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REVIEW 4 major objections 7 minor 16 references

Feasibility Study of CNNs and MLPs for Radiation Heat Transfer in 2-D Furnaces with Spectrally Participative Gases

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper shows that CNN and MLP surrogates trained on ICARUS2D data learn the wall radiative heat flux of a 2D furnace with spectrally participative gases, with the CNN reaching 7.40% mean relative error and roughly 7000–11000× faster…

desk verdict Plausible feasibility study of NN surrogates for 2D furnace radiation, but missing input ranges and overclaimed robustness/industrial applicability keep it from being a strong paper. read the letter →

arxiv 2506.08033 v3 pith:27U4OAED submitted 2025-06-02 eess.SY cs.LGcs.SY

Axel TahmasebiMoradi , Vincent Ren , Benjamin Le-Creurer , Chetra Mang , Mouadh Yagoubi This is my paper
classification eess.SYcs.LGcs.SY
keywords radiativeheattransferspectrallyparticipativegasesconvolutionalneuralnetworkmulti-layerperceptronsurrogatemodeldiscreteradiationmethodstatisticalnarrowband2Dfurnace
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

The paper is a feasibility study: can a convolutional neural network or a multi-layer perceptron replace a classical radiative transfer solver inside an industrial 2D furnace simulation? The authors answer yes for the tested configurations, using high-fidelity data generated by the ICARUS2D solver, which applies the discrete transfer radiation method with a statistical narrow band gas model. The CNN reaches a mean relative error of 7.40% and the MLP 19.67% on the larger dataset, with inference about 7000–11000 times faster than the classical solver. The stated contribution is an input encoding that lets a CNN treat a radiation problem as an image: each physical field (gas temperature, wall temperature, wall emissivity) becomes a separate input channel. A sympathetic reader would care because radiation solvers are often the computational bottleneck in furnace and combustion design, and a fast surrogate with a few percent error opens the door to many-query workflows.

What carries the argument

The load-bearing object is the CNN input encoding, which arranges the problem’s physical fields as channels of an image: wall emissivity, boundary temperature, and gas temperature each occupy one channel, with zeroes where a quantity is not defined (for instance, wall temperature inside the domain). This lets standard convolutional filters and average-pooling layers process the 120×20 furnace mesh and map the flattened representation to the 280 boundary irradiation values. The MLP receives the same information as a flat vector. Both networks are trained with mean-absolute-error loss and hyperparameters selected by an automated search; the trained models absorb the 367-band spectral loop that the classical DTRM/SNB solver must execute, which is the mechanism behind the speedup.

What would settle it

Regenerate or reuse a test set whose inputs fall outside the sampled ranges described only vaguely in Section 4, or vary the geometry (aspect ratio, mesh resolution) or gas fractions (e.g., xCO2 and xH2O away from 0.1 and 0.2), then compare the trained CNN’s wall irradiation predictions against ICARUS2D; a mean relative error well above the reported 7.40% would show the surrogate’s validity is confined to the training distribution rather than to industrial furnaces generally.

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Extended reading notes

Core claim

The central discovery is that the full mapping from gas temperature, boundary temperature, and boundary emissivity fields to hemispherical irradiation on all wall points can be learned end-to-end by both a CNN and an MLP, with no explicit spectral band loop. On dataset B (3000 training, 900 test samples) the CNN achieves a mean relative error of 7.40% with standard deviation 1.55%, while the MLP achieves 19.67% with 5.77%. The trained networks reduce inference per case from about 138 seconds in ICARUS2D to roughly 0.012 seconds, a speedup of about 7000–11000×. The authors also report that when the output is restricted to a single wall, CNN accuracy improves (south wall 5.57%, east wall 2.58%) while MLP accuracy does not, which they read as evidence that the CNN is more robust and stable to changes in hyperparameters.

Load-bearing premise

The load-bearing premise is that the fixed 2D geometry, fixed gas composition, and the unstated Latin-Hypercube sampling ranges for temperature and emissivity are representative of the industrial furnaces the surrogate is meant to replace; the paper never states those ranges, so any furnace condition outside them is untested.

