OpenBreastUS: Benchmarking Neural Operators for Wave Imaging Using Breast Ultrasound Computed Tomography

Hao Hu; He Sun; Jinzhuo Wang; Linfeng Zhang; Xinliang Liu; Yihang Zheng; Youjia Zheng; Yubing Li; Zeyuan Dong; Zhijun Zeng

REVIEW 4 major objections 5 minor 32 references

OpenBreastUS: Benchmarking Neural Operators for Wave Imaging Using Breast Ultrasound Computed Tomography

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read OpenBreastUS lets neural wave solvers image real breast tissue for the first time.

desk verdict A genuinely useful large-scale USCT dataset and benchmark, undermined by an internally inconsistent report of the in vivo experiment that needs fixing before the headline claim can be trusted. read the letter →

arxiv 2507.15035 v1 pith:YN7ISEQG submitted 2025-07-20 cs.CV cs.LG

Zhijun Zeng , Youjia Zheng , Hao Hu , Zeyuan Dong , Yihang Zheng , Xinliang Liu , Jinzhuo Wang , Zuoqiang Shi

show 3 more authors

Linfeng Zhang Yubing Li He Sun

This is my paper · ORCID

classification cs.CVcs.LG

keywords ultrasoundcomputedtomographyneuraloperatorsfull-waveforminversionbreastimagingHelmholtzequationbenchmarkdatasetinvivovalidationFourieroperator

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

OpenBreastUS is a large-scale dataset of anatomically realistic breast phantoms paired with frequency-domain wavefields, built to test whether neural operator surrogates can replace classical Helmholtz solvers in ultrasound computed tomography. The paper argues that existing PDE datasets are too simplified, so it generates 8,000 virtual breasts across four density classes and 16.4 million simulations using the geometry and frequencies of a real 256-transducer ring system. On these data, it benchmarks five forward solvers and four inverse-imaging approaches, finding that multigrid and Born-type Fourier operators give the most accurate wavefields, and that surrogate-driven gradient optimization beats direct inversion networks. The central claim is that a Born Fourier Neural Operator trained on OpenBreastUS, embedded in iterative full-waveform inversion, reconstructs a malignant tumor and a benign cyst on clinical in vivo data, which is the first demonstration of in vivo breast imaging with neural operator solvers.

What carries the argument

The load-bearing object is the frequency-domain heterogeneous Helmholtz equation, solved by the Convergent Born Series algorithm to create ground-truth wavefields for 8,000 virtual breast anatomies under a real annular-array USCT configuration. Neural operator baselines, including FNO, BFNO, AFNO, MgNO, and U-Net, learn the map from sound-speed map and source to complex wavefield; the best forward models are then plugged into the adjoint-state gradient, replacing the two Helmholtz solves per iteration with one network evaluation. The mixture-of-experts frequency-specific operators, together with the adjoint-gradient formula $-2(\omega^j)^2 \lambda u / c^3$, are what make the in vivo inversion tractable.

What would settle it

A decisive check would be to run the same BFNO-driven FWI pipeline on a held-out clinical USCT dataset from a different scanner, with tumor locations confirmed by biopsy or pathology; if reconstructed lesion boundaries do not match pathology within the expected margin, or if image quality collapses on this second dataset, the claimed transfer is not general.

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Extended reading notes

Core claim

The paper's central claim is that a neural surrogate trained purely on synthetic breast anatomy can replace the numerical Helmholtz solver inside full-waveform inversion and still produce clinically useful reconstructions of real patient breasts. Using gradient-based optimization with a Born Fourier Neural Operator (BFNO) as the forward map, the authors reconstruct a malignant tumor with irregular boundaries and a benign cyst with smooth boundaries from clinical USCT data restricted to the dataset's eight frequencies, while direct inversion networks (NIO, InversionNet, DeepONet) fail to recover interior structure. The result is presented as evidence that the OpenBreastUS phantoms capture the scattering statistics of real tissue closely enough for transfer, and that forward operators, which learn only the conditional mapping from medium to wavefield, are more robust than inverse operators that must also learn the anatomical prior.

Load-bearing premise

The whole transfer result rests on the assumption that synthetic breast anatomies, after hand-set scaling and small random sound-speed perturbations, have the same spatial statistics as real breast tissue; the in vivo validation also assumes models trained on three frequencies and 64 sources apply to eight frequencies and 256 transmitters without explicit retraining.

