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REVIEW 2 major objections 7 minor 49 references

BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces

T0 review · 2 major / 7 minor · reviewed 2026-07-09 · glm-5.2

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

Pith's one-line read Bubbles get a compact shape language, enabling 58,000x faster swarm sims

desk verdict Dataset is a real contribution; the emulator benchmark oversells what it demonstrates. read the letter →

arxiv 2607.07275 v1 pith:NNX3OQQM submitted 2026-07-08 cs.LG physics.flu-dyn

Rachna Ramesh , Kiet Bennema ten Brinke , Douwe Orij , Ivo Roghair , Vlado Menkovski This is my paper
classification cs.LGphysics.flu-dyn
keywords bubblyflowssphericalharmonicsdirectnumericalsimulationgenerativemodeltrajectorypredictionshapedeformationmultiphaseflowbenchmarkdataset
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

The paper introduces BubbleSH, a dataset of three-dimensional bubble swarms rising through liquid, captured from high-fidelity direct numerical simulations that track every bubble's position, velocity, and deforming surface over time. The central innovation is representing each bubble's shape as a vector of 225 spherical harmonics coefficients, compressing raw mesh data by roughly 173-fold while preserving geometric fidelity to within 0.1% surface-area error. This compression makes it feasible to train machine-learning emulators on swarm dynamics that include both trajectory coupling and time-varying deformation, a combination absent from existing benchmarks of rigid particles or mesh-based continua. The authors demonstrate a probabilistic generative model that predicts future bubble positions and shapes conditioned on a short observed prefix, achieving four to five orders of magnitude speedup over the underlying simulator while reproducing the statistical distributions of kinematic, morphological, and interaction quantities. They also propose evaluation metrics that compare predicted and ground-truth distributions rather than pointwise errors alone, arguing that for chaotic systems where multiple futures are physically valid, distributional fidelity matters more than matching a single trajectory.

What carries the argument

The load-bearing mechanism is the projection of triangulated bubble surface meshes onto a truncated spherical harmonics basis of order L=14, yielding 225 coefficients per bubble. This representation assumes each bubble is star-like with respect to its centroid. The benchmark model is a conditional flow matching generative emulator with permutation-equivariant graph neural network spatial layers and a temporal U-Net, trained to denoise an informed random-walk prior into target velocity and shape-coefficient trajectories. Evaluation combines relative displacement and Chamfer distance metrics with normalized 1-Wasserstein distances over eight domain-informed distributional quantities.

What would settle it

If bubbles in the simulated regimes frequently develop concave regions or highly non-convex shapes where rays from the centroid intersect the surface multiple times, the spherical harmonics projection would systematically misrepresent those morphologies, and the dataset's fidelity claim would fail for those configurations.

Watch

Extended reading notes

Core claim

The core claim is that deformable bubble interfaces in turbulent swarms can be compactly and faithfully represented as truncated spherical harmonics coefficient vectors, and that this representation is sufficient to train generative emulators reproducing swarm-scale dynamics orders of magnitude faster than direct numerical simulation while preserving physically meaningful statistics. The paper establishes both the dataset and a benchmarking framework, including distributional metrics based on the 1-Wasserstein distance over kinematic, morphological, and interaction quantities, as a foundation for data-driven multiphase flow modeling.

Load-bearing premise

The spherical harmonics truncation at order 14, combined with the assumption that every bubble surface is star-like with respect to its centroid, faithfully captures all physically meaningful deformation across the entire simulated parameter space. All downstream metrics, model training, and evaluation operate on these compressed coefficients rather than raw interface meshes, so if significant deformation modes are lost in truncation or if bubbles violate the star-like shape,

Editorial extensions

If this is right

  • If the spherical harmonics representation generalizes beyond the simulated air-water regimes, data-driven emulators trained on similar compressed shape descriptors could replace expensive direct numerical simulation closures in industrial-scale Euler-Lagrange models, preserving per-bubble variability currently lost to averaged correlations.
  • The distributional evaluation framework proposed here, comparing predicted and ground-truth probability mass functions of physically meaningful quantities, could become a standard for benchmarking generative models in other chaotic dynamical systems where pointwise trajectory matching is ill-posed.
  • The dataset's combination of n-body interaction with deformable surfaces fills a gap between rigid-particle benchmarks and mesh-based continuum simulation benchmarks, potentially guiding the development of geometric deep learning architectures that jointly handle collective dynamics and evolving geometry.
  • The demonstrated speedup of 58,000 to 260,000 times suggests that surrogate models trained on high-fidelity simulation data could enable real-time or large-scale multiphase flow prediction previously blocked by computational cost.

