctuations from wall quantities is most sensitive to wall pressure, not to wall shear stress, and that the wall regions driving its predictions are moderate-intensity streak-like clusters rather than the strongest fluctuation events. The authors compute deep-SHAP importance fields over 1000 snapshots, rank every input grid point, and show that the top-importance points are concentrated in clusters whose averaged wall pressure lies one to two standard deviations from the mean. These clusters are streamwise-elongated, have a typical area of 80 by 40 wall units and a size range of 20 to 120 wall units, and coincide with low-velocity streaks and ejection-like regions; the shear-stress-driven clusters connect with sweep-like structures. The paper also shows that removing the top 1% of important pressure points distorts predictions over a much larger area, consistent with the network's 15 by 15 receptive field.

Load-bearing premise

The load-bearing premise is that deep-SHAP attributions correctly rank input importance even though they are computed assuming independent features and a linear local model, while the actual inputs—wall pressure and wall shear stress—are strongly correlated.

Editorial extensions

If this is right

  • Non-intrusive sensing systems for near-wall flow estimation should prioritize wall-pressure accuracy over shear-stress accuracy, since corrupting pressure raises reconstruction error fastest.
  • A sensor array for this reconstruction task needs to resolve streak-like wall structures of roughly 20 to 120 wall units; in aircraft-like conditions this is about 100 to 600 micrometers, which current wall-stress sensor sizes may not resolve.
  • The most influential wall regions are not the extreme fluctuation peaks but moderate-intensity regions at one to two standard deviations from the mean, so targeting extreme events alone would miss what the model relies on.
  • Only the top and bottom importance deciles form clusters large enough to pass the minimum-area filter, meaning the useful information for reconstruction is concentrated in a small fraction of the wall plane.
  • Because the CNN's receptive field is 15 x 15 grid points, sparse but well-placed pressure sensors can have an outsized effect on the reconstructed velocity field.

Reading between the lines

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

  • The paper stops short of testing how reconstruction degrades as sensor spacing exceeds the cluster size; a natural extension would be to downsample the input fields to the inferred cluster scale and measure the error curve.
  • The independence assumption in the attribution may shift some importance between pressure and shear stress; a correlation-aware attribution or causal ablation would test whether pressure remains dominant.
  • If the pressure-dominance result carries to higher Reynolds numbers and boundary layers, it would motivate flush-mounted micro-pressure-sensor arrays for closed-loop drag control rather than shear-stress micro-fences.
  • The coincidence of high-importance wall regions with low-velocity streaks suggests the CNN has implicitly learned the near-wall streak cycle; comparing SHAP-identified regions with an independent streak-detection algorithm would make that link quantitative.
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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 paper extends the non-intrusive sensing CNN of Guastoni et al. (2021) for a turbulent open channel at Re_tau=180 by applying deep-SHAP to attribute the prediction of velocity fluctuations at y+=15 to the wall-pressure and wall-shear-stress input fields. The central findings are that wall pressure is the most influential input, that high-importance input regions are not the most intense pressure or shear regions but rather have values one to two standard deviations from the mean, that these regions form streak-like clusters with a typical size of about 80 by 40 wall units and a reported range of 20 to 120 wall units, and that this scale sets resolution requirements for non-intrusive sensor arrays. The analysis includes joint histograms of input values and SHAP scores, perturbation experiments that remove top-ranked pixels, and a decile-based clustering of the importance field. The paper also translates the cluster sizes into sensor-resolution constraints for a commercial-aircraft context.

Significance. If the central claims hold, the paper provides practically useful guidance for non-intrusive sensing in wall-bounded turbulence: prioritize pressure-sensor accuracy and resolve structures on the 20-120 wall-unit scale. The framework is coherent, uses an established estimator, and the perturbation experiments in Figure 4 are internally consistent with the SHAP ranking. There is no equation-level circularity: the SHAP values are attributions of a pretrained model, and the ablations are consistency checks rather than fitted constants. The physical interpretation connecting high-importance regions to streaks and sweeps is plausible and consistent with prior work on near-wall structure. However, the main conclusions rest on the deep-SHAP independence assumption applied to inputs that the paper itself states are strongly correlated. Because the same SHAP ranking is thresholded, clustered, and converted into a sensor-resolution recommendation, the independence assumption is load-bearing. The paper would be strengthened by a correlation-aware attribution test and by sensitivity analysis of the clustering thresholds.