Editorial extensions

If this is right

In iterative full-waveform inversion, replacing each pair of Helmholtz solves with a forward neural operator cuts per-gradient cost to a single network pass, making quasi-real-time USCT reconstruction a realistic target instead of a numerical bottleneck.
Forward surrogate models outperform direct inversion networks on realistic tissue because they learn the likelihood rather than the posterior, so they are less prone to memorizing the training anatomy distribution.
OpenBreastUS-trained operators generalize to unseen breast types, unseen source locations, and even to media like Gaussian random fields, while models trained on simplified random media fail on breast tissue.
Higher breast density and higher frequency systematically degrade all baselines, so future neural solvers will need to target dense-tissue scattering and high-wavenumber behavior.
In the two clinical cases, gradient-based optimization with BFNO distinguishes malignant from benign lesions by boundary regularity, indicating a path toward computer-assisted breast-disease screening.

Reading between the lines

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

A likely consequence the paper leaves implicit is that the same phantom-generation approach could synthesize training pairs for almost any ring-array USCT geometry, making scanner-specific retraining cheap once a forward surrogate is trusted.
Because the in vivo test used one dataset and two patients, the strongest next test is external validation on a different device and population; positive results there would convert the demonstration into a general method.
The frequency and source mismatch between training (three frequencies, 64 sources) and application (eight frequencies, 256 transmitters) suggests the model transfers more broadly than the benchmark explicitly trains for, and isolating whether that generalization is physics or coincidence would be a clean ablation.
Extending the forward model to include acoustic attenuation, which the paper lists as future work, would likely improve tumor characterization and is a natural test of whether the dataset's realism bottleneck is tissue structure or missing physics.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this paper is worth referee time for the dataset alone, but the in vivo headline is not supported as written. The main benchmark is fine; the clinical transfer section has a load-bearing reporting gap.

What is new and good: OpenBreastUS is a real contribution. 8,000 VICTRE-based breast phantoms across four density classes, 16M frequency-domain wavefields with realistic ring-array geometry (256 transducers, 300–650 kHz), and detailed documentation of the generation pipeline. The CBS solver is a credible reference for the ground-truth fields. The benchmark of five forward solvers and four inverse pipelines is thorough, and the ranking (MgNO best forward; surrogate-based FWI beats direct inversion) is plausible and consistent with the physics argument that direct inversion memorizes priors. The OOD source-location and breast-type tables add useful evidence. The GRF comparison is a nice demonstration that simplified media overestimate generalization.

The soft spots, in order of severity. First, the in vivo experiment is internally inconsistent with the benchmark. Section IV-C trains the baselines on three frequencies and 64 sources; Section IV-D says the models were trained on eight frequencies and uses 256 transmitters in the figures, with no retraining step described. That is a qualitative jump in input dimension and distribution. If the same models were applied outside their training configuration, the clean tumor delineation is inexplicable; if they were retrained, the paper must say so and report the setup. Either way the abstract's 'for the first time' claim is unverifiable as written. Second, the in vivo evaluation is purely visual. No same-configuration classical FWI baseline, no quantitative metric, no error bars. The FDFD reference from [15] is at 20 frequencies and 1024 sensors, so it is not a matched comparison. Third, there are no seed variations anywhere in the paper, so it is impossible to tell whether the benchmark gaps are significant. Fourth, the 'first in vivo imaging using neural operator solvers' is not reconciled with the authors' own prior Neural Born Series paper [30]. Minor: the dataset URL has no commit hash or checksum.

The phantom-realism worry (VICTRE + random perturbations) is real but downstream of the training-configuration problem. The benchmark numbers on held-out phantoms stand on their own; the in vivo transfer is the only place where realism matters, and that section is currently too thin to validate it.

Recommendation: send this to peer review. The dataset and benchmark are valuable enough to warrant serious referee time, but the paper needs major revision: clarify/retrain for the in vivo configuration, add quantitative in vivo evaluation with a matched baseline, add error bars, and resolve the prior-work claim. I would not cite the in vivo result until that is fixed, but I would likely cite the dataset.