Editorial extensions

If this is right

  • Within the tested geometry, gas composition, and input ranges, wall irradiation can be obtained in milliseconds with roughly 7% mean relative error, making optimization, design-space exploration, and uncertainty quantification practical for cases where the classical solver would need many expensive runs.
  • Dedicated per-wall surrogates are more accurate than a single all-boundary model, with the CNN reaching 5.57% on the south wall and 2.58% on the east wall, so industrial users with one wall of interest can train smaller, better networks.
  • A larger training set improves both architectures, but it improves the CNN about twice as much as the MLP, suggesting the CNN extracts more benefit from additional high-fidelity data.
  • Inference cost no longer scales with the number of spectral bands, because the 367-band loop is replaced by one forward pass; this removes a structural cost of spectral radiation modeling, not just a constant factor.

Reading between the lines

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

  • The paper leaves the sampled ranges for temperature and emissivity unstated, so a strict reading is that the 7.4% error holds inside an unspecified input box; an obvious editorial extension is to publish those ranges and test immediately outside them, since any real furnace condition beyond the box has no data support.
  • The speed comparison of 138 seconds versus 0.012 seconds compares a Fortran DTRM code against optimized neural-network inference on a different software stack, so the practical speedup in an integrated industrial workflow may be smaller once data generation and integration overhead are counted.
  • The channel-stacking idea is not tied to this particular 2D rectangular furnace; a testable extension would be to apply the same multi-channel encoding to other meshed domains (different aspect ratios, curved walls, or 3D slices) and measure how far the learned map generalizes.
  • Because CO and H2O are listed among the gases but only CO2 and H2O concentrations are fixed in the dataset table, a natural follow-up is to vary gas composition as an input channel and check whether the surrogate preserves accuracy across industrial fuel mixtures.
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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

4 major / 7 minor

Summary. The paper proposes CNN and MLP surrogate models to approximate the solution of the radiative transfer equation in a fixed 2-D rectangular furnace geometry with spectrally participating gases, using ICARUS2D (DTRM/SNB) as the reference solver. Two LHS-generated datasets of different sizes are used to train and test the networks, with hyperparameters optimized by Optuna. The reported results show mean relative wall-irradiation errors of 7.40% (CNN, dataset B) and 19.67% (MLP, dataset B), inference speedups of roughly x7000 to x11000 relative to the classical solver, and a claim that CNNs are more robust and stable to hyperparameter changes than MLPs. The paper also reports per-wall experiments for south and east walls and a dataset-size sensitivity analysis.

Significance. If the reported accuracy and speedup generalize beyond the specific test distribution, the paper would be a useful feasibility demonstration of neural-network surrogates for spectral radiative heat transfer with participating gases, a setting where data-driven surrogates are less common than for gray media. The strengths are that the reference solver is external and physics-based, the test metrics are computed on held-out samples, the inference-time measurements are concrete and reproducible in spirit, and the authors explicitly acknowledge the cost of generating high-fidelity training data and the trade-off involved in replacing classical solvers. The main significance is therefore as a carefully scoped feasibility study, not yet as a general-purpose replacement for RTE solvers.

