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REVIEW 3 major objections 5 minor 65 references

A data-driven two-microphone method for in-situ sound absorption measurements

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

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Pith's one-line read A trained neural network recovers the infinite-sample sound absorption coefficient from a two-microphone measurement over a finite porous slab.

desk verdict 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. read the letter →

arxiv 2502.04143 v1 pith:JOXBY7GU submitted 2025-02-06 cs.SD cs.LGeess.AS

Leon Emmerich , Patrik Aste , Eric Brandão , Mélanie Nolan , Jacques Cuenca , U. Peter Svensson , Marcus Maeder , Steffen Marburg
show 1 more author
Elias Zea
This is my paper · ORCID
classification cs.SDcs.LGeess.AS
keywords soundabsorptioncoefficienttwo-microphonemethodin-situmeasurementedgediffractionneuralnetworkboundaryelementporousmaterialsdeeplearning
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 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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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 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.

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 (3)
  1. [IV.C.1 and Figs. 6-8] 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.
  2. [IV.C.2 and Eqs. (10)-(12)] 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.
  3. [III.B, III.C.2, and IV.C.2] 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.
minor comments (5)
  1. [III.C.2, Eq. (13)] 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.
  2. [Fig. 7 caption] The caption of Fig. 7 begins with the word 'Preliminary', which looks like a leftover from an earlier draft and should be removed.
  3. [IV.C.3 and Fig. 8] 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.
  4. [III.C.2] 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.
  5. [IV.C.3] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the network learns a mapping from simulated finite-sample transfer functions to Miki-model infinite-sample absorption, and the central claim is externally grounded by independent impedance-tube validation.

full rationale

The paper's derivation chain is a supervised-learning pipeline: BEM simulations generate finite-sample two-microphone transfer functions H12, and the same Miki/BEM model supplies the infinite-sample absorption target via Eqs. (4), (5), (7), and (3). Both input and target derive from the same forward model, which introduces model dependence but not circularity: the target is not defined in terms of the network, and the network's mapping is learned rather than analytically forced. The numerical validation on a held-out set drawn from the same simulation distribution tests interpolation, not external validity, and is not a by-construction identity. The experimental validation uses independently measured transfer functions from free-field two-microphone measurements and compares the network's normal-incidence predictions to impedance-tube measurements, which are external to the BEM/Miki training pipeline. At oblique incidence the reference is the Miki model, the same family used to generate training targets, so that comparison is a weaker form of evidence, but it is not circular because the measured inputs are independent and the agreement is not guaranteed by construction. The BEM simulator is openly accessible, and the Miki model is an external empirical model. Self-citations to Zea et al. and Brandão et al. are methodological and not load-bearing: the BEM code is independently reproducible and no uniqueness theorem or ansatz is smuggled in via self-citation. No equation reduces to another by construction, and no fitted parameter is renamed as a prediction. The documented sim-to-real mismatch above 1400 Hz (Fig. 6) is a correctness/generalization limitation, not circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the validity of the BEM/Miki simulations as a stand-in for real measurements. The axioms above capture the modeling assumptions (local reaction, Miki model, rigid baffle, specular reflection, numerical quadrature) and the free parameters capture the key design choices (microphone heights, filtering, network hyperparameters) that are not derived from first principles.

free parameters (3)
  • Microphone heights z1, z2 = 1 cm, 3 cm
    Chosen to balance near-surface placement and inter-microphone distance; directly affects the transfer function that is the network input.
  • Moving-average filter window size = 20 frequency steps (applied twice)
    Applied to measured transfer functions to smooth artifacts; affects the input to the network and the traditional method.
  • Network training hyperparameters = initial learning rate 1e-3, weight decay 1e-3, early stopping after 125 epochs
    Chosen by hand; influence generalization but are not derived from first principles.
assumptions (5)
  • domain assumption The porous sample is locally reacting.
    The surface impedance model in Eq. (7) assumes local reaction, which may not hold for all materials.
  • domain assumption The Miki (Delany-Bazley-Miki) model accurately describes the acoustic behavior of the tested fibrous material.
    Used for BEM training data and reference absorption; if inaccurate, the network's target is biased.
  • domain assumption The sample is flush-mounted in a rigid, infinite baffle.
    The BEM model and experimental setup assume an infinite rigid baffle; real baffles are finite, and slits cause artifacts.
  • domain assumption Specular reflection from an image source is valid for the infinite-sample reference.
    Eq. (2) assumes specular reflection, used to compute the traditional two-microphone reference absorption.
  • domain assumption Gauss-Legendre quadrature with 36 points per element is sufficiently accurate.
    Used in BEM discretization; the paper notes a more sophisticated adaptive integration is recommended for general use.

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Cite this review

Pith. "Pith review of A data-driven two-microphone method for in-situ sound absorption measurements." pith.science (2026). https://pith.science/paper/JOXBY7GU

@misc{pith2026250204143,
  author       = {Pith},
  title        = {Pith review of: A data-driven two-microphone method for in-situ sound absorption measurements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JOXBY7GU}},
  note         = {Machine review of arXiv:2502.04143}
}
read the original abstract

This work presents a data-driven approach to estimating the sound absorption coefficient of an infinite porous slab using a neural network and a two-microphone measurement on a finite porous sample. A 1D-convolutional network predicts the sound absorption coefficient from the complex-valued transfer function between the sound pressure measured at the two microphone positions. The network is trained and validated with numerical data generated by a boundary element model using the Delany-Bazley-Miki model, demonstrating accurate predictions for various numerical samples. The method is experimentally validated with baffled rectangular samples of a fibrous material, where sample size and source height are varied. The results show that the neural network offers the possibility to reliably predict the in-situ sound absorption of a porous material using the traditional two-microphone method as if the sample were infinite. The normal-incidence sound absorption coefficient obtained by the network compares well with that obtained theoretically and in an impedance tube. The proposed method has promising perspectives for estimating the sound absorption coefficient of acoustic materials after installation and in realistic operational conditions.

Figures

Figures reproduced from arXiv: 2502.04143 by the authors.

Figure 1
Figure 1. FIG. 1: Schematic of the two-microphone method above a baffled porous layer, flush [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Experimental setup of the two-microphone method in the anechoic chamber at the [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Schematic of the network architecture. The total number of trainable parameters [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Training and validation loss over 125 training epochs. [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Histograms of the recorded error per sample for the two-microphone method and [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Comparison between measurement I (upper row) and measurement V (lower row) [PITH_FULL_IMAGE:figures/full_fig_p023_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Preliminary: Comparison of the results for the normal sound absorption coefficient [PITH_FULL_IMAGE:figures/full_fig_p027_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Comparison of the network predictions of measurements IV (a) and VIII (b) in [PITH_FULL_IMAGE:figures/full_fig_p030_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

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