major comments (3)
  1. [Section 2, Eq. (2.3); Section 3] The claim that wall pressure is the most influential input is derived from deep-SHAP values computed under the independence assumption stated in Eq. (2.3), yet Section 3 acknowledges a strong correlation between pressure and shear-stress fluctuations. Under input correlation, the independent-feature Shapley value can assign the joint contribution of a correlated pressure-shear pattern to a single input, inflating the apparent influence of pressure. Indeed, the paper explains the pressure dominance as resulting from 'higher errors when the correlation between the input variables is broken,' which is exactly the effect introduced by the independence approximation. Please add a correlation-aware attribution test, for example conditional SHAP with a joint baseline, grouped-coalition Shapley values treating the three wall fields as one coalition, or a permutation test that holds the correlated partner fixed, and report whether pressure remains first in the ranking and whether the cluster-size estimates are unchanged.
  2. [Section 3, Figure 4] The perturbation experiment in Figure 4 removes pixels selected by the SHAP ranking, so it verifies that the selected pixels matter for the prediction, but it does not independently validate that the ranking itself is unbiased. If the independence approximation misallocates importance to pressure-dominated pixels, the same misallocation guides the pixel removal and produces the observed MSE increase. Please compare the SHAP-based removal curve against occlusion baselines that remove random pixels, least-important pixels, and pixels selected by an alternative attribution method (e.g., gradient-based or occlusion-based importance), and show that the ranking-specific behavior is not an artifact of correlated input patterns.
  3. [Section 3, Figure 7 and Conclusions] The cluster-size statement, including the typical 80 x 40 wall-unit size and the 20-120 wall-unit range, depends on several user-chosen thresholds: the 99th-percentile SHAP threshold, the decile segmentation, and the minimum-area filter S+ = 30^2. The manuscript does not report how the reported size range changes when these thresholds are varied. Since the size range is directly converted into a sensor-resolution recommendation for commercial aircraft, please add a sensitivity analysis over these thresholds and report the resulting spread in cluster sizes, or justify the threshold choices physically.
minor comments (5)
  1. [Data availability] The Data availability statement contains the placeholder '[doi]' rather than an actual DOI; please provide the complete link before publication.
  2. [Section 3, Figure 6] The text refers to 'black contours' in the top-right image while the caption refers to 'black dots'; please make the terminology consistent.
  3. [Section 3 (near Figure 8)] The word 'simetrical' should be 'symmetrical'.
  4. [Acknowledgements heading] The heading 'Aknowledgements' should be 'Acknowledgements'.
  5. [Section 3, Eq. (3.2)] The phrase 'instantaneous standarized wall pressure' should read 'instantaneous standardized wall pressure'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the pressure-dominance and cluster-size claims are SHAP attributions of a fixed pretrained CNN, not fitted constants or self-citation-derived predictions.

full rationale

The derivation chain is: take the CNN of Guastoni et al. (2021), train/modify it to predict velocity fluctuations at y+ = 15 from wall pressure and shear stress; compute deep-SHAP attributions of each input grid point on the MSE-augmented model output; rank inputs by those attributions; threshold, cluster and quantify the high-importance regions. No step reduces to its inputs by construction. The SHAP values are attributions of a pretrained model and are not parameters fitted to the claimed outputs; Eq. (2.3) is the standard linearized deep-SHAP rule, and Eq. (3.1) only normalizes the already-computed fields. The Figure 4 ablation removes pixels selected by the SHAP ranking and therefore verifies that the selected pixels matter to the model, but it is a consistency check, not an independent confirmation of the ranking itself; this is a validation limitation, not circularity. The paper explicitly states that "SHAP values are calculated assuming independent features and a linear model" and later notes "This effect is produced by the strong correlation between the pressure and shear stress fluctuations," which is a genuine methodological caveat about correlated inputs, but an approximate or even biased attribution method is not equivalent to the target conclusion by definition. Self-citations to Guastoni et al. (2021) and Cremades et al. (2024) supply the CNN and a physical comparison, respectively, but the central pressure-dominance and cluster-size findings are computed from the present SHAP analysis rather than imported from those citations. No uniqueness theorem from the authors' prior work is invoked to force the interpretation. The 20-120 wall-unit cluster sizes are descriptive statistics of thresholded SHAP fields under stated criteria (99th percentile, S+ = 30^2 filter), not a fitted parameter renamed as a prediction. Overall, no significant circularity is present.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The analysis does not introduce new physical entities or fitted physics constants. It rests on the pretrained CNN, on the deep-SHAP approximation, and on several hand-chosen thresholds (area filter, deciles, percentile levels) that materially affect the reported cluster sizes and importance rankings.