major comments (4)
  1. [Section 4, Datasets A/B and Table 1] The LHS sampling ranges for gas temperature T, wall temperature T0, and wall emissivity ε are never stated, and the spatial structure of the temperature/emissivity fields is not described. Table 1 fixes the geometry, mesh, gas mixture, pressure, and spectral grid. Consequently, all accuracy numbers in Table 5, including the headline CNN mean relative error of 7.40% on dataset B, are interpolation results inside an unstated operating box for one geometry and one gas composition. Because radiative intensity depends strongly and nonlinearly on temperature and composition, the abstract's 'industrially acceptable' claim and Section 5's statement that the networks 'can replace, with a trade-off, the classical solvers' go beyond the support of the experiments. The authors should report the exact sampling ranges, the field parameterization, and either restrict the conclusions to the tested box or provide evidence for broader validity.
  2. [Section 4, hyperparameter optimization] Optuna is used to select hyperparameters, but no validation split is described. If the test sets were used directly or indirectly during hyperparameter selection, the reported test errors in Tables 5, 9, and 10 are optimistically biased and the MLP/CNN comparison is not on equal footing. The paper should state whether a separate validation set was used, how many Optuna trials were run, and how the final hyperparameters were chosen.
  3. [Section 4, Tables 7-10 and robustness claim] The claim that CNNs are 'more robust and stable to hyper-parameter changes than the MLPs' is based on a single observation: on the south-wall task, the MLP mean error worsened from 9.77% (dataset A) to 12.07% (dataset B) while the CNN improved from 7.48% to 5.57%. This comparison is not a controlled hyperparameter-robustness study. The text says new optimized hyperparameters were found for each network and dataset in Tables 7 and 8, so the change in error conflates dataset size, model re-optimization, and architectural differences. The robustness conclusion should either be supported by deliberate hyperparameter perturbation experiments (e.g., varying one hyperparameter at a time around the optimum) or removed and replaced by a more limited statement about the observed performance under the authors' optimization protocol.
  4. [Section 4, relative error definition] The reported 'mean and standard deviation values of relative errors' are never defined precisely: it is unclear whether the mean is taken over boundary points within a sample and then averaged over test samples, or pooled over all boundary points and all test samples, and whether the denominator is the reference |H| value, |H| plus a small constant, or something else. Since H can vary strongly along the walls, this ambiguity affects the interpretation of all accuracy claims. A formula for the relative error and the averaging procedure should be given.
minor comments (7)
  1. [Section 4, Datasets A/B] Please specify the number of LHS samples, the seed(s), and the exact ranges for every sampled input; without this information the datasets cannot be reproduced.
  2. [Abstract and Section 1] 'The originality of this work lays in the adaptation' should read 'lies in the adaptation'.
  3. [Section 4, Tables 7-10] The wording 'For the same dataset A... The new optimized hyper-parameters... Having kept the same hyper-parameters' is contradictory and should be clarified: are the reported reduced-output results obtained with the new optimized hyperparameters of Tables 7-8, or with the all-wall hyperparameters of Table 4?
  4. [Section 2.4 and Figure 1] The paper mentions CO, CO2, and H2O gases, but Table 1 only lists mole fractions for CO2 and H2O; the treatment of CO should be clarified or removed from the text.
  5. [Section 4, Table 6] The speedup factor is computed as a ratio of average inference time to the classical solver runtime, but the classical solver runtime (138 s) is reported without hardware and compilation details; adding these details and reporting the variance of the inference times would strengthen the comparison.
  6. [Section 5] The summary refers to 'two high precision datasets'; since the datasets are solver-generated, 'high-fidelity' or 'reference' would be more accurate than 'high precision'.
  7. [General] No code or data availability statement is provided; making the datasets and training scripts available would substantially improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the neural networks are validated against held-out ICARUS2D outputs, which is standard surrogate-model testing, not a self-referential derivation.

full rationale

The paper's central claim is that CNN and MLP surrogates can approximate the ICARUS2D radiative heat transfer solver and run much faster. The training data and the accuracy benchmark both come from ICARUS2D, but that is the intended ground truth for a surrogate emulator: the networks are trained on a subset of samples and evaluated on held-out samples generated by the same solver. This is not circular because the reference solver is external to the neural network and the network weights are not fitted to the test outputs. The reported relative errors (e.g., CNN 7.40% mean on dataset B) are genuine generalization errors on unseen input parameter combinations within the sampled range. No load-bearing claim is justified by a self-citation: the references to EM2C and Air Liquide are institutional pointers to the classical solver's origin, not citations of the present authors' prior results, and they do not constitute the argument for the surrogate's accuracy. The paper also acknowledges the trade-off that generating training samples is computationally costly, and that classical solvers remain preferable when only a few simulations are needed. The main weakness is that the Latin-Hypercube sampling ranges for temperatures and emissivities are never stated, and geometry, gas composition, and pressure are fixed, so the 'industrially acceptable' conclusion is only supported inside that unstated input box. That is a validity and generalization concern, not a circularity concern. Overall, the derivation chain is self-contained and the empirical evaluation is standard for machine-learning surrogate studies.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central empirical claims rest on fitted neural network parameters and optimized hyperparameters, plus domain assumptions about the fidelity of the reference solver and the representativeness of the chosen geometry and input ranges. No new physical entities are introduced.

