Pith. sign in

REVIEW 3 major objections 6 minor 42 references

Quadrature-Aware Complex-Linear Neural Operator for Boundary-to-Field Prediction in Resonant Acoustics

T0 review · 3 major / 6 minor · reviewed 2026-07-11 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Hard-coding complex-linear boundary physics into a neural operator cuts acoustic field error roughly in half and keeps exact superposition.

desk verdict Careful structure-preserving operator for fixed-cavity acoustics: real gains over matched DeepONet, scoped to one linear resonant box. read the letter →

arxiv 2607.04407 v1 pith:P2ZXS5MG submitted 2026-07-05 physics.flu-dyn cs.LG

Muhammad Idrees Khan , Hua-Dong Yao This is my paper
classification physics.flu-dyncs.LG
keywords neuraloperatorcomplexlinearityboundaryexcitationresonantacousticslatticeBoltzmannmethodsurfacequadratureDeepONet
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

Predicting the sound field inside a cavity from a vibrating wall is expensive if every new wall-velocity pattern needs a full wave simulation. This paper builds a neural operator that keeps the known complex-linear map from wall normal velocity to interior pressure exact by construction: learned nonlinear bases for source and receiver locations are contracted only through an explicit surface quadrature of the complex velocity. Because the source amplitude never enters a nonlinear network, superposition, scaling, and zero-input response hold to machine precision, and the source can be represented by coordinates, normals, and areas rather than a fixed sensor vector. Against a matched fixed-sensor DeepONet baseline on verified lattice-Boltzmann cavity data, the model roughly halves held-out field error, remains accurate on newly simulated mixed sources, and is orders of magnitude faster than the reference solver. A sympathetic reader cares because design, control, and uncertainty studies in vibroacoustics are limited by repeated linear solves; a structure-preserving surrogate removes that bottleneck while staying faithful to the physics.

What carries the argument

The quadrature-aware complex-linear boundary operator (CLBO): learned complex source and receiver basis functions of rank R are coupled only by a weighted surface sum of prescribed normal velocity, so pressure is a low-rank inner product that is exactly linear in the boundary excitation.

What would settle it

Train both models on the same cavity data, then evaluate on independently simulated complex mixtures of held-out wall-velocity fields at the same frequencies; if CLBO no longer shows lower relative field error and near-zero superposition residual than the nonlinear-branch baseline, the central claim fails.

Watch

Extended reading notes

Core claim

Enforcing the known complex-linear boundary-to-field structure through a quadrature-aware complex-linear boundary operator (CLBO) improves physical consistency and generalization under distributed acoustic excitation: mean complex relative field error 0.184 ± 0.00771 versus 0.367 ± 0.00742 for a fixed-sensor DeepONet, measured superposition error 1.31 × 10^-7, and mean error 0.237 versus 0.415 on newly simulated mixed-source cases.

Load-bearing premise

The acoustic problem is treated as a complex-linear map from wall normal velocity to pressure on one fixed cavity and frequency set, so hard-coding that algebra is the right inductive bias for the reported gains.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes a quadrature-aware complex-linear boundary operator (CLBO) that maps complex normal wall velocity to complex pressure by coupling learned source and receiver bases through an explicit surface-quadrature contraction, so the source enters linearly by construction. On a fixed resonant rectangular cavity with verified MRT-LBM labels, CLBO is compared under matched splits and optimization to a fixed-sensor complex DeepONet. Across five seeds it reports lower complex relative field error (0.184 vs 0.367), near-machine-precision superposition, better receiver interpolation and source-family holdout, and lower error on five newly simulated mixed-source cases (0.237 vs 0.415), with large inference speedup relative to LBM. The central claim is that hard-coding complex-linear boundary-to-field structure improves physical consistency and generalization under distributed acoustic excitation within this scoped linear, fixed-geometry setting.

