{"id":"108266bc-dba3-4d02-bea3-4ce2d5bd543e","arxiv_id":"2502.04143","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A 1D convolutional neural network maps two-microphone transfer functions from finite porous samples to the sound absorption coefficient of an equivalent infinite sample, validated with BEM simulations and free-field experiments.","lead":"This paper trains a neural network to estimate the sound absorption of a porous material from a simple two-microphone measurement, correcting for edge effects that occur when the sample is not infinitely large. The method could make in-situ acoustic absorption testing easier and more realistic than standard lab or large-array approaches.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Sim-to-real mismatch documented in Fig. 6 above 1400 Hz is not reflected in the validation: network reliability over 100–2000 Hz is unsupported at high frequencies; per-band experimental errors would settle it.","rationale":"The reader and I agree that the simulation-to-real gap is the load-bearing assumption. I sharpen that concern: the paper itself supplies evidence of a specific regime where the assumption breaks, namely above 1400 Hz in Fig. 6. This is not an ad hominem or a circularity objection: the BEM transfer functions do match the measurements up to 1400 Hz, and the impedance-tube measurements are an independent reference at normal incidence. The numerical test set shows that the network can undo edge diffraction in simulation, and the experimental full-band curves look plausible. However, full-band errors can hide a systematic high-frequency failure, especially because the network output is a smooth sigmoid curve and the measured high-frequency input is demonstrably outside the training distribution. A band-wise error analysis on the already-collected experimental data would settle whether the high-frequency mismatch matters; if it does, the central claim should be re-scoped to the band where the input simulations are representative. This does not move the verdict: the paper remains a conditional acceptance pending that check and the broader experimental validation already called for by the reader.","tokens_in":16420,"tokens_out":5580,"duration_ms":61820,"concrete_test":"Split the 100–2000 Hz range at 1400 Hz and compute the network prediction error against the impedance-tube and Miki references separately for each measurement (I–VIII). If the mean absolute error above 1400 Hz is not significantly larger than below, the concern fails. If it is larger, the claim should be restricted to ≤1400 Hz or the network retrained with noise-augmented, high-frequency-realistic BEM data. A useful additional control: feed the network with measured H12 whose components above 1400 Hz are removed; if the predictions are nearly unchanged, the network is ignoring the corrupted band and the over-scoping is less severe.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the network reliably estimates the infinite-sample absorption over the full 100–2000 Hz band. Since the network is trained on noise-free BEM/Miki simulations, experimental validation is the only guard against simulation-to-real mismatch. Section IV.C.1 documents that mismatch: measured and simulated transfer functions agree only up to 1400 Hz, while above that the real and imaginary parts diverge, with a sharp peak and a steep decline (Fig. 6). Yet the validation reports only full-band curves (Figs. 7 and 8) and no per-frequency error statistics, and the measured transfer functions are smoothed with two consecutive 20-step moving-average filters before inference. If the network relies on high-frequency input features that are corrupted in real measurements, predictions above 1400 Hz could be biased while the full-band MSE remains small. The concerning part is not merely hypothetical sensor noise: the paper's own comparison shows the training distribution does not cover the measured high-frequency regime. Without band-resolved experimental error, the headline claim that the network 'reliably' predicts the in-situ absorption 'as if the sample were infinite' is over-scoped relative to the evidence presented.