Referee Report

4 major / 5 minor

Summary. OpenBreastUS is a large-scale dataset of 8,000 anatomically realistic breast phantoms (VICTRE-based) together with 16.4 million frequency-domain Helmholtz wave simulations using a 256-transducer ring array at 8 frequencies. The paper benchmarks five forward neural operators (U-Net, FNO, AFNO, BFNO, MgNO), four inverse approaches (DeepONet, InversionNet, NIO, and optimization-based FWI with neural surrogates), and reports that BFNO-based gradient inversion reconstructs a malignant tumor and a benign cyst on two in vivo cases from the Karmanos Cancer Institute. The central claim is that models trained on OpenBreastUS generalize to clinical USCT data, enabling efficient in vivo imaging with neural operator solvers.

Significance. If the central claim holds, OpenBreastUS would be a substantial resource for neural operator research in wave imaging, combining realistic anatomy with a credible CBS reference solver, and the in vivo transfer would be a notable first. The paper's strengths include the scale and realism of the dataset, the use of an external clinical dataset never seen in training, the held-out phantom evaluation, and the comparison against a CBS numerical solver rather than a weaker reference. The OOD experiments (source locations, breast types, GRF media) also provide useful evidence about generalization. However, the internal inconsistency in training configuration and the purely qualitative in vivo evaluation mean the headline claim is not yet established.

major comments (4)

[§IV-C, §IV-D, Fig. 5] §IV-C states that forward baselines were evaluated on a subset of three frequencies (300, 400, 500 kHz) and 64 of 256 sources, and that inverse baselines were trained and tested on the same three frequencies. §IV-D then says the neural operators 'were trained on data at 8 frequencies (300–650 kHz)' and the Figure 5 caption specifies BFNO with 8 frequencies and 256 transmitters. No retraining step is described anywhere in the paper. If the §IV-D models are the same as the §IV-C models, the 8-frequency/256-source clinical input is a large out-of-distribution shift; if they were retrained, the training setup is undocumented. Either way, the in vivo experiment as reported is not reproducible, and the headline claim depends on it.
[Table II, §IV-C, §IV-D] Table II includes a 600 kHz row, while §IV-C says only 300, 400, and 500 kHz were used, and §IV-D says 8 frequencies (300–650 kHz). This inconsistency makes the actual training frequencies for the benchmark models ambiguous. The paper must state exactly which frequencies and source counts were used for each model in Tables II–III and for the Section IV-D in vivo experiments.
[§IV-D, Figs. 5–6] The in vivo demonstration is entirely qualitative. There are no quantitative metrics (e.g., SSIM/PSNR against the FDFD reference, lesion contrast, or boundary error) and no statistical assessment. The claim that BFNO 'successfully reconstructed a clear malignant tumor' is supported only by visual inspection of two clinical cases. Since the abstract's 'first in vivo imaging' claim rests on these figures, quantitative evaluation should be added.
[Tables II, III, V, VI, VII] The benchmark tables report a single point estimate per model and condition, with no standard deviation across training seeds or test folds. The paper's stated purpose is to benchmark neural operators, so the reported rankings (e.g., MgNO at RRMSE 0.0028 vs. BFNO at 0.0113 in Table II) cannot be assessed for statistical significance. At least three seeds with error bars and, where possible, significance tests should be reported.

minor comments (5)

[§III-B] Section III-B refers to 'OpenWaves dataset' instead of OpenBreastUS.
[Appendix B, InversionNet] In Appendix B, 'WIn this paper' appears to be a typo for 'In this paper'.
[§IV-C] Section IV-C contains the typo 'neural operatos', which should be 'neural operators'.
[Figs. 5–6] Figures 5(a) and 6(a) are labeled 'Ground Truth' but are themselves reconstructions produced by an FDFD solver; relabel them as 'Reference reconstruction' to avoid implying true ground truth.
[§III-C2, Appendix A] The phantom generation relies on hand-set VICTRE parameters (a1b, a1t, a2l, a2r, a3, targetFatFrac ranges) with no sensitivity analysis; a brief discussion of how these choices affect the benchmark would help users interpret the dataset.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the FWI/operator framework is derived in-paper from the Helmholtz equation, benchmarks are checked against an independent CBS solver, and the only overlapping-author citation [30] is a non-load-bearing baseline credit; the training-configuration gap flagged by reviewers is a reproducibility concern, not a circular reduction.

