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REVIEW 4 major objections 5 minor 77 references

Diffusion-corrected Autoregressive Fourier Neural Operator for Droplet Evolution Prediction

T0 review · 4 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read This paper claims that pairing an autoregressive neural operator with a diffusion-based detail corrector yields high-fidelity 550-frame droplet-evolution forecasts, cutting the cost of a CFD simulation from about 4 hours to about 40 seconds

desk verdict Solid applied combination of autoregressive operator + DDIM corrector, but the long-horizon gains rest on an unaddressed training/inference mismatch and overstated significance. read the letter →

arxiv 2607.16238 v1 pith:PQQLOYUO submitted 2026-06-25 cs.LG cs.AIphysics.comp-phphysics.flu-dyn

Jinghao Cao , Minsung Kang , Hongyue Sun , Chi Zhou , Jihoon Chung , Xubo Yue , Sanchoy Das , Bo Shen This is my paper
classification cs.LGcs.AIphysics.comp-phphysics.flu-dyn
keywords dropletevolutioninkjetprintingneuraloperatordiffusionmodelDDIMFourier-MIONetautoregressiveforecastingcomputationalfluiddynamics
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 sets out to solve a specific hard problem: given 50 frames of an inkjet droplet's evolution plus its material properties (density, viscosity, surface tension), predict the next 550 frames, including ligament thinning, pinch-off, and satellite-droplet formation. The proposed solution, DiffARFNO, splits the task in two: a Fourier-MIONet neural operator rolls out coarse predictions autoregressively, and a conditional DDIM diffusion corrector refines each sliding window to restore the fine, high-frequency structures that pure operators blur. On 42 held-out ANSYS Fluent droplet videos, the authors report the best scores among six models on all six metrics, with MSE 0.0003, SSIM 0.976, IoU 0.871, and a velocity error about 39% lower than the next-best model. The practical claim is that this makes near-CFD-quality droplet forecasts available in about 40 seconds instead of about 4 hours of simulation. A sympathetic reader would take the paper as evidence that decoupling coarse operator rollout from diffusion-based detail correction is a viable route to long-horizon physical video prediction.

What carries the argument

The load-bearing mechanism is the two-stage composition. Stage 1 is Fourier-MIONet, a branch-trunk multiple-input neural operator: a video branch encodes the input window, a property branch encodes the material parameters, a coordinate branch encodes the normalized spatiotemporal grid, and a shared UFNO-style decoder fuses them to produce the coarse next window. A linear-blending step fuses overlapping window boundaries to prevent droplet 'shaking' at seams, and a binary mask loss (Otsu-thresholded grayscale of the prediction vs. ground truth) pushes the model to preserve sharp droplet boundaries. Stage 2 is a conditional DDIM corrector: a 3D U-Net denoiser is conditioned on the coarse predi

What would settle it

A decisive check: run the trained DiffARFNO and Fourier-MIONet on a new, unseen batch of CFD droplet videos (or, ideally, on experimental high-speed footage of the same material-property ranges). If the reported IoU gap (0.871 vs 0.839) and the 39% velocity-MAE reduction do not persist, the claimed benefit of the diffusion corrector is an artifact of the training distribution.

Watch

Extended reading notes

Core claim

DiffARFNO's central discovery is that the failure mode of autoregressive neural operators over long horizons—progressive smoothing and loss of thin, small-scale structures—can be corrected by a lightweight diffusion module that does not regenerate the whole sequence. The Fourier-MIONet backbone is trained once and frozen; a conditional DDIM denoiser, conditioned on the coarse prediction, is trained to remove the residual between that prediction and the true next window. During inference, the refined windows are fed back as context for the next rollout step, and the authors report that this combination preserves pinch-off timing and satellite droplets that each baseline misses, while also imp

Load-bearing premise

The entire quantitative evaluation assumes the ANSYS Fluent VOF simulations, with their stated material ranges, are a faithful stand-in for real inkjet droplet behavior; if the synthetic distribution differs from real high-speed experimental footage, the reported accuracy gains may not transfer.