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a data-driven extension of the classical two-microphone in-situ absorption measurement method. A 1D residual convolutional network is trained on synthetic boundary-element-method (BEM) simulations, using the complex-valued two-microphone transfer function and the source elevation angle as inputs, to predict the absorption coefficient of an infinite porous slab. The training set comprises 50,000 BEM/Miki simulations and the numerical test set of 3,000 unseen simulations yields a mean squared error of 8.42e-5. The method is then validated experimentally on two sizes of baffled glass-wool samples (600x600x20 mm and 300x600x20 mm) at normal and oblique incidence, with comparisons to the Miki model and impedance-tube measurements. The authors conclude that the network can reliably predict the in-situ sound absorption coefficient as if the sample were infinite, while acknowledging sensitivity to low-frequency input variations and the absence of noise in the training data.","tokens_in":16610,"tokens_out":3713,"duration_ms":42750,"significance":"If the claims are fully supported, the method is practically attractive because it augments a standard, widely used two-microphone setup with a data-driven correction for edge diffraction, avoiding microphone arrays or complex analytical finite-sample models. The numerical validation is strong in scale (3,000 test samples) and the authors make the BEM simulator openly available, which aids reproducibility. The experimental campaign, however, covers only one material (one nominal flow resistivity), two sample sizes, and eight configurations, and the published validation curves are full-band only. The central claim of reliable prediction over the full 100-2000 Hz band therefore rests on experimental evidence that is currently less resolved than the claim. The work is nevertheless a meaningful step toward practical in-situ absorption estimation, provided the indicated validation gaps are addressed.","major_comments":[{"comment":"Section IV.C.1 and Fig. 6 document that the measured and BEM-simulated transfer functions agree only up to about 1400 Hz, while above that the real and imaginary parts diverge sharply. The subsequent validation in Figs. 7 and 8, however, reports only full-band absorption curves and gives no per-frequency or per-band error statistics. Because the network was trained exclusively on BEM simulations, a mismatch above 1400 Hz could directly bias the network predictions in exactly the range where the training distribution does not match the measurements. To support the claim of reliable prediction over the full 100-2000 Hz band, the authors should provide band-resolved errors (for example, mean and standard deviation of the network-minus-reference absorption in 1/3-octave or 100-500, 500-1400, 1400-2000 Hz bands) for each experimental configuration.","section":"IV.C.1 and Figs. 6-8"},{"comment":"The paper itself states in Section IV.C.2 that the network was trained solely on noise-free numerical data, and it identifies a sensitivity to low-frequency input variations amplified by the input standardization in Eqs. (10)-(12). Since the experimental transfer functions are smoothed with two moving-average filters before inference, the effect of noise and measurement uncertainty on the network output is not quantified. A concrete robustness test on the numerical test set with added noise (for example, varying signal-to-noise ratios on the transfer function) would show how the 8.42e-5 test MSE degrades with realistic perturbations. Without such a test, the experimental agreement in Figs. 7-8 cannot be confidently attributed to the network rather than to the smoothing and the particular measured configurations.","section":"IV.C.2 and Eqs. (10)-(12)"},{"comment":"Both the training inputs and the training targets are generated with the same BEM model using the Miki material model, and the experimental validation uses a single material with one manufacturer-provided flow resistivity value. The network therefore learns the mapping between finite-sample transfer functions and infinite-sample absorption coefficients as defined by that specific model family; any systematic Miki/BEM bias or material-model mismatch would be inherited. The comparison with impedance-tube measurements is a useful independent reference, but it is reported only qualitatively for full-band curves. To reduce this model-dependence concern, the authors should either validate on at least one additional material with known properties or provide a quantitative per-band comparison of the network predictions against the impedance-tube results, acknowledging that the Miki-model target itself may deviate from the physical infinite-sample absorption.","section":"III.B, III.C.2, and IV.C.2"}],"minor_comments":[{"comment":"Equation (13) writes the MSE as (α_n(f_m) - α_n(f_m))^2, which appears to use the same symbol for the prediction and the reference; the intended target should be denoted differently (for example, with a hat or a separate symbol) to avoid ambiguity.","section":"III.C.2, Eq. (13)"},{"comment":"The caption of Fig. 7 begins with the word 'Preliminary', which looks like a leftover from an earlier draft and should be removed.","section":"Fig. 7 caption"},{"comment":"The text in Section IV.C.3 misassigns the panels of Fig. 8: it refers to the small-sample oblique measurement at 27 degrees as appearing in Fig. 8a, whereas the caption and the measurement table indicate