Reading between the lines

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

  • If the star-like surface assumption breaks down at higher gas fractions or for larger bubbles exhibiting strong wobbling or concave deformations, the spherical harmonics truncation may silently lose physically significant deformation modes, and the dataset's fidelity claim would need validation against raw mesh statistics in those regimes.
  • The ablation showing that removing inter-bubble message passing barely changes performance suggests the current model architecture does not effectively learn spatial interactions, implying that the benchmark may not yet discriminate between models that capture collective dynamics and those that treat bubbles independently.
  • Extending the parameter space to include bubble breakup, coalescence, or surfactant effects would likely require augmenting the spherical harmonics representation, since topology-changing events violate the star-like assumption and fixed-coefficient-count structure.
  • The fixed-window forecasting approach limits long-horizon stability assessment; autoregressive rollout evaluation would reveal whether distributional fidelity degrades over extended prediction horizons, a critical question for practical deployment.
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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

2 major / 7 minor

Summary. The manuscript introduces BubbleSH, a dataset of three-dimensional, time-resolved bubble-swarm dynamics derived from high-fidelity Front-Tracking direct numerical simulations. The dataset covers 24 parameter configurations (three bubble diameters, eight gas volume fractions) with 32 bubbles each, representing bubble shapes compactly via spherical harmonics (SH) coefficients up to order L=14. The authors characterize the dataset through kinematic, morphological, and interaction statistics, propose evaluation metrics combining point-displacement errors with distributional Wasserstein distances, and benchmark a probabilistic generative emulator (based on conditional flow matching) on the dataset. The work addresses a genuine gap: there is no widely available, reusable dataset of transient, deformable bubble-swarm dynamics at the individual-bubble level, and the SH representation offers a principled compression of mesh data.

Significance. The dataset fills a real need in multiphase flow modeling and geometric deep learning. The SH compression to 225 coefficients per bubble with <0.1% MAPE on surface area (Section 4.1) is well-validated and yields a ~173x compression ratio, making the dataset practical for machine learning. The proposed distributional metrics (normalized W1 on kinematic, morphological, and interaction quantities) are a thoughtful contribution for evaluating probabilistic emulators on stochastic systems. The public release on Zenodo and the inclusion of conversion code [31] enhance reproducibility. The positioning between rigid-particle benchmarks and mesh-based simulation benchmarks is well-motivated.

