{"id":"a28631a5-cb13-4a89-aca9-39448219c747","arxiv_id":"2506.08033","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A CNN surrogate predicts wall radiative fluxes in a 2D furnace about 10,000 times faster than the DTRM solver, with 7 to 9 percent mean relative error, beating an MLP in accuracy and stability.","lead":"A CNN and an MLP were trained to mimic a radiative heat transfer solver for a 2D furnace with absorbing gases, predicting wall irradiation in milliseconds instead of minutes. The CNN was more accurate and stable, with around 7 to 9 percent mean relative error, but the study relies on a fixed geometry and unspecified input ranges.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported 'industrially acceptable' errors cover only an unstated LHS input box and a fixed geometry/gas mixture; no evidence supports extrapolation to the broader furnace conditions claimed.","rationale":"The reader's conditional verdict is well calibrated. I looked for a reason to reject the on-distribution feasibility claim and did not find one: the CNN channel encoding of spatially distributed inputs is a reasonable adaptation, the speedup figures follow from Tables 6, 11, and 12, and the summary honestly acknowledges that generating enough training samples is computationally costly. The main soft spot is that the exact support of the training distribution is never given. Table 1 fixes geometry, composition, pressure, and spectral discretization, but the LHS ranges for T, T0, epsilon and the way spatial fields are generated are absent. Without these, the 7.40% error is only a statement about interpolation on an unknown box. Extrapolating to 'industrial furnaces' is unsupported because radiative transfer is strongly nonlinear in temperature and composition. This does not invalidate the feasibility result for the tested conditions, but it justifies keeping the verdict conditional and asking for the ranges plus an explicit out-of-support test.","tokens_in":6840,"tokens_out":7985,"duration_ms":84566,"concrete_test":"Obtain the exact LHS ranges and field-generation procedure from the authors or code, then build an extended ICARUS2D test set with T, T0, and epsilon widened by 25% beyond the stated or assumed bounds, plus a second geometry (e.g., 14 m x 2.5 m) or gas composition (xCO2=0.15, xH2O=0.25). Recompute the CNN/MLP mean relative errors on this out-of-support test set. If the mean error stays below the same roughly 10% threshold, the industrial-applicability claim is supported; if it degrades markedly, the claim should be restricted to the tested ranges.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4 creates Dataset A/B with Latin-Hypercube Sampling but never states the sampling ranges for gas temperature T, wall temperature T0, wall emissivity epsilon, nor how the spatial fields are parameterized. Table 1 fixes geometry (12 m x 2 m, 120 x 20 mesh), gas composition (xCO2=0.1, xH2O=0.2, 1 atm), and the spectral grid. All reported numbers, including the CNN 7.40% mean relative error on Dataset B and the x7000-x11000 speedup, are therefore interpolation within one fixed operating box and one fixed geometry. The abstract's 'industrially acceptable' and the summary's claim that the networks 'can replace classical solvers' go beyond that support. Radiative intensity depends strongly and nonlinearly on T and gas composition, so outside this box the surrogate has no tested support; if real industrial ranges are wider, errors could be much larger. This is load-bearing because the stated purpose is industrial applicability, not merely interpolation on a fixed test distribution.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":7058,"tokens_out":3180,"duration_ms":37228,"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":[{"comment":"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.","section":"Section 4, Datasets A/B and Table 1"},{"comment":"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.","section":"Section 4, hyperparameter optimization"},{"comment":"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.","section":"Section 4, Tables 7-10 and robustness claim"},{"comment":"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.","section":"Section 4, relative error definition"}],"minor_comments":[{"comment":"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.","section":"Section 4, Datasets A/B"},{"comment":"'The originality of this work lays in the adaptation' should read 'lies in the adaptation'.","section":"Abstract and Section 1"},{"comment":"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?","section":"Section 4, Tables 7-10"},{"comment":"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.","section":"Section 2.4 and Figure 1"},{"comment":"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.","section":"Section 4, Table 6"},{"comment":"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'.","section":"Section 5"},{"comment":"No code or data availability statement is provided; making the datasets and training scripts available would substantially improve reproducibility.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper is a feasible feasibility study, but the missing experimental details around the LHS input ranges and the validation protocol are load-bearing for the stated industrial-applicability claims. The robustness claim is also substantially overstated relative to the evidence. These issues are fixable within the scope of the manuscript, so I do not recommend rejection; however, the revision should be verified by an expert in both radiative transfer and neural-network surrogate validation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague—\n\nThe takeaway: this is a plausible feasibility study of CNN and MLP surrogates for the radiative transfer equation in a 2D rectangular furnace with spectral participating gases. The CNN hits a 7.4% mean relative error on wall irradiation on the larger dataset, with inference speedups around 10,000x, but the paper never states the LHS input ranges for temperature or emissivity, so the accuracy is only known for an unspecified box. The 'industrially acceptable' and 'can replace classical solvers' claims in the abstract go beyond what the evidence supports.