full rationale

The derivation chain is self-contained: the forward model (Helmholtz equation, Eq. 1, with the Sommerfeld condition, Eq. 2) and the full-waveform-inversion Lagrangian/adjoint machinery (Eqs. 3–10) are derived in the paper itself, and the forward surrogate G and inverse map G^-1 are defined by Eqs. 9 and 10 with no fitted constant defined in terms of the target quantity. Benchmark accuracy is measured against an independent Convergent Born Series solver [29] on held-out phantoms (Tables II and III), and the in vivo validation uses external Karmanos clinical data whose reference reconstructions come from the independent FDFD/block-LU work of Ali and Duric [15]; neither the simulated benchmarks nor the in vivo evaluation relabels a fitted parameter as a prediction. The only citation with overlapping authorship is [30] (Zeng et al., "Neural Born Series Operator"), used in Section IV-B solely to name the gradient-based-optimization baseline; its mathematical content is derived in Section III-B, so the self-citation is minor and non-load-bearing. One internal-consistency gap should be flagged as a non-circularity concern: Section IV-C reports that the baselines were trained on three frequencies (300, 400, and 500 kHz) from 64 of 256 sources, while Section IV-D and the Figure 5 caption state that the in vivo models were trained on eight frequencies (300–650 kHz) with 256 transmitters, and no retraining step is documented; Table II also includes a 600 kHz row beyond the stated three-frequency configuration. This is a missing-support and reproducibility problem for the headline in vivo claim, but it is not a circular reduction, because the reported reconstructions are not forced by construction from the training inputs and the clinical data were never part of any fit.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claims rest on domain assumptions about phantom realism, solver fidelity, and transfer from simulation to clinic; no new physical entities are introduced. The free parameters are hand-set dataset-generation choices that affect the benchmark numbers and the realism of the data.

free parameters (4)

VICTRE geometry scale parameters (a1b, a1t, a2l, a2r, a3) = truncated Gaussian with mean 5.0 cm, sigma 2.0, range [3.5,7.5]; a3/a1b ~ TN(1.4, 0.1, 1.0, 1.5)
Hand-chosen to generate breast shape diversity; the realism of the resulting phantoms is assumed, not derived from data.
targetFatFrac ranges = EXD (0,0.25), HET (0.25,0.5), FIB (0.5,0.75), FAT (0.75,1.0)
Hand-set to partition the four breast density classes; adjusted for Asian populations without a stated quantitative basis.
Tissue sound speed perturbations = not quantified, described as small random perturbations
Adds variability to assigned tissue sound speeds; the magnitude is unspecified, so generation is not fully reproducible from the text.
Training frequency and source subset = 8 frequencies (300-650 kHz); 64 of 256 source locations for main benchmark
The hand-made computational budget affects all benchmark results and creates ambiguity for the in vivo transfer experiment.

assumptions (5)

domain assumption Scalar heterogeneous Helmholtz equation with Sommerfeld radiation condition is an adequate model of USCT wave propagation (Eqs. 1-2).
Shear motion, nonlinearity, and attenuation are neglected; this is standard for soft-tissue USCT but is stated without validation on the clinical data.
domain assumption The Convergent Born Series (CBS) solver produces an accurate ground truth for the training wavefields.
Solver discretization error becomes label error; no convergence study is reported for the 480x480 grid at 650 kHz.
domain assumption The VICTRE breast phantom generator produces anatomically realistic tissue distributions.
The realism of the phantoms is imported from the VICTRE project and is not verified against the Karmanos clinical data in the paper.
domain assumption The clinical dataset from Karmanos Cancer Institute is valid reference data and the FDFD reconstruction in [15] is a fair ground truth.
The reference itself is a reconstruction, not a true ground truth; any errors in the FDFD solution transfer to the comparison.
standard math The adjoint-state gradient formula (Eq. 8) follows from the KKT conditions (standard math).
The derivation is standard and correct, assuming the neural surrogate is differentiable and its output approximates the true field.