major comments (2)
  1. Section 6 (Conclusion) and Table 4: The headline speedup claim of 'four to five orders of magnitude' is presented as comparing emulator inference time for 0.1s against FT simulation time for 0.1s. However, Section 5.2 states that the emulator predicts only 40ms conditioned on 20ms of observed DNS data (Tc=10 frames at 2ms resolution, total window 60ms). The emulator therefore cannot autonomously generate 0.1s of simulation—it requires DNS-generated conditioning data as input. Table 4 should either (a) compare like-for-like prediction horizons, or (b) explicitly state that the speedup figure refers to conditional short-horizon prediction, not autonomous rollout. The conclusion's phrasing ('practical path toward predictive swarm-scale modeling') overstates what has been demonstrated. This is load-bearing because the speedup is a central practical claim of the paper.
  2. Table 3 and Section 5.2: The ablation removing spatial interaction layers ('w/ independence') yields nearly identical performance to the full model (R-ADE 0.188 vs 0.185; Interaction W1 0.0013 vs 0.0010). The authors acknowledge this ('the model does not yet learn to capture spatial inter-bubble interactions well'), but the dataset is motivated primarily by bubble-bubble interactions (Abstract, Section 1). If the baseline emulator cannot leverage interaction structure, the benchmark's value for interaction-aware modeling is not yet demonstrated. The authors should either discuss what model architectures or evaluation protocols would be needed to test interaction learning, or temper the interaction-focused framing of the benchmark. This does not undermine the dataset itself, but it affects the claimed benchmark utility.
minor comments (7)
  1. Section 3.2: The star-like assumption (each ray from centroid intersects interface exactly once) is stated to exclude 'extreme cases such as toroidal or highly concave interfaces,' but no quantification is given of how often this assumption is violated across the 24 configurations, particularly at higher gas fractions (ε=30-40%) where deformation is strongest. A brief statement on the frequency or severity of star-like violations would strengthen the fidelity claim.
  2. Section 4.1, Table 2: The temporal resolution varies between 10^-4 s and 10^-3 s across configurations, but the rationale for this variation is not explained. Is this due to numerical stability constraints at certain parameter combinations? This should be clarified.
  3. Section 4.3: The normalization of W1 distances by the interquartile range of ground truth distributions is sensible, but the final scalar benchmark metric is obtained by 'averaging across all normalized W1 distances.' Are the eight quantities weighted equally? The sensitivity of the aggregate score to this choice should be briefly discussed.
  4. Figure 3: The y-axis labels on the probability mass function plots are not clearly readable. The units and quantities should be labeled explicitly on each subplot for standalone interpretability.
  5. Section 5.1: The model uses cylindrical coordinates for positions and velocities to align with translational and vertical-axis rotational symmetry. However, the SH coefficients are defined in a local spherical coordinate system (Section 3.2). How is consistency maintained between these two coordinate representations? This should be clarified.
  6. The reference to 'STFlow [38]' points to a 2026 arXiv preprint. If this work is not yet peer-reviewed, the dependency should be noted, and key architectural details sufficient for independent reproduction should be summarized in the appendix rather than deferred entirely.
  7. Section 3.2, Eq. (2): The spherical coordinate convention uses θ for azimuthal and φ for polar angle, which is the reverse of the common physics convention. This is not necessarily wrong but should be explicitly noted to avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: dataset is generated from independent DNS physics, metrics are defined against held-out ground truth, and the baseline model is evaluated on an independent test split

full rationale

BubbleSH is a dataset/benchmark paper, not a theoretical derivation. The core pipeline is: independent Front-Tracking DNS simulations produce raw bubble meshes, which are compressed to spherical harmonics coefficients (Eq. 2) with validated reconstruction error (MAPE < 0.1%). All evaluation metrics (R-ADE, R-FDE, IoU, R-ACD, W1) are defined against held-out ground truth from the same simulations — standard benchmark practice, not circular. The baseline model uses STFlow [38], co-authored by present authors, but this is a method choice evaluated on an independent 15% test split, not a self-referential derivation. The speedup claim in Table 4 is computed from measured wall-clock times, not from a definition that presupposes its conclusion. The skeptic's concerns about conditional vs. autonomous prediction and the independence ablation performing similarly are validity/correctness concerns, not circularity — no equation or claim reduces to its own inputs by construction. Self-citations ([38], [14], [31]) are method/tool references, not load-bearing mathematical facts invoked to force a conclusion.

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

No new physical entities, particles, forces, or dimensions are introduced. The dataset is derived from established physics simulations. The free parameters are modeling and dataset construction choices, not new physical postulates.

free parameters (5)
  • SH truncation order L=14 = 14
    Chosen such that MAPE on reconstructed surface area remains below 0.1%. Not fitted to the target result but selected based on reconstruction quality.
  • Number of bubbles N=32 = 32
    Fixed across all simulations; no justification given for this specific choice vs. other swarm sizes.
  • Prior noise parameter s=2 = 2
    Controls additional noise in the informed prior by scaling velocity variance (Table 5). Selected empirically.
  • Graph connectivity threshold 16mm = 16
    Edge construction distance for message passing network (Table 5). Not justified physically.
  • Learning rate 5e-4 = 5e-4
    Standard AdamW learning rate, not a scientific parameter.
assumptions (4)
  • domain assumption Front-Tracking DNS faithfully resolves bubble interface dynamics for the simulated regimes (Re 100-1000, Eo 2-5)
    The entire dataset's fidelity rests on the FT method producing physically accurate results. This is supported by prior validation in cited works [10, 11, 27, 28] but is assumed rather than re-validated here.
  • domain assumption Bubbles are star-like with respect to their centroid (each ray from centroid intersects interface exactly once)
    Section 3.2: required for spherical harmonics representation. Stated to exclude 'extreme cases' but frequency of violation not quantified.
  • domain assumption Periodic boundary conditions in a cubic domain adequately represent infinite bubble swarms without wall effects
    Section 3.1: the FT code simulates in a fully periodic domain. Standard assumption in homogeneous bubbly flow research but limits applicability.
  • domain assumption 32 bubbles are sufficient to capture swarm statistics representative of larger systems
    N=32 is fixed across all configurations. No convergence study on swarm size is provided.