\n\nWhat is new: the channel-based encoding—emissivity, wall temperature, and gas temperature as separate input channels—is a clean way to feed spatially varying fields into a CNN. The systematic comparison of MLP vs CNN on two dataset sizes, the per-wall error decomposition, and the dataset-size scaling analysis are useful. The held-out test protocol is sound, and the authors do acknowledge that generating training data is costly, which adds nuance.\n\nWhere it is soft: the missing input ranges are the load-bearing issue. Without them, the 7-9% error might be trivial or impressive; the reader cannot tell. The robustness claim about CNN over MLP rests on a single comparison where dataset B worsened per-wall MLP errors, but the hyperparameters were not retuned for the reduced output vector, so the failure may be due to a bad hyperparameter choice rather than architecture instability. There are no repeated-seed experiments, so the reported means and stds could be noisy. The claim that the surrogate can 'replace classical solvers' is only valid for the fixed geometry, fixed gas composition, and the same input distribution; any real industrial use would need to sample wider ranges or retrain.\n\nBottom line: the paper is an honest empirical exploration with a clear experimental design, and the central result—that NNs can emulate the solver on this configuration—is solid. It needs a major revision to specify the sampling ranges, add uncertainty over seeds, and tone down the generalizability claims. I'd send it to peer review for that revision; the method and dataset are worth engaging with.\n\nRecommendation: accept for review with major revision, not desk reject.","headline":"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.","tokens_in":7571,"tokens_out":2843,"would_cite":false,"duration_ms":29371,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["radiative heat transfer","spectrally participative gases","convolutional neural network","multi-layer perceptron","surrogate model","discrete transfer radiation method","statistical narrow band model","2D furnace"],"falsifier":"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.","tokens_in":6680,"feed_emoji":"🔥","tokens_out":8075,"duration_ms":74261,"temperature":0.7,"pith_summary":"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.","feed_headline":"CNN surrogate reproduces furnace heat solver at 7 percent error","feed_subtitle":"MLP and CNN models cut inference from 138 seconds per case to milliseconds, with CNN the more stable net.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Provides the form of the radiative transfer equation that the solver and therefore the surrogate are emulating.","marker":"[1]"},{"why":"Supplies the standard RTE reference used to define the spectral intensity and boundary conditions.","marker":"[2]"},{"why":"Introduces the statistical narrow band model used to compute spectral gas transmissivity in the reference solver.","marker":"[3]"},{"why":"Provides the Curtis approximation used within the SNB-CG model for band-averaged gas absorption.","marker":"[4]"},{"why":"Provides the Godson approximation used within the SNB-CG model for raypath transmissivity.","marker":"[5]"},{"why":"Introduces the discrete transfer radiation method that ICARUS2D implements to solve the rays.","marker":"[14]"},{"why":"Supplies the minimum-width universal approximation result that motivates the hyperparameter search ranges for the networks.","marker":"[15]"},{"why":"Identifies the laboratory that co-developed the ICARUS2D solver used to generate the training data.","marker":"[12]"},{"why":"Identifies the industrial partner behind ICARUS2D, grounding the claim that the reference solver reflects industrial furnace practice.","marker":"[13]"}],"fun_headline_variants":["Neural nets speed furnace radiation solver 7000x","CNN beats MLP for furnace heat transfer, 7% error","AI mimics radiation heat transfer in 2D furnaces","CNN cuts furnace simulation time to milliseconds"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Neural nets speed furnace radiation solver 7000x","CNN beats MLP for furnace heat transfer, 7% error","AI mimics radiation heat transfer in 2D furnaces","CNN cuts furnace simulation time to milliseconds"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000519,"raw_usage":{"total_tokens":2519,"prompt_tokens":958,"completion_tokens":1561,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":574,"completion_tokens_details":{"reasoning_tokens":1496}},"tokens_in":574,"tokens_out":1561,"duration_ms":11063,"temperature":1.0,"reasoning_tokens":1496,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:34:54.960443+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Calculation of radiative heat transfer in combustion systems.Clean Air, 3(1):113–143, 2002","cited_arxiv_id":null,"evidence_quote":"Provides the form of the radiative transfer equation that the solver and therefore the surrogate are emulating."},{"cited_title":"CRC press, 2020","cited_arxiv_id":null,"evidence_quote":"Introduces the statistical narrow band model used to compute spectral gas transmissivity in the reference solver."},{"cited_title":"A statistical model for watervapour absorption.QJ Roy","cited_arxiv_id":null,"evidence_quote":"Provides the Curtis approximation used within the SNB-CG model for band-averaged gas absorption."},{"cited_title":"The evaluation of infra-red radiative fluxes due to atmospheric water vapour.Quarterly Journal of the Royal Meteorological Society, 79(341):367–379, 1953","cited_arxiv_id":null,"evidence_quote":"Provides the Godson approximation used within the SNB-CG model for raypath transmissivity."},{"cited_title":"A new radiation solution method for incorporation in general combustion prediction procedures","cited_arxiv_id":null,"evidence_quote":"Introduces the discrete transfer radiation method that ICARUS2D implements to solve the rays."},{"cited_title":"Available athttp://em2c.centralesupelec.fr","cited_arxiv_id":null,"evidence_quote":"Identifies the laboratory that co-developed the ICARUS2D solver used to generate the training data."},{"cited_title":"Available athttp://www.airliquide.com","cited_arxiv_id":null,"evidence_quote":"Identifies the industrial partner behind ICARUS2D, grounding the claim that the reference solver reflects industrial furnace practice."}],"review_version":1}