free parameters (4)
  • Structure area filter S+ threshold = 302 wall units
    Clusters with area below 30^2 wall units are discarded, following Lozano-Duran et al. (2012); this filtering directly determines which importance deciles yield structures and biases the reported cluster sizes.
  • Importance decile segmentation = 10 equal-percentile bins
    The domain is divided into deciles of SHAP importance before clustering; the number of bins and the decision to keep only the top and bottom deciles shape the structure statistics in Figures 7-10.
  • 99th percentile SHAP threshold = p99 of the SHAP distribution
    Used to define 'high importance' and to compare input-output pairs in Figure 3; the sensitivity of the conclusions to this arbitrary threshold is not tested.
  • SHAP reference value = mean of each input field
    deep-SHAP compares inputs against the mean wall-pressure and shear-stress fields as the non-informative baseline; importance values and rankings depend on this choice.
assumptions (5)
  • standard math Shapley value axioms (local accuracy, missingness, consistency) define the attribution framework
    Equations (2.1)-(2.2) rely on Lundberg and Lee (2017) and on Shapley (1953).
  • domain assumption The deep-SHAP approximation assumes independent input features and linear components
    This assumption is stated in Section 2 but its error is not quantified for the strongly correlated wall-pressure and shear-stress inputs.
  • domain assumption The pretrained CNN from Guastoni et al. (2021) accurately reconstructs velocity fluctuations
    The paper inherits the model and cites a reconstruction error below 1%, but no model weights, training details, or validation on this dataset are provided; if the CNN is biased, the SHAP explanations describe the wrong estimator.
  • ad hoc to paper Mean-field reference is non-informative for SHAP
    Section 3 states SHAP values compare inputs with the mean wall-shear stress and pressure as reference; this choice defines the zero of the attribution and is not justified beyond convenience.
  • domain assumption Near-wall physics at Re_tau=180 scales to flight Reynolds numbers
    The commercial-aircraft size estimate (100 to 600 micrometers) assumes a viscous length of 5 micrometers and that important cluster sizes in wall units are unchanged at much higher Reynolds numbers; no supporting evidence is given.

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Cite this review

Pith. "Pith review of Assessment of non-intrusive sensing in wall-bounded turbulence through explainable deep learning." pith.science (2026). https://pith.science/paper/SGCGJS74

@misc{pith2026250207610,
  author       = {Pith},
  title        = {Pith review of: Assessment of non-intrusive sensing in wall-bounded turbulence through explainable deep learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SGCGJS74}},
  note         = {Machine review of arXiv:2502.07610}
}
abstract

In this work we present a framework to explain the prediction of the velocity fluctuation at a certain wall-normal distance from wall measurements with a deep-learning model. For this purpose, we apply the deep-SHAP method to explain the velocity fluctuation prediction in wall-parallel planes in a turbulent open channel at a friction Reynolds number ${\rm{Re}}_\tau=180$. The explainable-deep-learning methodology comprises two stages. The first stage consists of training the estimator. In this case, the velocity fluctuation at a wall-normal distance of 15 wall units is predicted from the wall-shear stress and wall-pressure. In the second stage, the deep-SHAP algorithm is applied to estimate the impact each single grid point has on the output. This analysis calculates an importance field, and then, correlates the high-importance regions calculated through the deep-SHAP algorithm with the wall-pressure and wall-shear stress distributions. The grid points are then clustered to define structures according to their importance. We find that the high-importance clusters exhibit large pressure and shear-stress fluctuations, although generally not corresponding to the highest intensities in the input datasets. Their typical values averaged among these clusters are equal to one to two times their standard deviation and are associated with streak-like regions. These high-importance clusters present a size between 20 and 120 wall units, corresponding to approximately 100 and 600${\rm\mu m}$ for the case of a commercial aircraft.

Figures

Figures reproduced from arXiv: 2502.07610 by the authors.

Figure 1
Figure 1. Workflow of the methodology. The figure shows the model used for calculating [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Instantaneous visualization of the wall measurements of the open channel [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Distribution of the SHAP values for the input feature values. The left figure [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Mean Squared Error of velocity fluctuations as a function of the fraction of pixels [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Probability density function of the wall-pressure and wall-shear stress in the streamwise direction (left) and the spanwise direction (right). the maximum importance was obtained for intense values of the standardized wall-pressure and wall-shear stress between 1.5 and…
Figure 6
Figure 6. Figure 6: Comparison between original (left) and modified (right) wall pressure with top [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Probability of the most important clusters for predicting the streamwise velocity [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: Probability of the importance clusters for predicting the wall-normal and spanwise [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Probability of the importance clusters for predicting the streamwise, wall [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Probability of the importance clusters for predicting the streamwise, wall [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.