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arxiv: 2606.29628 · v1 · pith:2OIYB4O4new · submitted 2026-06-28 · ⚛️ physics.flu-dyn · cs.LG

Kriging and neural network models for pressure losses across perforated plates

Shuai Li This is my paper

Pith reviewed 2026-06-30 01:39 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn cs.LG
keywords krigingneural networkspressure lossperforated platesturbulent flowdata-driven modelsRANS simulationsempirical models
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The pith

Kriging and neural network models outperform empirical formulas for pressure losses across perforated plates.

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

Two data-driven models, one using kriging and the other neural networks, are built from published experimental measurements to forecast how much pressure is lost when turbulent flow passes through plates with circular holes. These models are compared to standard empirical equations and give closer matches to the measured values across most of the tested plate designs. The same models are then inserted into Reynolds-averaged Navier-Stokes calculations of simple channel flows as an added force term, and the resulting flow fields line up with what the models themselves predict. Engineers who simulate devices containing perforated plates would benefit from having a more accurate, data-based way to account for the resistance these plates impose.

Core claim

The authors establish that kriging and neural-network regressions trained on two existing experimental datasets produce pressure-loss predictions that agree with measurements and exceed the accuracy of commonly used empirical relations for the majority of plate geometries in those datasets. When the models are implemented as momentum source terms inside two-dimensional RANS channel-flow computations, the simulated pressure drops remain consistent with the standalone model outputs, showing that the approach can be used inside existing CFD solvers.

What carries the argument

Kriging interpolation and neural-network regression functions fitted to experimental pressure-drop data, serving as replacements for empirical pressure-loss correlations.

If this is right

  • The proposed models can be coded directly into CFD software for routine engineering calculations.
  • Both kriging and neural-network versions remain viable even when trained on small experimental collections.
  • The RANS results confirm that the new source-term implementation reproduces the expected pressure loss without additional tuning.
  • The framework offers an alternative modelling route whenever new perforated-plate data become available.

Where Pith is reading between the lines

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

  • Extending the training set with measurements from additional plate geometries would likely improve generalization to unseen designs.
  • The same data-driven strategy could be applied to pressure losses in other flow-obstructing components such as screens or grids.
  • In three-dimensional simulations the models might reveal how hole arrangement affects overall system performance beyond the two-dimensional tests shown.
  • Because the data are scarce, the current models may need periodic retraining as more experiments are published.

Load-bearing premise

The two published experimental datasets capture enough variety in plate geometry and flow conditions that the trained models will give reliable results for other perforated plates.

What would settle it

Direct comparison of the model predictions against new laboratory measurements of pressure loss for a perforated plate whose porosity, hole diameter, or thickness lies outside the range of the original training data.

Figures

Figures reproduced from arXiv: 2606.29628 by Shuai Li.

Figure 1
Figure 1. Figure 1: Illustrations of (a) a perforated plate with circular perforations and (b) the B2A wind-tunnel test section. Pressure losses across perforated plates usually depend on several geometric parameters of perforated plates, such as plate thickness, pore diameter, and pore spacing, as well as on flow conditions and regimes. Capturing the combined effects of these parameters in a predictive manner remains a chall… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the pressure drop predicted by the present kriging and NN models with experimental pressure-drop data from the training dataset and with predictions from previously published models [34, 41, 43–45]. For Plate 3, the results have been scaled by a factor of 0.1 to improve plot readability. Experimental pressure-drop values represent averages over all measurements corresponding to different pore… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of prediction errors of different pressure-drop models relative to experimental data in the training dataset [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the pressure drop predicted by the present kriging and NN models with experimental pressure-drop data from the test dataset and with predictions from previously published models [34, 41, 43–45]. Experimental pressure￾drop values represent averages over all measurements corresponding to different pore-scale Reynolds numbers for each plate. discrepancies for Plates 9 and 10, compared to previou… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of prediction errors of different pressure-drop models relative to experimental data in the test dataset. (𝑎) (𝑏) [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Response surfaces of the present (a) kriging model and (b) NN model, shown alongside the training data points. However, the slopes of the response surfaces at low porosity differ slightly among the models. The influence of the thickness ratio is more pronounced in the models proposed by Miller [34] and Holt [45]. In particular, these models predict higher pressure drops at low thickness ratios compared wit… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of response surfaces from the present kriging and NN models and previous models [34, 41, 43–45]. 𝜕(𝜌 ̄𝑢𝑖 ) 𝜕𝑡 + 𝜕(𝜌 ̄𝑢𝑖 ̄𝑢𝑗 ) 𝜕𝑥𝑗 = − 𝜕 ̄𝑝 𝜕𝑥𝑖 + 𝜕 ̄𝜎𝑖𝑗 𝜕𝑥𝑗 + 𝜕𝜎𝑖𝑗,𝑅𝐴𝑁𝑆 𝜕𝑥𝑗 + 𝑆𝑖 , (6) where ̄𝑢𝑖 represents the velocity components (for two-dimensional flows, 𝑖 =1, 2), ̄𝑝 is the pressure, ̄𝜎𝑖𝑗 is the viscous stress tensor, and 𝜎𝑖𝑗,𝑅𝐴𝑁𝑆 denotes the Reynolds-stress tensor. Outside the perforated-plate… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of pressure drops predicted by the present kriging and NN models with those from previously published models [34, 41, 43–45] for different thickness ratios 𝛿∕𝐷. 3.2.3. RANS-based pressure drop predictions using the present models as source terms [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Two-dimensional coarse computational mesh with a uniform cell size of Δ = 0.5 mm used for the RANS simulations. The dashed line indicates the location at which the source term is applied in the momentum equations. thermal and fluid systems in engineering applications. In this study, two data-driven models based on kriging and neural networks are proposed to predict pressure losses across perforated plates … view at source ↗
Figure 10
Figure 10. Figure 10: RANS-predicted pressure drops obtained using coarse, medium, and fine meshes. Simulation results are shown for (a) Plate 1 with the present kriging model, (b) Plate 1 with the present NN model, (c) Plate 9 with the present kriging model, and (d) Plate 9 predicted by RANS with the present NN model. The source term in the momentum equations is applied at 𝑥 = 0. where 𝐾 is the permeability of the porous medi… view at source ↗
Figure 11
Figure 11. Figure 11: RANS-predicted pressure drops illustrating the effect of the number of streamwise cells used to represent the perforated plate in the simulations. For the coarse mesh (Δ = 0.5 mm), simulations are performed using 2 and 4 streamwise cells to model the perforated plate, while for the medium mesh (Δ = 0.25 mm), 4 and 8 streamwise cells are used. Simulation results are shown for (a) Plate 1 with the coarse me… view at source ↗
read the original abstract