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Cite this review

Pith. "Pith review of BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces." pith.science (2026). https://pith.science/paper/NNX3OQQM

@misc{pith2026260707275,
  author       = {Pith},
  title        = {Pith review of: BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NNX3OQQM}},
  note         = {Machine review of arXiv:2607.07275}
}
read the original abstract

Bubbly flows exhibit complex multiscale dynamics, with deformable bubbles interacting through the surrounding liquid and giving rise to strongly coupled kinematic and morphological behavior. We present BubbleSH, a bubbly flows dataset consisting of transient, three-dimensional bubble-swarm dynamics obtained from high-fidelity direct numerical simulations of bubbles rising in a periodic domain. The dataset provides time-resolved bubble trajectories, velocities, and shape evolution, with bubble morphology compactly represented using spherical harmonics. Designed to be lightweight yet physically expressive, the dataset enables data-driven modeling of bubbly flow simulators where shape deformation and bubble-bubble interactions play a central role. We characterize the dataset with bubble kinematics, morphology, and interaction patterns, and introduce evaluation metrics for both trajectory and shape prediction. The sensitivity of bubble-swarm dynamics to local perturbations makes BubbleSH particularly well suited to generative models that learn distributions over possible future trajectories. We evaluate a permutationally and translationally equivariant probabilistic emulator on BubbleSH given the proposed metrics. Therefore, we establish a compact, high-fidelity dataset and a benchmark for developing and evaluating data-driven models of deformable, chaotic multiphase systems.

Figures

Figures reproduced from arXiv: 2607.07275 by the authors.

Figure 1
Figure 1. BubbleSH contains trajectories of bubble centroids (left) and spherical harmonics coefficients (right), calculated from simulated interface meshes (left) While Direct Numerical Simulations (DNS) provide an exceptional level of detail, their applicability is limited to small scales due to computational cost. Larger-scale sim￾ulations therefore rely on Euler–Lagrange (EL) models, which describe the liquid phase throug… view at source ↗
Figure 2
Figure 2. Snapshots of simulations of d = 6 mm bubbles with void fractions of 0.10 (top) and 0.30 (bottom). The background slice indicates the vortic￾ity of the liquid phase. The FT code simulates multiple bubbles in a single, fully periodic domain, effectively representing an infinite bubble swarm without wall effects. As bubbles approach, the inter￾vening liquid film is naturally resolved and drains dynam￾ically under hydro… view at source ↗
Figure 3
Figure 3. Probability mass functions of kinematic and morphological quantities defined in Section [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Probability mass functions of in￾teraction quantities from Section 4.2 for two diameters d and gas fractions ε. Dotted line indicates the median, arrows indicate median shift, number of bins is 30, see [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Probability mass functions of predicted and ground truth trajectories from the Model [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Visualizations of centered 32 bubble centroid trajectories. Duration is 200 ms, number of [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: Visualizations of the shape of one bubble changing over time. [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]

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Works this paper leans on

49 extracted references · 49 canonical work pages

  1. [31]

    Ivo Roghair, Martin Van Sint Annaland, and Hans J.A.M. Kuipers. Drag force and clustering in bubble swarms.AIChE Journal, 59:1791–1800, 5 2013. ISSN 00011541. doi: 10.1002/aic. 13949

    work page doi:10.1002/aic 2013

  2. [1]

    I. A. Aganin. Dynamics of Gas Bubbles in a Spherical Cluster Under a Single Harmonic Pulse of Liquid Compression.Lobachevskii Journal of Mathematics, 43(5):1057–1063, May 2022. ISSN 1995-0802, 1818-9962. doi: 10.1134/S1995080222080030

    work page doi:10.1134/s1995080222080030 2022

  3. [2]