Editorial extensions

If this is right

  • If DiffARFNO is right, a 550-frame droplet evolution that currently costs about 4 hours of VOF CFD can be predicted in about 40 seconds with pixel-level accuracy sufficient for IoU 0.87, making real-time in-process monitoring of material jetting feasible.
  • The model's ability to keep pinch-off timing and satellite droplets across the horizon implies that long-horizon operator predictions are not limited by the operator's capacity but by missing high-frequency correction, a fixable defect.
  • Because the property encoder takes density, viscosity, and surface tension as inputs, the same trained model can be queried at new material-property combinations without rerunning CFD, enabling fast screening of printable ink formulations.
  • The reported velocity-error reduction (MAE 0.0117 vs 0.0191 for Fourier-MIONet) indicates the corrected frames are not just visually sharper but physically more faithful, supporting use for process-control feedback.
  • The frame-wise IoU curves show the corrector slows long-horizon degradation rather than eliminating it; gains are largest in the hardest regime (satellites), which is where purely operator-based baselines fail earliest.

Reading between the lines

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

  • Testable extension: apply the same frozen-operator plus DDIM-corrector split to other autoregressive operator rollouts with decaying high-frequency detail (turbulence, weather, cardiac flow); the paper's mechanism predicts the corrector will restore spectral content without retraining the operator.
  • The Otsu-threshold mask loss is a cheap, parameter-free structural regularizer; it could be dropped into other video-prediction losses to bias models toward sharp interfaces, even outside droplets.
  • The stated synthetic-to-real gap suggests a concrete next step the authors do not explore: fine-tune only the DDIM corrector on a small set of experimental high-speed droplet videos and measure whether the IoU gap over Fourier-MIONet persists; if it does not, the reported gains are distribution-specific.
  • Because the method conditions on material properties, a natural application left implicit is offline design of experiments: replace CFD sweeps with DiffARFNO rollouts to map printable Ohnesorge-number windows at about 1/350th of the compute cost.
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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

4 major / 5 minor

Summary. The paper proposes DiffARFNO, a two-stage framework for long-horizon droplet evolution prediction from CFD-generated video data. Stage 1 trains an autoregressive Fourier-MIONet (a multiple-input neural operator) to produce coarse predictions in sliding windows of 50 frames; Stage 2 trains a conditional DDIM denoiser to refine these coarse predictions. The refined outputs are fed back as contexts for subsequent windows. The authors evaluate on 212 ANSYS Fluent VOF droplet videos (600 frames each) spanning ligament thinning, pinch-off, and satellite formation regimes. They report 10-run means/stds for MSE, MAE, PSNR, SSIM, R^2, IoU and for a velocity-extraction metric, comparing against FNO, UFNO, GeoFNO, PIANO, and Fourier-MIONet. The central claim is that DiffARFNO 'significantly outperforms existing state-of-the-art models' across all metrics and regimes.

Significance. The combination of a neural-operator backbone with a diffusion corrector for long-horizon fluid-dynamics forecasting is a reasonable and timely idea, and the paper applies it to a practically motivated problem (inkjet printing). The empirical setup is more careful than many ML papers: 10 repeated runs, a consistent train/validation/test split, and evaluation on several regimes. If the reported gains are statistically reliable and survive the autoregressive distribution shift, the method would be a useful surrogate for costly droplet simulations. However, the strength of the central claim is not yet supported by the evidence: there are no statistical significance tests; the IoU metric is directly optimized through a mask loss on the same Otsu-thresholded representation; and the corrector is trained under teacher forcing but deployed on predicted contexts. These issues need to be addressed before the 'significantly outperforms' claim can be accepted.