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Cite this review

Pith. "Pith review of OpenBreastUS: Benchmarking Neural Operators for Wave Imaging Using Breast Ultrasound Computed Tomography." pith.science (2026). https://pith.science/paper/YN7ISEQG

@misc{pith2026250715035,
  author       = {Pith},
  title        = {Pith review of: OpenBreastUS: Benchmarking Neural Operators for Wave Imaging Using Breast Ultrasound Computed Tomography},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YN7ISEQG}},
  note         = {Machine review of arXiv:2507.15035}
}

read the original abstract

Accurate and efficient simulation of wave equations is crucial in computational wave imaging applications, such as ultrasound computed tomography (USCT), which reconstructs tissue material properties from observed scattered waves. Traditional numerical solvers for wave equations are computationally intensive and often unstable, limiting their practical applications for quasi-real-time image reconstruction. Neural operators offer an innovative approach by accelerating PDE solving using neural networks; however, their effectiveness in realistic imaging is limited because existing datasets oversimplify real-world complexity. In this paper, we present OpenBreastUS, a large-scale wave equation dataset designed to bridge the gap between theoretical equations and practical imaging applications. OpenBreastUS includes 8,000 anatomically realistic human breast phantoms and over 16 million frequency-domain wave simulations using real USCT configurations. It enables a comprehensive benchmarking of popular neural operators for both forward simulation and inverse imaging tasks, allowing analysis of their performance, scalability, and generalization capabilities. By offering a realistic and extensive dataset, OpenBreastUS not only serves as a platform for developing innovative neural PDE solvers but also facilitates their deployment in real-world medical imaging problems. For the first time, we demonstrate efficient in vivo imaging of the human breast using neural operator solvers.

Figures

Figures reproduced from arXiv: 2507.15035 by the authors.

**Figure 1.** Schematic diagram of a USCT system and the OpenBreastUS dataset.The imaging target is placed inside an annular transducer array, with each transducer emitting waves sequentially while the others act as receivers.The OpenBreastUS dataset includes anatomically realistic human breast phantoms and their corresponding wavefields at different frequencies. ically realistic human breast phantoms across four categories and s… view at source ↗

**Figure 2.** Comparison of existing wave PDE dataset. Representative data samples (scattering media and wavefields) from OpenFWI, PDEBench, WaveBench and OpenBreastUS datasets are illustrated. A. Problem Definition The primary goal of the OpenBreastUS dataset is to facilitate the development of neural operators and other deep learning techniques for real-world wave imaging applications, with USCT serving as a representative exa… view at source ↗

**Figure 3.** Forward simulation results at 300 kHz. Comparison of wavefield predictions for four breast types using a numerical solver (CBS) and five baseline neural operators. Metric Models DeepONet InversionNet NIO Gradient-based Optimization Method UNet FNO AFNO BFNO MgNO PSNR↑ 16.65 20.26 18.06 20.02 25.84 24.85 27.91 30.48 SSIM↑ 0.8572 0.8640 0.8692 0.8674 0.9104 0.8506 0.9193 0.9381 TABLE III QUANTITATIVE EVALUATION OF INV… view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Inverse imaging results. Comparison of reconstructed breast sound speeds for four breast types using three direct inversion baselines and an optimization-based method with FNO surrogate. Results from gradient-based optimization with a numerical solver (CBS) are provide…

**Figure 5.** Figure 5: Validation on reconstructing in vivo human breast with a malignancy using different models. The reconstruction results on the clinical USCT dataset, using forward models and a direct inversion model trained on OpenBreastUS. (a) Ground Truth: a breast phantom reconstruc…

**Figure 6.** Figure 6: Reconstruction results of in vivo human breast with a benign cyst using different models. The reconstruction results on the clinical USCT dataset, using forward models and a direct inversion model trained on OpenBreastUS. (a) Ground Truth: reconstruction of a breast ph…

**Figure 7.** Figure 7: Analysis of Data Complexity, Model Scalability, and Generalization. (a) RRMSE variation of neural operators trained on data at different frequencies. (b) RRMSE variation of neural operators trained with different numbers of breast phantoms. (c) RRMSE variation of neura…

**Figure 8.** Figure 8: Forward simulation results of GRF media and breast phantom at 500kHz. Comparison of wavefield prediction of GRF media and breast phantom using FNO and UNet. The (GRF) suffix denotes models trained on the GRF dataset, while the (OpenBreastUS) suffix indicates models tra…

**Figure 9.** Figure 9: Comparison of forward simulation errors across different breast categories. RRMSE (a) and Max Errors (b) of five forward simulation baselines are reported across four breast categories. Larger errors in heterogeneous and extremely dense breasts indicate that their mor…