    Brechbühler, G

    Ch. Brechbühler, G. Gerig, and O. Kübler. Towards Representation of 3D Shape: Global Surface Parametrization. In Carlo Arcelli, Luigi P. Cordella, and Gabriella Sanniti Di Baja, editors,Visual Form, pages 79–88. Springer US, Boston, MA, 1992. ISBN 978-1-4899-0717-2 978-1-4899-0715-8. doi: 10.1007/978-1-4899-0715-8_9

    work page doi:10.1007/978-1-4899-0715-8_9 1992

  4. [3]

    Brenn, V

    G. Brenn, V . Kolobaric, and F. Durst. Shape oscillations and path transition of bubbles rising in a model bubble column.Chemical Engineering Science, 61(12):3795–3805, June 2006. ISSN 00092509. doi: 10.1016/j.ces.2005.12.016

    work page doi:10.1016/j.ces.2005.12.016 2006

  5. [4]

    A. G. Bridge, L. Lapidus, and J. C. Elgin. The mechanics of vertical gas-liquid fluidized systems. i. countercurrent flow.AIChE Journal, 10(6):819–826, 1963. doi: 10.1002/aic.690090603

    work page doi:10.1002/aic.690090603 1963

  6. [5]

    Dynamics of homogeneous bubbly flows part 1

    Bernard Bunner and Grétar Tryggvason. Dynamics of homogeneous bubbly flows part 1. rise velocity and microstructure of the bubbles.Journal of Fluid Mechanics, 466:17–52, 9 2002. ISSN 00221120. doi: 10.1017/S0022112002001179

    work page doi:10.1017/s0022112002001179 2002

  7. [6]

    Dynamics of homogeneous bubbly flows part 2

    Bernard Bunner and Grétar Tryggvason. Dynamics of homogeneous bubbly flows part 2. velocity fluctuations.Journal of Fluid Mechanics, 466:53–84, 2002. doi: 10.1017/S0022112002001180

    work page doi:10.1017/s0022112002001180 2002

  8. [7]

    Shape modes and jet formation on ultrasound-driven wall-attached bubbles.Journal of Fluid Mechanics, 1017:A9, August 2025

    Marco Cattaneo, Louan Presse, Gazendra Shakya, Thomas Renggli, Bratislav Luki´c, Anunay Prasanna, Daniel Werner Meyer, Alexander Rack, and Outi Supponen. Shape modes and jet formation on ultrasound-driven wall-attached bubbles.Journal of Fluid Mechanics, 1017:A9, August 2025. ISSN 0022-1120, 1469-7645. doi: 10.1017/jfm.2025.10457

    work page doi:10.1017/jfm.2025.10457 2025

Show all 49 references
  1. [8]

    Darmana, N

    D. Darmana, N. G. Deen, and J. A. M. Kuipers. Detailed 3d modeling of mass transfer processes in two-phase flows with dynamic interfaces.Chemical Engineering & Technology, 29(9):1027– 1033, 2006. doi: https://doi.org/10.1002/ceat.200600156. URL https://onlinelibrary. wiley.com...

    2006 doi

  2. [9]

    Diffusion Models Beat GANs on Image Synthesis

    Prafulla Dhariwal and Alexander Quinn Nichol. Diffusion Models Beat GANs on Image Synthesis. In Marc’Aurelio Ranzato, Alina Beygelzimer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan, editors,Advances in Neural Information Processing Systems 34: Annual Conference ...

    2021

  3. [10]

    Dijkhuizen, I

    W. Dijkhuizen, I. Roghair, M. Van Sint Annaland, and J. A.M. Kuipers. Dns of gas bubbles be- haviour using an improved 3d front tracking model-model development.Chemical Engineering Science, 65:1427–1437, 2010. ISSN 00092509. doi: 10.1016/j.ces.2009.10.022

    2010 doi

  4. [11]

    Dijkhuizen, I

    W. Dijkhuizen, I. Roghair, M. Van Sint Annaland, and J. A.M. Kuipers. Dns of gas bubbles behaviour using an improved 3d front tracking model-drag force on isolated bubbles and comparison with experiments.Chemical Engineering Science, 65:1415–1426, 2010. ISSN 00092509. doi: 10....