Significance. If the reported advantage holds, the work is a clear, useful contribution to structure-preserving operator learning for linear acoustics: it turns a known physical property (complex linearity of the boundary-to-field map) into an architectural constraint rather than a soft training target, and it pairs that constraint with a solver-agnostic surface data contract and a verified LBM pipeline. Strengths that should be credited include algebraic guarantees by construction (Eqs. 12–14) with measured implementation errors near floating-point floor, fixed case-level splits with multi-seed statistics, independent MRT-LBM mixed-source targets rather than algebraic rearrangements alone, and an explicit evaluation suite (structure, interpolation, remeshing, family holdout, data efficiency, cost). Within the stated single-cavity linear regime this is a solid methods result; broader industrial impact depends on geometry-varying extensions the authors already flag.

major comments (3)
  1. [§6.2, Table 4] Table 4 and §6.2: the mixed-source generalization claim is load-bearing for the paper’s central message, but rests on only five newly simulated mixtures (seed-2026 checkpoints). The paired bootstrap interval is welcome, yet n=5 is thin for a headline generalization result. Please either expand the mixed-source suite (more frequencies, more coefficient draws, more seeds) or temper the abstract/conclusion language to match the sample size and report case-level errors explicitly.
  2. [§6.4, Fig. 8(b)] §6.4 and Fig. 8(b): CLBO’s source-sampling transfer relative error is reported as 1.00 (vs 2.33 for DeepONet). An O(1) relative error means the variable-discretization interface does not yet deliver usable accuracy under remeshing, even though contribution 2 advertises coordinates/normals/quadrature weights instead of a fixed flattened vector. Clarify what “transfer error” normalizes against, whether native-mesh accuracy is preserved under mild coarsening, and revise the contribution wording so it claims only the tested (limited) transfer, not practical mesh independence.
  3. [§2.1, §6.1–6.2] §2.1 and §6.1: the inductive bias assumes the map is adequately complex-linear under the trained frequencies and finite MRT damping (away from exact lossless eigenfrequencies). Verification (Fig. 4, piston benchmark, solver superposition 1.59e-5) supports this in aggregate, but primary and mixed-source errors are not stratified by proximity to resonance or by frequency. Because resonant cases dominate acoustic difficulty, please report error versus frequency (or distance to the first longitudinal mode) for both models so readers can judge whether the linearity assumption and the reported advantage hold near the peaks that matter.
minor comments (6)
  1. [Throughout] Notation for the model name is inconsistent (clbo / CLBO /clbo). Standardize to one form in text, figures, and tables.
  2. [Fig. 5, Table 3] Fig. 5 phase panels report radians while Table 3 reports phase MAE in degrees; state units in every panel caption.
  3. [§6.6, Table 5] Table 5: at 10% training data CLBO is slightly worse than DeepONet (1.04 vs 1.00). Mention this explicitly in §6.6 so the data-efficiency narrative is not read as uniform dominance.
  4. [§3.5, Table 3] Parameter counts differ (CLBO 653952 vs DeepONet 770432). A brief capacity-matched or FLOPs-matched note would strengthen the claim that the gain is structural rather than capacity-driven.
  5. [Data availability] Data and code are “available upon reasonable request.” For a methods paper whose value is the operator structure and evaluation protocol, a public checkpoint, split manifests, and training script would substantially improve reproducibility.
  6. [§3.1] Eq. (9) Fourier features: state whether bands are shared across coordinates and how frequency is normalized before banding; a one-line formula for the frequency feature map would help reimplementation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: algebraic guarantees are by construction and honestly labeled; predictive claims rest on independent MRT-LBM fields.

full rationale

The paper's derivation chain is self-contained and non-circular. Section 2.1 states the standard complex-linear acoustic map (Eqs. 5–6) as known physics under fixed geometry, frequency, and passive BCs, not as a result derived from the model. CLBO then hard-codes that structure via the surface quadrature (Eq. 12) and low-rank decode (Eq. 13); Section 3.3 explicitly proves superposition, homogeneity, and zero-input consistency by substitution, and Section 6.4 reports the measured superposition error (1.31×10⁻⁷) as an implementation check of those algebraic guarantees—not as an empirical prediction of nature. Predictive claims (primary held-out error 0.184 vs 0.367, mixed-source 0.237 vs 0.415) are scored against verified MRT-LBM reference fields, including five newly simulated complex mixtures that are not algebraic rearrangements of model outputs. Residual weights appear only in ablations; the principal comparison is supervised-only. Self-citations (e.g., [36] on LBM turbulence) are peripheral and not load-bearing for the CLBO advantage. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors, and no known empirical pattern is merely re-labeled. Within the stated single-cavity linear regime, the inductive bias is enforced by construction and tested against independent data.