free parameters (2)
  • Neural network weights and biases = Millions of values, e.g., MLP with 7405 nodes in one hidden layer and CNN with 9 filters
    All network parameters are fitted to the ICARUS2D training data; the claim of learning RTE is an empirical fit rather than a derivation.
  • Optuna-selected hyperparameters = Table 4: MLP 7405 nodes; CNN 9 filters, filter size (2,3), pooling (1,1)
    Hyperparameters are chosen by minimizing validation error on the same datasets; the test errors are affected by this selection and no separate validation split is reported.
assumptions (5)
  • domain assumption SNB with Curtis-Godson approximation accurately models gas spectral absorption coefficients
    Invoked in Section 2.2 to justify the reference solver's spectral treatment; not verified in this paper.
  • domain assumption DTRM with 32 rays and 367 spectral bands yields converged reference solutions
    The dataset labels are generated with these discretizations; no convergence study is presented.
  • domain assumption The LHS sampling ranges for temperature, wall temperature, and emissivity cover the intended operating envelope
    The paper never states these ranges in Section 4, so the generalization domain is undefined.
  • domain assumption Fixed geometry and gas composition are representative of industrial furnaces
    The authors acknowledge the simplification in Section 2.4 but then claim industrial applicability.
  • standard math Neural networks with sufficient width can approximate the RTE mapping
    Based on universal approximation [15]; standard for surrogate papers.

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Cite this review

Pith. "Pith review of Feasibility Study of CNNs and MLPs for Radiation Heat Transfer in 2-D Furnaces with Spectrally Participative Gases." pith.science (2026). https://pith.science/paper/27U4OAED

@misc{pith2026250608033,
  author       = {Pith},
  title        = {Pith review of: Feasibility Study of CNNs and MLPs for Radiation Heat Transfer in 2-D Furnaces with Spectrally Participative Gases},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/27U4OAED}},
  note         = {Machine review of arXiv:2506.08033}
}
read the original abstract

Aiming to reduce the computational cost of numerical simulations, a convolutional neural network (CNN) and a multi-layer perceptron (MLP) are introduced to build a surrogate model to approximate radiative heat transfer solutions in a 2-D walled domain with participative gases. The originality of this work lays in the adaptation of the inputs of the problem (gas and wall properties) in order to fit with the CNN architecture, more commonly used for image processing. Two precision datasets have been created with the classical solver, ICARUS2D, that uses the discrete transfer radiation method with the statistical narrow bands model. The performance of the CNN architecture is compared to a more classical MLP architecture in terms of speed and accuracy. Thanks to Optuna, all results are obtained using the optimized hyper parameters networks. The results show a significant speedup with industrially acceptable relative errors compared to the classical solver for both architectures. Additionally, the CNN outperforms the MLP in terms of precision and is more robust and stable to changes in hyper-parameters. A performance analysis on the dataset size of the samples have also been carried out to gain a deeper understanding of the model behavior.

Figures

Figures reproduced from arXiv: 2506.08033 by the authors.

Figure 1
Figure 1. schematics of an industrial furnace for methane reforming process, a) 3D and b) 2D [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. As can be seen, each input parameter (emissivity, boundary temperature, domain temperature) is considered as a channel. We just set the values to zero for those that don’t exist, e.g. wall temperature and emissivity in the domain, domain temperature on the wall. The output layer is the same as the one used with MLP architecture. 4 Results and discussions The geometrical and physical properties of the 2D furnace are … view at source ↗
Figure 2
Figure 2. MLP architecture (a) (b) (c) (d) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: CNN architecture spatial discretization lengths (m) angular discretization nx ny Lx Ly #rays 120 20 12.0 2.0 32 molar concentration of gases wave number (cm−1 ) pressure (atm) xCO2 xH2O νmin νmax ∆ν p 0.1 0.2 150.0 9300.0 25.0 1.0 [PITH_FULL_IMAGE:figures/full_fig_p00…
Figure 4
Figure 4. Figure 4: relative error of boundary points, a) MLP and b) CNN [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: relative error of south wall points, a) MLP and b) CNN [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: relative error of east wall points, a) MLP and b) CNN [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Reference graph

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