that Fig. 8a corresponds to measurement IV (large sample, 30 degrees) and Fig. 8b to measurement VIII (small sample, 27 degrees). The cross-references should be corrected.","section":"IV.C.3 and Fig. 8"},{"comment":"The phrase 'as Scikit-Learn recommends' for the Adam optimizer weight decay is imprecise; the recommended setting refers to a specific deep-learning framework and should be cited accordingly or rephrased.","section":"III.C.2"},{"comment":"The oblique-incidence experimental validation contains only two measurements (one per sample size) and the authors already note that further angled measurements are needed; this limitation should be stated prominently in the conclusions, not only in the body text.","section":"IV.C.3"}],"recommendation":"major_revision","confidential_remarks":"I see no citation or authorship concerns. The main issue is that the experimental validation is currently presented at a coarser frequency resolution than the claim of full-band reliability, and the noise-free training is acknowledged but not stress-tested. A revision that adds per-band experimental errors and a numerical robustness test would make the central claim much more defensible. The paper fits the journal's scope and the authors' open BEM simulator is a reproducibility asset."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The short version: this is a legitimate incremental contribution, not a breakthrough. It takes the two-microphone method, which everyone knows, and replaces the analytic infinite-sample assumption with a learned correction for edge diffraction. The novelty is modest—it extends Zea et al.'s ResNet idea to a simpler 1D input and adds incidence angle—but that is not a flaw. The numerical study is well done: 3000 held-out BEM samples, MSE ~8e-5, and the error histogram shows the network clearly beats the classical two-mic on finite samples. The experimental work is honest: eight measurements on one glass-wool material, with impedance-tube and Miki references, and the authors explicitly note the network's sensitivity to low-frequency input variations and the absence of noise in training data.\n\nThe soft spots are real but not fatal. First, circularity: the network learns to map finite-sample transfer functions to infinite-sample absorption, but both input and target come from the same BEM/Miki forward model. The experimental validation partially breaks that loop, since the measured transfer functions are not from the simulator, but the target references (Miki, impedance tube) are still model- or lab-dependent. Second, the sim-to-real mismatch: their own Fig. 6 shows measured and simulated transfer functions agree only up to ~1400 Hz for both sample sizes, after which they diverge markedly. The validation plots show full-band curves only, so we cannot see whether the network's errors are concentrated above 1400 Hz. That makes the headline claim 'reliably predict ... as if the sample were infinite' over the full 100–2000 Hz band under-supported. A per-band RMSE table would settle it. Third, the paper is light on practical details: no code or trained model released, data 'available upon reasonable request,' and the input standardization issue that amplifies low-frequency noise is acknowledged but not solved.\n\nFor a reader in acoustic material characterization, this paper is worth a careful look. It is clearly written, the method is reproducible in principle (BEM simulator is open-source), and the idea of using the two-mic method with a learned edge-diffraction correction is practical and likely to be built upon. I would not trust the full-band reliability claim as stated, but I would send it to review—it deserves referee time to push for band-resolved experimental error statistics and a cleaned-up data availability statement.","headline":"Useful incremental step that combines a 1D CNN with the two-mic method, but the 'reliable over 100–2000 Hz' claim is stronger than the experimental evidence supports.","tokens_in":17202,"tokens_out":1616,"would_cite":true,"duration_ms":16586,"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":"A trained neural network recovers the infinite-sample sound absorption coefficient from a two-microphone measurement over a finite porous slab.","keywords":["sound absorption coefficient","two-microphone method","in-situ measurement","edge diffraction","neural network","boundary element method","porous materials","deep learning"],"falsifier":"Take a 30-by-30 cm sheet of open-cell melamine foam, measure it with the same two-microphone geometry and several source heights, and compare the network's output with impedance-tube absorption from 100 to 2000 Hz. A systematic low-frequency discrepancy would show that the network learned the Miki target curves and the simulated edge effect rather than a material-independent