Assumptions & free parameters 5 free parameters · 4 assumptions · 1 invented entities

The central claim rests on standard linear acoustics, a verified numerical label generator, and architectural hyperparameters chosen for the study. No new physical entity is postulated; CLBO is an engineered operator model. Free parameters are network and training choices that affect reported errors but are matched across models for the main comparison.

free parameters (5)
  • latent rank R = 96
    Chosen as 96 for both models; controls capacity of the low-rank source–receiver factorization and affects error/cost tradeoff.
  • encoder depth and hidden width = depth 5, width 256
    Depth 5 and width 256 set by configuration; not derived from first principles.
  • Fourier feature band counts = 6 coord / 7 freq bands
    6 coordinate bands and 7 frequency bands chosen for oscillatory representation; training-split statistics normalize inputs.
  • physics residual weights λH, λR = λH=2.25e-3, λR=1e-3, λV=0
    Hand-set for the physics ablation (λH=2.25e-3, λR=1e-3, λV=0 after calibration); not used in the principal supervised claim but affect ablation numbers.
  • DeepONet branch sensor count M = 256
    Fixed at 256 sensors with linear resampling when Ns≠M; defines the baseline input encoding.
assumptions (4)
  • domain assumption For fixed geometry, medium, frequency, and passive BCs, the acoustic map from complex normal velocity to complex pressure is complex-linear away from exact lossless eigenfrequencies or with finite damping.
    Section 2.1, Eqs. 5–6; load-bearing for hard-coding source linearity.
  • domain assumption Verified MRT-LBM fields are adequate ground truth for training and evaluation of the learned operators.
    Section 4 verification suite and two-stage hierarchy; all reported errors are relative to LBM labels.
  • domain assumption Surface quadrature with coordinates, normals, and areas approximates the continuous boundary integral sufficiently for the tested discretizations.
    Sections 2.2 and 3.3; remeshing study measures residual discretization error.
  • standard math Standard complex arithmetic, Fourier features, and low-rank inner-product decoding are valid building blocks for the operator.
    Sections 3.1–3.2; used without new proof beyond construction.
invented entities (1)
  • CLBO (quadrature-aware complex-linear boundary operator)
    purpose: Structure-preserving neural surrogate mapping distributed complex wall velocity to complex pressure via learned bases and explicit surface quadrature.
    Architectural construct, not a new physical particle or force; independent evidence is empirical performance against LBM, not an external physical detection.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quadrature-Aware Complex-Linear Neural Operator for Boundary-to-Field Prediction in Resonant Acoustics." pith.science (2026). https://pith.science/paper/P2ZXS5MG

@misc{pith2026260704407,
  author       = {Pith},
  title        = {Pith review of: Quadrature-Aware Complex-Linear Neural Operator for Boundary-to-Field Prediction in Resonant Acoustics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P2ZXS5MG}},
  note         = {Machine review of arXiv:2607.04407}
}
read the original abstract

Repeated prediction of acoustic fields from spatially distributed boundary excitation is computationally expensive when each source realization requires a new wave simulation. This work introduces a quadrature-aware complex-linear boundary operator (CLBO) that maps complex normal velocity on a vibrating surface to complex pressure at receiver locations. The model couples learned source and receiver basis functions through an explicit complex surface-quadrature contraction, so the boundary excitation enters linearly by construction. This preserves complex superposition, homogeneity, and zero response to zero excitation, while representing the source through coordinates, normals, and quadrature weights rather than a fixed flattened input vector. Reference data were generated using a verified three-dimensional multiple-relaxation-time (MRT) lattice Boltzmann solver and stored in a solver-agnostic boundary-to-field format. CLBO was compared with a fixed-sensor complex DeepONet under matched case splits and optimization settings, with additional tests of structural consistency, receiver-coordinate interpolation, source discretization, source-family holdout, label efficiency, physics-informed ablations, unseen source mixtures, and computational cost. Across five training seeds, CLBO achieved a mean complex relative field error of 0.184 +/- 0.00771, compared with 0.367 +/- 0.00742 for DeepONet. Its measured source-superposition error was 1.31 x 10^-7, and its mean error on newly simulated mixed-source cases was 0.237, compared with 0.415 for DeepONet. Inference was 1.83 x 10^4 faster than the reference calculation for the reported query size. These results show that enforcing the known complex-linear boundary-to-field structure improves physical consistency and generalization under distributed acoustic excitation.