    2010 doi

  5. [12]

    Bubgan: Bubble generative adversarial networks for synthesizing realistic bubbly flow images.Chemical Engineering Science, 204:35–47, 2019

    Yucheng Fu and Yang Liu. Bubgan: Bubble generative adversarial networks for synthesizing realistic bubbly flow images.Chemical Engineering Science, 204:35–47, 2019. ISSN 0009-

    2019

  6. [13]

    URL https://www.sciencedirect

    doi: https://doi.org/10.1016/j.ces.2019.04.004. URL https://www.sciencedirect. com/science/article/pii/S0009250919303677

    2019 doi

  7. [14]

    Schoenholz, Patrick F

    Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, and George E. Dahl. Neural message passing for quantum chemistry. In Doina Precup and Yee Whye Teh, editors, Proceedings of the 34th International Conference on Machine Learning, volume 70 ofPro- ceedings of...

    2017

  8. [15]

    Fleur Hendriks, Ond ˇrej Rokoš, Martin Doškáˇr, Marc G. D. Geers, and Vlado Menkovski. Equivariant flow matching for symmetry-breaking bifurcation problems, 2026. URL https: //arxiv.org/abs/2509.03340

    2026 arXiv

  9. [16]

    3d detection and tracking of deformable bubbles in swarms with the aid of deep learning models

    Hendrik Hessenkemper, Lantian Wang, Dirk Lucas, Shiyong Tan, Rui Ni, and Tian Ma. 3d detection and tracking of deformable bubbles in swarms with the aid of deep learning models. International Journal of Multiphase Flow, 179:104932, 2024. ISSN 0301-9322. doi: https:// doi.org/1...

    2024 doi

  10. [17]

    V olume of fluid (vof) method for the dynamics of free boundaries

    C W Hirt and B D Nichols. V olume of fluid (vof) method for the dynamics of free boundaries. Journal of Computational Physics, 39:201–225, 1981. ISSN 0021-9991. doi: https://doi. org/10.1016/0021-9991(81)90145-5. URL https://www.sciencedirect.com/science/ article/pii/0021999181901455

    1981 doi

  11. [18]

    Doinikov

    Claude Inserra, Cyril Mauger, Philippe Blanc-Benon, and Alexander A. Doinikov. Mathematical modelling for acoustic microstreaming produced by a gas bubble undergoing asymmetric oscillations.Journal of Fluid Mechanics, 1010:A48, May 2025. ISSN 0022-1120, 1469-7645. doi: 10.1017...

    2025 doi

  12. [19]

    Deep learning-based automated and universal bubble detection and mask extraction in complex two-phase flows.Scientific reports, 11(1):8940, April 2021

    Yewon Kim and Hyungmin Park. Deep learning-based automated and universal bubble detection and mask extraction in complex two-phase flows.Scientific reports, 11(1):8940, April 2021. ISSN 2045-2322. doi: 10.1038/s41598-021-88334-0. URL https://europepmc.org/ articles/PMC8076184

    2021 doi

  13. [20]

    Neu- ral relational inference for interacting systems

    Thomas Kipf, Ethan Fetaya, Kuan-Chieh Wang, Max Welling, and Richard Zemel. Neu- ral relational inference for interacting systems. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, volume 80 ofPro- ceedings of Mac...

    2018

  14. [21]

    Non-linear shape oscillations of rising drops and bubbles: Experiments and simulations.Physics of Fluids, 27(12):123305, December 2015

    Benjamin Lalanne, Nicolas Abi Chebel, Jiˇrí Vejražka, Sébastien Tanguy, Olivier Masbernat, and Frédéric Risso. Non-linear shape oscillations of rising drops and bubbles: Experiments and simulations.Physics of Fluids, 27(12):123305, December 2015. ISSN 1070-6631, 1089-7666. doi...