**Figure 10.** Figure 10: Comparison of direct inversion quality across different breast categories. SSIM (a) and PSNR (b) of three direct inversion baselines are reported for four breast categories. Lower reconstruction quality in heterogeneous and extremely dense breasts suggests that their…

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Reference graph

Works this paper leans on

32 extracted references · 24 canonical work pages

[15]

2-d slicewise waveform inversion of sound speed and acoustic attenuation for ring array ultrasound tomography based on a block lu solver,

R. Ali, T. M. Mitcham, T. Brevett, `O. C. Agudo, C. D. Martinez, C. Li, M. M. Doyley, and N. Duric, “2-d slicewise waveform inversion of sound speed and acoustic attenuation for ring array ultrasound tomography based on a block lu solver,”IEEE Transactions on Medical Imaging, 2024

work page 2024
[30]

A convergent born series for solving the inhomogeneous helmholtz equation in arbitrarily large media,

G. Osnabrugge, S. Leedumrongwatthanakun, and I. M. Vellekoop, “A convergent born series for solving the inhomogeneous helmholtz equation in arbitrarily large media,”Journal of Computational Physics, vol. 322, pp. 113–124, 2016

work page 2016
[1]

DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators,

L. Lu, P. Jin, and G. Karniadakis, “DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators,”arXiv, 2019

work page 2019
[2]

Neural operator: Graph kernel network for partial differential equations,

Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar, “Neural operator: Graph kernel network for partial differential equations,”arXiv, 2020. [Online]. Available: http://arxiv.org/abs/2003.03485

arXiv 2020
[3]

Fourier neural operator for parametric partial differential equa- tions,

——, “Fourier neural operator for parametric partial differential equa- tions,” inICLR, 2021

work page 2021
[4]

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators,

L. Lu, P. Jin, G. Pang, Z. Zhang, and G. E. Karniadakis, “Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators,”Nature Machine Intelligence, vol. 3, 2021. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021 13

work page 2021
[5]

Pdebench: An extensive benchmark for scientific machine learning,

M. Takamoto, T. Praditia, R. Leiteritz, D. MacKinlay, F. Alesiani, D. Pfl ¨uger, and M. Niepert, “Pdebench: An extensive benchmark for scientific machine learning,”Advances in Neural Information Processing Systems, vol. 35, pp. 1596–1611, 2022

work page 2022
[6]

Openfwi: Large-scale multi-structural benchmark datasets for full waveform inversion,

C. Deng, S. Feng, H. Wang, X. Zhang, P. Jin, Y . Feng, Q. Zeng, Y . Chen, and Y . Lin, “Openfwi: Large-scale multi-structural benchmark datasets for full waveform inversion,”Advances in Neural Information Processing Systems, vol. 35, pp. 6007–6020, 2022

work page 2022

Show all 32 references

[7]

Wavebench: Benchmarking data-driven solvers for linear wave propagation pdes,

T. Liu, J. A. L. Benitez, A. Khorashadizadeh, F. Faucher, M. V . de Hoop, and I. Dokmani ´c, “Wavebench: Benchmarking data-driven solvers for linear wave propagation pdes,”Transactions on Machine Learning Research Journal, 2024

2024
[8]

Full-waveform inversion imaging of the human brain,

L. Guasch, O. Calder ´on Agudo, M.-X. Tang, P. Nachev, and M. Warner, “Full-waveform inversion imaging of the human brain,”npj Digital Medicine, vol. 3, no. 1, p. 28, 2020

2020
[9]

3-d stochastic numerical breast phantoms for enabling virtual imaging trials of ultrasound com- puted tomography,

F. Li, U. Villa, S. Park, and M. A. Anastasio, “3-d stochastic numerical breast phantoms for enabling virtual imaging trials of ultrasound com- puted tomography,”IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 69, no. 1, pp. 135–146, 2022

2022
[10]

Spatial response identification enables ro- bust experimental ultrasound computed tomography,

C. Cueto, L. Guasch, J. Cudeiro, O. C. Agudo, T. Robins, O. Bates, G. Strong, and M.-X. Tang, “Spatial response identification enables ro- bust experimental ultrasound computed tomography,”IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 69, no. 1,...