Figures

Figures reproduced from arXiv: 2607.04407 by the authors.

Figure 1
Figure 1. Architecture of the proposed clbo. A source basis network maps each source location, normal, and frequency to R complex basis functions after normalized coordinate and frequency features. The prescribed boundary velocity enters only through the weighted surface sum in Eq. (12). A receiver basis network maps each query location and frequency to R complex basis functions, and the predicted pressure follows from the lo… view at source ↗
Figure 2
Figure 2. Architecture of the fixed-sensor DeepONet baseline. The branch network encodes [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Geometry and sampling layout used for reference-data generation. The rectangular [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Verification of the MRT-LBM reference solver. Frequencies and response amplitudes [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Complex pressure predictions for one held-out test case near the median per-case [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: Primary model comparison on the shared held-out test split. Both models were [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Receiver interpolation on held-out receiver coordinates. Both models were retrained [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]
Figure 8
Figure 8. Figure 8: Algebraic structure and source-wall sampling transfer on the primary supervised [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: Data efficiency and controlled ablations on the fixed test manifest. Panel (a) shows [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: Accuracy and computational cost from the inference benchmark on the primary [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

42 extracted references · 13 canonical work pages

  1. [1]

    Morse and K

    Philip M. Morse and K. Uno Ingard.Theoretical Acoustics. Princeton University Press, 1968

    1968

  2. [2]

    CRC Press, 6 edition, 2016

    Heinrich Kuttruff.Room Acoustics. CRC Press, 6 edition, 2016

    2016

  3. [3]

    Springer, New York, 1998.doi:10.1007/b98828

    Frank Ihlenburg.Finite Element Analysis of Acoustic Scattering, volume 132 ofApplied Mathematical Sciences. Springer, New York, 1998.doi:10.1007/b98828. 23

    work page doi:10.1007/b98828 1998

  4. [4]

    T. W. Wu, editor.Boundary Element Acoustics: Fundamentals and Computer Codes, volume 7 ofAdvances in Boundary Elements. WIT Press, 2000

    2000

  5. [5]

    Revisiting Image Aesthetic Assessment via Self-Supervised Feature Learning

    Doug L. James, Jernej Barbič, and Dinesh K. Pai. Precomputed acoustic transfer: Output-sensitive, accurate sound generation for geometrically complex vibration sources. ACM Transactions on Graphics, 25(3):987–995, 2006.doi:10.1145/1141911.1141983

    work page Pith review arXiv doi:10.1145/1141911.1141983 2006

  6. [6]

    Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3:218–229, 2021

    Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3:218–229, 2021. doi:10.1038/ s42256-021-00302-5

    2021

  7. [7]

    Neural operator: Learning maps between function spaces with applications to PDEs.Journal of Machine Learning Research, 24(89):1–97, 2023

    Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhat- tacharya, Andrew Stuart, and Anima Anandkumar. Neural operator: Learning maps between function spaces with applications to PDEs.Journal of Machine Learning Research, 24(89):1–97, 2023. URL:http://jmlr.org/papers/v24/21-1524.html

    2023

  8. [8]

    Fourier neural operator for paramet- ricpartialdifferentialequations

    Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhat- tacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for paramet- ricpartialdifferentialequations. InInternational Conference on Learning Representations,

Show all 42 references
  1. [9]

    URL:https://arxiv.org/abs/2010.08895

    2010 arXiv

  2. [10]

    Geometry-informed neural operator for large-scale 3d PDEs

    Zongyi Li, Nikola Kovachki, Chris Choy, Boyi Li, Jean Kossaifi, Shourya Prakash Otta, Mohammad Amin Nabian, Maximilian Stadler, Christian Hundt, Kamyar Azizzade- nesheli, and Anima Anandkumar. Geometry-informed neural operator for large-scale 3d PDEs. InAdvances in Neural Info...