In this paper, two novel data-driven models based on kriging and neural networks (NN) are proposed to predict pressure losses across perforated plates with circular perforations in turbulent flows. The models are developed using two sets of experimental data available in the literature. The predictive performance of the proposed models is assessed and compared against widely used empirical formulae. It is found that the proposed models consistently outperform existing empirical models for most perforated plate configurations contained in the experimental datasets. Besides, the predicted pressure losses generally show good agreement with experimental measurements, demonstrating that data-driven approaches based on kriging and NN provide a feasible framework for modelling pressure losses across perforated plates. Overall, both approaches are promising, despite being trained on a relatively limited amount of experimental data, owing to the scarcity of measurements reported in the literature. To demonstrate the applicability of the proposed models in numerical simulations, two-dimensional channel flows are simulated using the Reynolds-averaged Navier-Stokes (RANS) equations, in which the new pressure-loss models are implemented as a source term in the momentum equations. The RANS predictions are found to be in excellent agreement with the model predictions, confirming the suitability of the proposed approaches for practical computational fluid dynamics applications.

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

2 major / 2 minor

Summary. The paper proposes kriging and neural network models trained on two experimental datasets from the literature to predict pressure losses across perforated plates with circular perforations in turbulent flows. It claims these data-driven models consistently outperform widely used empirical formulae for most configurations in the datasets, show good agreement with measurements, and can be implemented as source terms in RANS simulations of 2D channel flows where the predictions match the model outputs.

Significance. If the outperformance claims are supported by rigorous quantitative validation, the work offers a practical data-driven alternative for pressure-loss modeling in CFD where empirical correlations have known limitations. The explicit RANS implementation and acknowledgment of data scarcity strengthen the applicability argument for engineering use cases.

major comments (2)
  1. [Abstract / Results] Abstract and results: The central claim of consistent outperformance over empirical models lacks any quantitative metrics (e.g., RMSE, MAE, R², or error bars) or details on data partitioning/cross-validation; without these, the assertion cannot be evaluated and is load-bearing for the paper's main conclusion.
  2. [Methods] Methods / validation: No information is provided on how the two datasets were split for training/testing, hyperparameter selection for the NN, or kriging kernel choice; this is required to assess whether the reported agreement reflects genuine predictive capability rather than interpolation on limited data.
minor comments (2)
  1. [Abstract] The abstract could specify the number of data points, ranges of porosity/Re, and exact empirical models used for comparison to improve clarity.
  2. [Numerical results] Figure captions for the RANS results should explicitly state the mesh resolution and turbulence model employed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help strengthen the validation and transparency of our work. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and results: The central claim of consistent outperformance over empirical models lacks any quantitative metrics (e.g., RMSE, MAE, R², or error bars) or details on data partitioning/cross-validation; without these, the assertion cannot be evaluated and is load-bearing for the paper's main conclusion.

    Authors: We agree that quantitative metrics are necessary to rigorously support the outperformance claims. In the revised manuscript, we will add explicit values for RMSE, MAE, and R² comparing the kriging and NN models to the empirical formulae on both datasets. We will also report the data partitioning approach and any cross-validation results to allow proper evaluation of predictive performance versus interpolation. revision: yes

  2. Referee: [Methods] Methods / validation: No information is provided on how the two datasets were split for training/testing, hyperparameter selection for the NN, or kriging kernel choice; this is required to assess whether the reported agreement reflects genuine predictive capability rather than interpolation on limited data.

    Authors: We acknowledge the lack of methodological detail. The revised manuscript will specify the training/testing split for each dataset, the procedure for NN hyperparameter selection, and the kriging kernel type with parameter optimization details. This will clarify the models' generalization capability. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper trains kriging and neural-network models on two external experimental datasets drawn from the literature, then evaluates predictive performance against empirical formulae on those same configurations. No derivation step reduces a claimed prediction to a fitted parameter or self-citation by construction; the central claim is simply that the data-driven models outperform the baselines on the training data, which is a standard and non-circular supervised-learning result. The text explicitly notes data scarcity and does not invoke any uniqueness theorem, ansatz smuggling, or renaming of known results. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; models are presented as standard data-driven fits to external measurements.

pith-pipeline@v0.9.1-grok · 5734 in / 1065 out tokens · 44174 ms · 2026-06-30T01:39:32.939620+00:00 · methodology

discussion (0)

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Reference graph

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