    2015 doi

  15. [22]

    Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le. Flow matching for generative modeling, 2023. URLhttps://arxiv.org/abs/2210.02747

    2023 arXiv

  16. [23]

    Flow straight and fast: Learning to generate and transfer data with rectified flow.ArXiv, abs/2209.03003, 2022

    Xingchao Liu, Chengyue Gong, and Qiang Liu. Flow straight and fast: Learning to generate and transfer data with rectified flow.ArXiv, abs/2209.03003, 2022. URL https://api. semanticscholar.org/CorpusID:252111177

    2022 arXiv

  17. [24]

    M. J. Lockett and R. D. Kirkpatrick. Ideal bubbly flow and actual flow in bubble columns. Transactions of the Institution of Chemical Engineers, 53:267–273, 1975

    1975

  18. [25]

    Nortje, Wil O

    Caitlin R. Nortje, Wil O. C. Ward, Bartosz P. Neuman, and Li Bai. Spherical Harmonics for Surface Parametrisation and Remeshing.Mathematical Problems in Engineering, 2015(1): 582870, 2015. ISSN 1563-5147. doi: 10.1155/2015/582870

    2015 doi

  19. [26]

    Battaglia

    Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, and Peter W. Battaglia. Learning mesh-based simulation with graph networks.CoRR, abs/2010.03409, 2020. URL https: //arxiv.org/abs/2010.03409

    2010 arXiv

  20. [27]

    Reconstructing volume tracking.Journal of Computational Physics, 141:112–152, 1998

    William J Rider and Douglas B Kothe. Reconstructing volume tracking.Journal of Computational Physics, 141:112–152, 1998. ISSN 0021-9991. doi: https://doi.org/10. 1006/jcph.1998.5906. URL https://www.sciencedirect.com/science/article/pii/ S002199919895906X

    1998

  21. [28]

    Roghair, Y

    I. Roghair, Y . M. Lau, N. G. Deen, H. M. Slagter, M. W. Baltussen, M. Van Sint Annaland, and J. A.M. Kuipers. On the drag force of bubbles in bubble swarms at intermediate and high reynolds numbers.Chemical Engineering Science, 66:3204–3211, 7 2011. ISSN 00092509. doi: 10.101...

    2011 doi

  22. [29]

    Roghair, M

    I. Roghair, M. Van Sint Annaland, and J. A.M. Kuipers. An improved front-tracking technique for the simulation of mass transfer in dense bubbly flows.Chemical Engineering Science, 152: 351–369, 10 2016. ISSN 00092509. doi: 10.1016/j.ces.2016.06.026

    2016 doi

  23. [30]

    Energy spectra and bubble velocity distributions in pseudo-turbulence: Numerical simulations vs

    Ivo Roghair, Julián Martínez Mercado, Martin Van Sint Annaland, Hans Kuipers, Chao Sun, and Detlef Lohse. Energy spectra and bubble velocity distributions in pseudo-turbulence: Numerical simulations vs. experiments.International Journal of Multiphase Flow, 37:1093–1098, 11 201...

    2011 doi

  24. [32]

    sph-bubble-convert

    Ivo Roghair, Douwe Orij, and Rachna Ramesh. sph-bubble-convert. https://github.com/ iroghair/sph-bubble-convert, 2026. GitHub repository, commit e182c11, 2026-04-09

    2026

  25. [33]

    Learning to simulate complex physics with graph networks

    Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Peter Battaglia. Learning to simulate complex physics with graph networks. In Hal Daumé III and Aarti Singh, editors,Proceedings of the 37th International Conference on Machine Learning, volum...

    2020

  26. [34]

    E(n) equivariant graph neural networks

    Víctor Garcia Satorras, Emiel Hoogeboom, and Max Welling. E(n) equivariant graph neural networks. In Marina Meila and Tong Zhang, editors,Proceedings of the 38th International Conference on Machine Learning, volume 139 ofProceedings of Machine Learning Research, pages 9323–933...

    2021

  27. [35]

    Li Shen and Moo K. Chung. Large-Scale Modeling of Parametric Surfaces Using Spherical Harmonics. InThird International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT’06), pages 294–301, Chapel Hill, NC, USA, June 2006. IEEE. ISBN 978-0-7695-2825-0. doi...

    2006 doi

  28. [36]

    Simonnet, C

    M. Simonnet, C. Gentric, and E. Olmos. Experimental determination of the drag coefficient in a swarm of bubbles.Chemical Engineering Science, 62(3):858–866, 2007. doi: 10.1016/j.ces. 2006.10.012

    2007 doi

  29. [37]

    Application of deep learning for segmentation of bubble dynamics in subcooled boiling.International Journal of Multiphase Flow, 169:104589, 2023

    Jerol Soibam, Valentin Scheiff, Ioanna Aslanidou, Konstantinos Kyprianidis, and Rebei Bel Fdhila. Application of deep learning for segmentation of bubble dynamics in subcooled boiling.International Journal of Multiphase Flow, 169:104589, 2023. ISSN 0301-9322. doi: https://doi....