    2023

  3. [11]

    Maziar Raissi, Paris Perdikaris, and George Em Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.Journal of Computational Physics, 378:686–707, 2019.doi:10.1016/j...

    2019 doi

  4. [12]

    Physics-informed neural operator for learning partial differential equations, 2024.arXiv:2111.03794, doi:10.1145/3648506

    Zongyi Li, Hongkai Zheng, Nikola Kovachki, David Jin, Haoxuan Chen, Burigede Liu, Kamyar Azizzadenesheli, and Anima Anandkumar. Physics-informed neural operator for learning partial differential equations, 2024.arXiv:2111.03794, doi:10.1145/3648506

    2024 doi arXiv

  5. [13]

    Aditi Krishnapriyan, Amir Gholami, Shandian Zhe, Robert Kirby, and Michael W. Mahoney. Characterizing possible failure modes in physics-informed neural networks. InAdvances in Neural Information Processing Systems, volume 34, pages 26548– 26560, 2021. URL: https://proceedings....

    2021

  6. [14]

    Brunton, Bernd R

    Steven L. Brunton, Bernd R. Noack, and Petros Koumoutsakos. Machine learning for fluid mechanics.Annual Review of Fluid Mechanics, 52:477–508, 2020.doi:10.1146/ annurev-fluid-010719-060214. 24

    2020

  7. [15]

    Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabás Póczos, Ruslan Salakhut- dinov, and Alexander J. Smola. Deep sets. InAdvances in Neural Information Processing Systems, volume 30, 2017. URL: https://proceedings.neurips.cc/paper_files/ paper/2017/file/f22e4747da1aa27e...

    2017

  8. [16]

    Qi, Hao Su, Kaichun Mo, and Leonidas J

    Charles R. Qi, Hao Su, Kaichun Mo, and Leonidas J. Guibas. PointNet: Deep learning on point sets for 3d classification and segmentation. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 652– 660, 2017. URL: https://openaccess.thecvf.com/co...

    2017

  9. [17]

    Kosiorek, Seungjin Choi, and Yee Whye Teh

    Juho Lee, Yoonho Lee, Jungtaek Kim, Adam R. Kosiorek, Seungjin Choi, and Yee Whye Teh. Set transformer: A framework for attention-based permutation-invariant neural networks. InProceedings of the 36th International Conference on Machine Learning, volume 97 ofProceedings of Mac...

    2019

  10. [18]

    Jakeman, Akil Narayan, Shandian Zhe, and Varun Shankar

    Matthew Lowery, John Turnage, Zachary Morrow, John D. Jakeman, Akil Narayan, Shandian Zhe, and Varun Shankar. Kernel neural operators for scalable, memory-efficient, geometrically flexible operator learning, 2024. URL: https://arxiv.org/abs/2407. 00809,arXiv:2407.00809

    2024 arXiv

  11. [19]

    Noam Koren, Ralf J. J. Mackenbach, Ruud J. G. van Sloun, Kira Radinsky, and Daniel Freedman. SVD-NO: Learning PDE solution operators with SVD integral kernels, 2026. doi:10.1609/aaai.v40i1.37016

    2026 doi

  12. [20]

    Learning only on boundaries: A physics- informed neural operator for solving parametric partial differential equations in complex geometries, 2024.doi:10.1162/neco_a_01647

    Zhiwei Fang, Sifan Wang, and Paris Perdikaris. Learning only on boundaries: A physics- informed neural operator for solving parametric partial differential equations in complex geometries, 2024.doi:10.1162/neco_a_01647

    2024 doi

  13. [21]

    Boundary integrated neural networks (BINNs) for acoustic radiation and scattering, 2023

    Wenzhen Qu, Yan Gu, Shengdong Zhao, and Fajie Wang. Boundary integrated neural networks (BINNs) for acoustic radiation and scattering, 2023. URL:https://arxiv. org/abs/2307.10521,arXiv:2307.10521