correction.","tokens_in":16205,"feed_emoji":"🔊","tokens_out":8566,"duration_ms":83864,"temperature":0.7,"pith_summary":"This paper tackles the known weakness of the classical two-microphone in-situ absorption measurement: its reflection-coefficient formula assumes an infinitely large sample, so measurements of real finite samples are contaminated by edge-diffraction oscillations. The authors train a one-dimensional residual convolutional neural network on boundary-element simulations of finite porous slabs to map the complex-valued transfer function between two microphones, together with the source elevation angle, straight to the absorption coefficient an infinite sample of the same material would give. On 3000 unseen simulations the network's mean error was about three orders of magnitude lower than the traditional two-microphone estimate, and on baffled glass-wool samples it removed most of the low-frequency oscillations and tracked both the Miki-model reference and impedance-tube measurements. The paper concludes that a routine two-microphone rig, trained only on synthetic data, can deliver in-situ absorption coefficients as if the sample were infinite.","feed_headline":"Neural net fixes edge effects in two-mic absorption tests","feed_subtitle":"Simulation-only training lets two microphones over a finite slab recover the infinite-sample absorption curve; glass-wool tests agree.","key_machinery":"The load-bearing object is a 1D residual convolutional network that receives $[\\Re H_{12}(f), \\Im H_{12}(f)] \\in \\mathbb{R}^{2\\times 190}$ and the source elevation $\\theta$, and outputs a 190-point absorption spectrum bounded to $[0,1]$ by a sigmoid. Four residual blocks with max-pooling halve the frequency dimension while doubling feature channels, then fully connected layers decode the bottleneck into the absorption curve. The boundary-element model of a finite baffled porous slab supplies the training inputs (finite-sample transfer functions), while the Miki model supplies the training targets (infinite-sample absorption), so the network's learned mapping is, in effect, a learned edge-diffraction correction.","core_discovery":"The paper's central claim is that the edge-diffraction artifact of finite samples is learnable from the transfer function itself. Feeding the real and imaginary parts of $H_{12}(f)$ over 100–2000 Hz plus the scalar source elevation into a 1D residual CNN yields the absorption coefficient $\\alpha(f,\\theta)$ of the equivalent infinite sample. The network is trained exclusively on noise-free boundary-element simulations using the Delany–Bazley–Miki material model, yet when applied to real measurements it suppresses the characteristic low-frequency oscillations of the classical method, predicts absorption slightly below the Miki reference, and reproduces the frequency shift caused by oblique incidence. This is offered as evidence that the traditional two-microphone method can be upgraded to an in-situ, angle-dependent, infinite-sample-equivalent measurement without a larger sample or a microphone array.","pith_inferences":["Beyond the paper: if the learned correction is truly about edge diffraction and not just about Miki-model curves, the same architecture could be retrained with a more general material model and made to output surface impedance or flow resistivity, extracting more physical information from the same two microphones.","Beyond the paper: the observed low-frequency sensitivity, where small changes in the transfer function near the zero-crossing of $\\Re H_{12}$ alter predictions, suggests that augmenting training with noisy, slit-perturbed, or baffle-imperfect simulations is a direct and testable path to field robustness.","Beyond the paper: the consistent offset between large-sample and small-sample experimental predictions (closer to Miki vs. closer to impedance-tube values) could indicate a sample-size-dependent bias; a single material measured at several sizes would disentangle material variability from network bias.","Beyond the paper: the practical scope is best stated as 'absorption of the material as modeled by Miki', since for non-fibrous or non-locally-reacting materials the infinite-sample reference itself is not defined by the training data."],"forward_implications":["A standard two-microphone setup can be used on finite samples without enforcing the large-sample condition, since the network compensates for edge diffraction.","The method generalizes to sample sizes down to at least 30 cm edges and source elevations up to 80 degrees in simulation, and to varied source distances in measurement.","Because the network is trained purely on simulations, new materials or geometries can be added by generating more boundary-element data rather than by collecting new measurements.","Normal-incidence predictions from the free field agree