    2023 doi

  30. [38]

    Prakash, Martin Van Sint Annaland, Hans Kuipers, Chao Sun, and Detlef Lohse

    Yoshiyuki Tagawa, Ivo Roghair, Vivek N. Prakash, Martin Van Sint Annaland, Hans Kuipers, Chao Sun, and Detlef Lohse. The clustering morphology of freely rising deformable bubbles. Journal of Fluid Mechanics, 721, 2013. ISSN 14697645. doi: 10.1017/jfm.2013.100

    2013 doi

  31. [39]

    Stflow: Data-coupled flow matching for geometric trajectory simulation, 2026

    Kiet Bennema ten Brinke, Koen Minartz, and Vlado Menkovski. Stflow: Data-coupled flow matching for geometric trajectory simulation, 2026. URL https://arxiv.org/abs/2505. 18647

    2026

  32. [40]

    La- grangebench: A lagrangian fluid mechanics benchmarking suite

    Artur Toshev, Gianluca Galletti, Fabian Fritz, Stefan Adami, and Nikolaus Adams. La- grangebench: A lagrangian fluid mechanics benchmarking suite. In A. Oh, T. Nau- mann, A. Globerson, K. Saenko, M. Hardt, and S. Levine, editors,Advances in Neu- ral Information Processing Syst...

    2023

  33. [41]

    A front-tracking method for viscous, incompress- ible, multi-fluid flows.Journal of Computational Physics, 100:25–37, 1992

    Salih Ozen Unverdi and Grétar Tryggvason. A front-tracking method for viscous, incompress- ible, multi-fluid flows.Journal of Computational Physics, 100:25–37, 1992. ISSN 0021-9991. doi: https://doi.org/10.1016/0021-9991(92)90307-K. URL https://www.sciencedirect. com/science/a...

    1992 doi

  34. [42]

    van Sint Annaland, N.G

    M. van Sint Annaland, N.G. Deen, and J.A.M. Kuipers. Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fluid method.Chemical Engineering Science, 60 (11):2999–3011, 2005. ISSN 0009-2509. doi: https://doi.org/10.1016/j.ces.2005.01.031. URL https:...

    2005 doi

  35. [43]

    van Sint Annaland, W

    M. van Sint Annaland, W. Dijkhuizen, N. G. Deen, and J. A. M. Kuipers. Numerical simulation of behavior of gas bubbles using a 3-d front-tracking method.AIChE Journal, 52(1):99–110,

  36. [44]

    URL https://aiche.onlinelibrary.wiley

    doi: https://doi.org/10.1002/aic.10607. URL https://aiche.onlinelibrary.wiley. com/doi/abs/10.1002/aic.10607

    doi

  37. [46]

    URLhttps://arxiv.org/abs/2111.12702

    arXiv

  38. [47]

    D. L. Youngs. Time-dependent multi-material flow with large fluid distortion. In K. W. Morton and M. J. Baines, editors,Numerical Methods in Fluid Dynamics, pages 273–285. Academic Press, London, January 1982

    1982

  39. [48]

    3DBubbles: An experimental dataset for model training and benchmarking.AIChE Journal, 72(1):e70029,

    Baodi Yu, Qian Chen, Yanwei Qin, Sunyang Wang, Xiaohui Su, and Fanyong Meng. 3DBubbles: An experimental dataset for model training and benchmarking.AIChE Journal, 72(1):e70029,

  40. [49]

    doi: 10.1002/aic.70029

    ISSN 1547-5905. doi: 10.1002/aic.70029

    doi

  41. [50]

    3D surface filtering using spherical harmonics

    Kun Zhou, Hujun Bao, and Jiaoying Shi. 3D surface filtering using spherical harmonics. Computer-Aided Design, 36(4):363–375, February 2004. ISSN 00104485. doi: 10.1016/ S0010-4485(03)00098-8. 13 A Technical appendices and supplementary material A.1 Model Training and Inference...

    2004

Pith tools

Reviewed July 9, 2026 · model on record in the stance chip above.