2022
[11]

Ultrasound computed tomography based on full waveform inversion with source directivity calibration,

X. Wu, Y . Li, C. Su, P. Li, X. Wang, and W. Lin, “Ultrasound computed tomography based on full waveform inversion with source directivity calibration,”Ultrasonics, vol. 132, p. 107004, 2023

2023
[12]

Frequency-domain full-waveform inversion-based musculoskeletal ultrasound computed tomography,

C. Zhou, K. Xu, and D. Ta, “Frequency-domain full-waveform inversion-based musculoskeletal ultrasound computed tomography,” The Journal of the Acoustical Society of America, vol. 154, no. 1, pp. 279–294, 2023. [Online]. Available: https://doi.org/10.1121/10.0020151

2023 doi
[13]

Ultrasonic computed tomography based on full-waveform inversion for bone quan- titative imaging,

S. Bernard, V . Monteiller, D. Komatitsch, and P. Lasaygues, “Ultrasonic computed tomography based on full-waveform inversion for bone quan- titative imaging,”Physics in Medicine and Biology, vol. 62, no. 17, pp. 7011–7035, 2017

2017
[14]

Time domain reconstruction of sound speed and attenuation in ultrasound computed tomography using full wave inversion,

M. P ´erez-Liva, J. L. Herraiz, J. M. Ud´ıas, E. Miller, B. T. Cox, and B. E. Treeby, “Time domain reconstruction of sound speed and attenuation in ultrasound computed tomography using full wave inversion,”J Acoust Soc Am, vol. 141, no. 3, p. 1595, 2017

2017
[16]

U-net: Convolutional networks for biomedical image segmentation,

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” inMedical Image Computing and Computer-Assisted Intervention–MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III

2015
[17]

U-FNO—an enhanced fourier neural operator-based deep-learning model for multiphase flow,

G. Wen, Z. Li, K. Azizzadenesheli, A. Anandkumar, and S. M. Benson, “U-FNO—an enhanced fourier neural operator-based deep-learning model for multiphase flow,”Advances in Water Resources, vol. 163, p. 104180, 2022. [Online]. Available: https://www.sciencedirect.com/ science/art...

2022
[18]

Springer, 2015, pp. 234–241

2015
[19]

Deep born operator learning for reflection tomographic imaging,

Q. Zhao, Y . Ma, P. Boufounos, S. Nabi, and H. Mansour, “Deep born operator learning for reflection tomographic imaging,” inICASSP, 2023

2023
[20]

Adaptive fourier neural operators: Efficient token mixers for transformers,

J. Guibas, M. Mardani, Z. Li, A. Tao, A. Anandkumar, and B. Catanzaro, “Adaptive fourier neural operators: Efficient token mixers for transformers,”arXiv, 2022. [Online]. Available: http: //arxiv.org/abs/2111.13587

2022 arXiv
[21]

Mgno: Efficient parameterization of linear operators via multigrid,

J. He, X. Liu, and J. Xu, “Mgno: Efficient parameterization of linear operators via multigrid,”arXiv preprint arXiv:2310.19809, 2023

2023 arXiv
[22]

InversionNet3d: Efficient and scalable learning for 3-d full-waveform inversion,

Q. Zeng, S. Feng, B. Wohlberg, and Y . Lin, “InversionNet3d: Efficient and scalable learning for 3-d full-waveform inversion,”IEEE Transac- tions on Geoscience and Remote Sensing, vol. 60, pp. 1–16, 2022

2022
[23]

DeepM&mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks,

S. Cai, Z. Wang, L. Lu, T. A. Zaki, and G. E. Karniadakis, “DeepM&mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks,”Journal of Computational Physics, vol. 436, p. 110296, 2021

2021
[24]

DeepONet prediction of linear instability waves in high-speed boundary layers,

P. C. Di Leoni, L. Lu, C. Meneveau, G. Karniadakis, and T. A. Zaki, “DeepONet prediction of linear instability waves in high-speed boundary layers,”arXiv, 2021

2021
[25]

Operator learning for predicting multiscale bubble growth dynamics,

C. Lin, Z. Li, L. Lu, S. Cai, M. Maxey, and G. E. Karniadakis, “Operator learning for predicting multiscale bubble growth dynamics,”J Chem Phys, vol. 154, no. 10, p. 104118, 2021

2021
[26]

Fourier-DeepONet: Fourier- enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness,

M. Zhu, S. Feng, Y . Lin, and L. Lu, “Fourier-DeepONet: Fourier- enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness,”Computer Methods in Applied Mechanics and Engineering, vol. 416, p. 116300, 2023. [Online]. Av...