    2023 arXiv

  14. [22]

    Engsig-Karup, and Cheol-Ho Jeong

    Nikolas Borrel-Jensen, Allan P. Engsig-Karup, and Cheol-Ho Jeong. Physics-informed neural networks for one-dimensional sound field predictions with parameterized sources and impedance boundaries.JASA Express Letters, 1(12):122402, 2021.doi:10.1121/ 10.0009057

    2021

  15. [23]

    Engsig-Karup, George Em Karni- adakis, and Cheol-Ho Jeong

    Nikolas Borrel-Jensen, Somdatta Goswami, Allan P. Engsig-Karup, George Em Karni- adakis, and Cheol-Ho Jeong. Sound propagation in realistic interactive 3d scenes with parameterized sources using deep neural operators.Proceedings of the National Academy of Sciences, 121(2):e231...

    2024 doi

  16. [24]

    Tarr, Joshua B

    Andrew Luo, Yilun Du, Michael J. Tarr, Joshua B. Tenenbaum, Antonio Torralba, and Chuang Gan. Learning neural acoustic fields. InAdvances in Neural Information Processing Systems, 2022. URL:https://arxiv.org/abs/2204.00628. 25

    2022 arXiv

  17. [25]

    Neuralsound: Learning- based modal sound synthesis with acoustic transfer.ACM Transactions on Graphics, 41(4):121:1–121:15, 2022.doi:10.1145/3528223.3530184

    Xutong Jin, Sheng Li, Guoping Wang, and Dinesh Manocha. Neuralsound: Learning- based modal sound synthesis with acoustic transfer.ACM Transactions on Graphics, 41(4):121:1–121:15, 2022.doi:10.1145/3528223.3530184

    2022 doi

  18. [26]

    Fei Ma, Sipei Zhao, and Ian S. Burnett. Sound field reconstruction using a compact acoustics-informed neural network.The Journal of the Acoustical Society of America, 156(3):2009–2021, 2024.doi:10.1121/10.0029022

    2009 doi

  19. [27]

    Room impulse response reconstruction with physics-informed deep learning.The Journal of the Acoustical Society of America, 155(2):1048– 1059, 2024

    Xenofon Karakonstantis, Diego Caviedes-Nozal, Antoine Richard, and Efren Fernandez-Grande. Room impulse response reconstruction with physics-informed deep learning.The Journal of the Acoustical Society of America, 155(2):1048– 1059, 2024. arXiv:https://pubs.aip.org/asa/jasa/ar...

    2024 doi

  20. [28]

    NAT: Neural acoustic transfer for interactive scenes in real time, 2025.doi:10.1109/TVCG

    Xutong Jin, Bo Pang, Chenxi Xu, Xinyun Hou, Guoping Wang, and Sheng Li. NAT: Neural acoustic transfer for interactive scenes in real time, 2025.doi:10.1109/TVCG. 2025.3617802

    2025 doi

  21. [29]

    Williams.Fourier Acoustics: Sound Radiation and Nearfield Acoustical Hologra- phy

    Earl G. Williams.Fourier Acoustics: Sound Radiation and Nearfield Acoustical Hologra- phy. Academic Press, 1999

    1999

  22. [30]

    Haqshenas, Pierre Gélat, Timo Betcke, and Nader Saffari

    Elwin van ’t Wout, Seyyed R. Haqshenas, Pierre Gélat, Timo Betcke, and Nader Saffari. Benchmarking preconditioned boundary integral formulations for acoustics.International Journal for Numerical Methods in Engineering, 2021. URL:https://arxiv.org/abs/ 2104.04594,doi:10.1002/nme.6777

    2021 doi arXiv

  23. [31]

    Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan T

    Matthew Tancik, Pratul P. Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan T. Barron, and Ren Ng. Fourier features let networks learn high frequency functions in low dimensional do- mains. InAdvances in Neural Inform...