with impedance-tube data, offering a free-field cross-check of laboratory tube measurements.","Oblique-incidence measurements produce the expected shift of the absorption spectrum with angle, something the classical finite-sample formula cannot deliver reliably."],"supporting_citations":[{"why":"Documents the infinite-sample assumption of in-situ methods and the edge-diffraction uncertainties this work addresses.","marker":"[4]"},{"why":"Gives the spherical-wave reflection-coefficient formula used to compute the traditional two-microphone absorption reference from the measured transfer function.","marker":"[8]"},{"why":"Provides the boundary-element model of finite baffled samples used to generate all training, validation, and test transfer functions.","marker":"[18]"},{"why":"Establishes the deep-residual-learning approach and the BEM data-generation procedure that this work adapts from absolute pressures to complex transfer functions.","marker":"[32]"},{"why":"Defines the empirical material model used to build the surface-impedance boundary condition and the infinite-sample absorption target.","marker":"[33]"},{"why":"Presents a related hybrid physics/data retrieval method that also exploits phase content and serves as the methodological alternative.","marker":"[36]"},{"why":"Introduces the two-microphone free-field measurement technique that the proposed network augments.","marker":"[37]"}],"fun_headline_variants":["Neural net removes edge effects in two-mic absorption","Simulation-trained AI upgrades two-mic absorption to infinite","Learned transfer function gives infinite-slab absorption","Two mics plus CNN mimic infinite porous slab absorption","Data-driven net fixes finite-sample artifact in absorption"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that noise-free boundary-element simulations built on the Miki empirical material model are close enough to real measurements that a network trained only on those simulations can remove edge diffraction correctly on real finite samples.","fun_headline_variants_meta":{"raw":{"variants":["Neural net removes edge effects in two-mic absorption","Simulation-trained AI upgrades two-mic absorption to infinite","Learned transfer function gives infinite-slab absorption","Two mics plus CNN mimic infinite porous slab absorption","Data-driven net fixes finite-sample artifact in absorption"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000193,"raw_usage":{"total_tokens":1325,"prompt_tokens":893,"completion_tokens":432,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":509,"completion_tokens_details":{"reasoning_tokens":356}},"tokens_in":509,"tokens_out":432,"duration_ms":4430,"temperature":1.0,"reasoning_tokens":356,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T23:21:15.606530+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a 30-by-30 cm sheet of open-cell melamine foam, measure it with the same two-microphone geometry and several source heights, and compare the network's output with impedance-tube absorption from 100 to 2000 Hz. A systematic low-frequency discrepancy would show that the network learned the Miki target curves and the simulated edge effect rather than a material-independent correction.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents the infinite-sample assumption of in-situ methods and the edge-diffraction uncertainties this work addresses."},{"cited_title":"Hald , author W","cited_arxiv_id":null,"evidence_quote":"Gives the spherical-wave reflection-coefficient formula used to compute the traditional two-microphone absorption reference from the measured transfer function."},{"cited_title":"De Bruijn , title A mathematical analysis concerning the edge effect of sound absorbing materials , journal Acta Acustica United with Acustica 28(1), pages 33--44 ( year 1973 )","cited_arxiv_id":null,"evidence_quote":"Provides the boundary-element model of finite baffled samples used to generate all training, validation, and test transfer functions."},{"cited_title":"Eser , author L","cited_arxiv_id":null,"evidence_quote":"Establishes the deep-residual-learning approach and the BEM data-generation procedure that this work adapts from absolute pressures to complex transfer functions."},{"cited_title":"Eser , author L","cited_arxiv_id":null,"evidence_quote":"Defines the empirical material model used to build the surface-impedance boundary condition and the infinite-sample absorption target."},{"cited_title":"Zea , author E","cited_arxiv_id":null,"evidence_quote":"Presents a related hybrid physics/data retrieval method that also exploits phase content and serves as the methodological alternative."},{"cited_title":"Aste , author E","cited_arxiv_id":null,"evidence_quote":"Introduces the two-microphone free-field measurement technique that the proposed network augments."}],"review_version":1}