2023 arXiv
[27]

Neural inverse operators for solving pde inverse problems,

R. Molinaro, Y . Yang, B. Engquist, and S. Mishra, “Neural inverse operators for solving pde inverse problems,” inInternational Conference on Machine Learning. PMLR, 2023, pp. 25 105–25 139

2023
[28]

Gradient-based learning applied to document recognition,

Y . LeCun, L. Bottou, Y . Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,”Proceedings of the IEEE, vol. 86, no. 11, pp. 2278–2324, 1998

1998
[29]

3-d stochastic numerical breast phantoms for enabling virtual imaging trials of ultrasound computed tomography,

F. L. et al., “3-d stochastic numerical breast phantoms for enabling virtual imaging trials of ultrasound computed tomography,”IEEE trans- actions on ultrasonics, ferroelectrics, and frequency control, vol. 69, no. 1, pp. 135–146, 2021

2021
[31]

Neural born series operator for biomedical ultrasound computed tomography,

Z. Zeng, Y . Zheng, Y . Zheng, Y . Li, Z. Shi, and H. Sun, “Neural born series operator for biomedical ultrasound computed tomography,”arXiv preprint arXiv:2312.15575, 2023

2023 arXiv
[32]

Approximate separability of the green’s function of the helmholtz equation in the high frequency limit,

B. Engquist and H. Zhao, “Approximate separability of the green’s function of the helmholtz equation in the high frequency limit,”Com- munications on Pure and Applied Mathematics, vol. 71, no. 11, pp. 2220–2274, 2018

2018

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [15]

2-d slicewise waveform inversion of sound speed and acoustic attenuation for ring array ultrasound tomography based on a block lu solver,

R. Ali, T. M. Mitcham, T. Brevett, `O. C. Agudo, C. D. Martinez, C. Li, M. M. Doyley, and N. Duric, “2-d slicewise waveform inversion of sound speed and acoustic attenuation for ring array ultrasound tomography based on a block lu solver,”IEEE Transactions on Medical Imaging, 2024

work page 2024

[2] [30]

A convergent born series for solving the inhomogeneous helmholtz equation in arbitrarily large media,

G. Osnabrugge, S. Leedumrongwatthanakun, and I. M. Vellekoop, “A convergent born series for solving the inhomogeneous helmholtz equation in arbitrarily large media,”Journal of Computational Physics, vol. 322, pp. 113–124, 2016

work page 2016

[3] [1]

DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators,

L. Lu, P. Jin, and G. Karniadakis, “DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators,”arXiv, 2019

work page 2019

[4] [2]

Neural operator: Graph kernel network for partial differential equations,

Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar, “Neural operator: Graph kernel network for partial differential equations,”arXiv, 2020. [Online]. Available: http://arxiv.org/abs/2003.03485

arXiv 2020

[5] [3]

Fourier neural operator for parametric partial differential equa- tions,

——, “Fourier neural operator for parametric partial differential equa- tions,” inICLR, 2021

work page 2021

[6] [4]

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators,

L. Lu, P. Jin, G. Pang, Z. Zhang, and G. E. Karniadakis, “Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators,”Nature Machine Intelligence, vol. 3, 2021. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021 13

work page 2021

[7] [5]

Pdebench: An extensive benchmark for scientific machine learning,

M. Takamoto, T. Praditia, R. Leiteritz, D. MacKinlay, F. Alesiani, D. Pfl ¨uger, and M. Niepert, “Pdebench: An extensive benchmark for scientific machine learning,”Advances in Neural Information Processing Systems, vol. 35, pp. 1596–1611, 2022

work page 2022

[8] [6]

Openfwi: Large-scale multi-structural benchmark datasets for full waveform inversion,

C. Deng, S. Feng, H. Wang, X. Zhang, P. Jin, Y . Feng, Q. Zeng, Y . Chen, and Y . Lin, “Openfwi: Large-scale multi-structural benchmark datasets for full waveform inversion,”Advances in Neural Information Processing Systems, vol. 35, pp. 6007–6020, 2022

work page 2022