    2020

  24. [32]

    Chiheb Trabelsi, Olexa Bilaniuk, Ying Zhang, Dmitriy Serdyuk, Sandeep Subrama- nian, João Felipe Santos, Soroush Mehri, Negar Rostamzadeh, Yoshua Bengio, and Christopher J. Pal. Deep complex networks. InInternational Conference on Learning Representations, 2018. URL:https://op...

    2018

  25. [33]

    Theory of the lattice boltzmann method: Dispersion, dissipation, isotropy, galilean invariance, and stability.Physical Review E, 61(6):6546– 6562, 2000.doi:10.1103/PhysRevE.61.6546

    Pierre Lallemand and Li-Shi Luo. Theory of the lattice boltzmann method: Dispersion, dissipation, isotropy, galilean invariance, and stability.Physical Review E, 61(6):6546– 6562, 2000.doi:10.1103/PhysRevE.61.6546

    doi

  26. [34]

    Multiple-relaxation-time lattice boltzmann models in three dimensions

    Dominique d’Humières, Irina Ginzburg, Manfred Krafczyk, Pierre Lallemand, and Li-Shi Luo. Multiple-relaxation-time lattice boltzmann models in three dimensions. Philosophical Transactions of the Royal Society A, 360:437–451, 2002.doi:10.1098/ rsta.2001.0955. 26

    2002

  27. [35]

    Girimaji, and Li-Shi Luo

    Huidan Yu, Sharath S. Girimaji, and Li-Shi Luo. DNS and LES of decaying isotropic turbulence with and without frame rotation using lattice boltzmann method.Journal of Computational Physics, 209(2):599–616, 2005.doi:10.1016/j.jcp.2005.03.022

    2005 doi

  28. [36]

    Chikatamarla, Christos E

    Shyam S. Chikatamarla, Christos E. Frouzakis, Iliya V. Karlin, Ananias G. Tomboulides, and Konstantinos B. Boulouchos. Lattice boltzmann method for direct numerical simulation of turbulent flows.Journal of Fluid Mechanics, 656:298–308, 2010.doi: 10.1017/S0022112010001388

    2010 doi

  29. [37]

    Validating the boltz- mann approach to the large-eddy simulations of forced homogeneous incompress- ible turbulence.International Journal of Modern Physics C, page 2750064, 2026

    Muhammad Idrees Khan, Sauro Succi, and Giacomo Falcucci. Validating the boltz- mann approach to the large-eddy simulations of forced homogeneous incompress- ible turbulence.International Journal of Modern Physics C, page 2750064, 2026. doi:10.1142/S0129183127500641

    2026 doi

  30. [38]

    Viscously damped acoustic waves with the lattice boltzmann method.Philosophical Transactions of the Royal Society A, 369(1944):2246–2254, 2011

    Erlend Magnus Viggen. Viscously damped acoustic waves with the lattice boltzmann method.Philosophical Transactions of the Royal Society A, 369(1944):2246–2254, 2011. doi:10.1098/rsta.2011.0040

    1944 doi

  31. [39]

    Thomas Astoul, Gauthier Wissocq, Jean-François Boussuge, Alois Sengissen, and Pierre Sagaut. Lattice boltzmann method for computational aeroacoustics on non-uniform meshes: A direct grid coupling approach.Journal of Computational Physics, 447:110667, 2021.doi:10.1016/j.jcp.2021.110667

    2021 doi

  32. [40]

    Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics.Journal of Computational Physics, 230(13):5353–5382, 2011.doi:10.1016/j.jcp.2011.03.040

    Hui Xu and Pierre Sagaut. Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics.Journal of Computational Physics, 230(13):5353–5382, 2011.doi:10.1016/j.jcp.2011.03.040

    2011 doi

  33. [41]

    Tibshirani.An Introduction to the Bootstrap

    Bradley Efron and Robert J. Tibshirani.An Introduction to the Bootstrap. CRC Press, 1994.doi:10.1201/9780429246593

    1994 doi

  34. [42]

    Battaglia

    Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, and Peter W. Battaglia. Learn- ing mesh-based simulation with graph networks. InInternational Conference on Learning Representations, 2021. URL:https://arxiv.org/abs/2010.03409. 27

    2021 arXiv

Pith tools

Reviewed July 11, 2026 · model on record in the stance chip above.