major comments (4)
  1. [§5.2, Table 2] The abstract and §5.2 state that DiffARFNO 'significantly outperforms' baselines, but no statistical significance tests are reported. For several metrics the gaps are small relative to the reported standard deviations (e.g., PSNR: 34.7104 ± 0.0243 vs 34.4669 ± 0.3820; SSIM: 0.9763 ± 0.0017 vs 0.9555 ± 0.0058). A paired test (e.g., Wilcoxon signed-rank or paired t-test) across the 10 repeated runs, or across the 42 test videos, is needed to support the wording. Please also report per-run results or effect sizes, especially for Fourier-MIONet, whose std is much larger than the others on PSNR and IoU.
  2. [§3.2, Eq. (14); §3.1, Eqs. (2)–(3)] The DDIM corrector is trained on ground-truth target sequences X_out(k) conditioned on coarse predictions bX_out(k) (Eq. 14), but at inference the coarse predictions are generated from previously predicted and corrected frames (Eqs. 2–3). The paper does not describe scheduled sampling, unrolled training, or any mechanism to expose the corrector to its own rollout distribution. This teacher-forcing mismatch is a load-bearing concern for the 600-frame claim. Please report an ablation that quantifies the gap: e.g., apply the corrector to ground-truth contexts vs to predicted contexts, or fine-tune with a rollout loss. Without such evidence, the long-horizon improvements may not generalize to the deployed setting.
  3. [§3.1, Eqs. (7)–(8); §5.2, IoU metric] The mask loss in Eq. (8) is computed on Otsu-thresholded masks M(·), and the headline IoU metric in Table 2 appears to be computed on the same Otsu-thresholded representation. This means the model is explicitly trained to optimize the exact thresholding used by the evaluation metric, so the IoU improvement is partly by construction. To establish that the improvement reflects genuine segmentation quality rather than metric-aligned training, either (a) compute IoU on masks obtained from a fixed, non-Otsu threshold, or (b) report IoU with a different segmentation method and clarify explicitly whether the evaluation masks use the same τ*(G) as in Eq. (7).
  4. [§6; §4.2] The paper acknowledges in §6 that transfer to real experimental conditions is unvalidated, which is appropriate. However, the motivation in §1 emphasizes real-world inkjet printing, and the entire quantitative evaluation relies on 212 CFD-generated videos. The paper should either explicitly scope the central claim to CFD-synthetic data only (without the broader 'high-fidelity prediction' framing) or discuss the domain-gap risk in the results section. This is a limitation rather than an error, but it affects how a reader interprets the significance of the reported numbers.
minor comments (5)
  1. [Appendix A, Table 1] The hyperparameter table is numbered 'Table 1' in Appendix A, but there is already a 'Table 1' in the main text (§4.1, material properties). Re-number appendix tables as Table A1, Table A2, etc., to avoid ambiguity.
  2. [§5.3, Figures 3–8] For the qualitative regime analysis, only one representative test sample is shown per regime. Since the quantitative claims are averaged over 42 test videos, it would be informative to show error maps or aggregated examples for a few samples, or to note that these are single representative cases.
  3. [§5.4, Figure 9] The frame-wise IoU curves in Figure 9 have no error bands or multiple-run overlays. Given that the paper reports 10 repeated runs, adding shaded confidence intervals would strengthen the temporal-evolution analysis and help the reader assess whether the shown gaps are stable.
  4. [References] Some references are incomplete or lack venue details (e.g., Cao et al., 2025 is given only as a title, with no journal/conference or publication status). Please check the reference list for consistency.
  5. [§5.5.1] The velocity extraction uses several hyperparameters (q=0.995, K=30, Gaussian smoothing widths). The paper does not report sensitivity to these choices. A brief robustness check or a justification that these are physical rather than tuned would be useful, since the velocity metric is used to support physical-fidelity claims.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claim is an empirical held-out comparison and does not reduce to its inputs.

full rationale

DiffARFNO's central claim is an empirical, held-out comparison. The model is trained on 149 CFD videos, validated on 21, and all reported metrics are computed on 42 held-out test videos (Section 5.1), with all benchmark models trained under the same split, preprocessing, window configuration, and autoregressive protocol. The mask-aligned loss in Eq. (8) uses Otsu-thresholded masks and the IoU metric in Table 2 is computed on binary masks, so IoU is partly aligned with a training objective; however, this is not a circular derivation because the masks are supervised outputs rather than fitted inputs, and the test IoU can still fail. The DDIM corrector is trained with the denoising loss in Eq. (14) conditioned on the frozen coarse prediction, and the reported long-horizon outputs are produced by the autoregressive deployment in Eqs. (2)-(3) and (13); no equation in Section 3 equates a reported prediction to a fitted parameter or to the training target. Self-citations such as the PIANO baseline and prior droplet-evolution work by the same group are background or comparison baselines, not load-bearing support for the claimed improvement. The Section 6 caveat that the model relies on CFD-generated data and may not transfer to real experimental conditions is an external-validity limitation, not a circularity. The autoregressive train/deploy distribution mismatch is a generalization risk, not a definitional circularity. No load-bearing step reduces a prediction to its own input by construction.

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

Everything beyond the CFD physics is either learned from data or chosen by hand. The main costs are the empirically selected mask loss weight, hand-picked velocity post-processing constants, the unreported window overlap Δ, and the assumption that CFD data stands in for reality. No new physical entities are introduced.

free parameters (5)
  • Mask loss weight λ_mask = 0.5
    Equation (8); chosen empirically from validation performance; directly shapes training and boosts the IoU metric that is also used for evaluation.
  • Otsu threshold τ*(G) for binary masks = per-frame gray-level threshold
    Equation (7); used in both the training mask loss and the IoU evaluation metric, coupling the metric to a per-frame fitted threshold.
  • Velocity extraction hyperparameters q and K = q=0.995, K=30
    Section 5.5.1; head-position definition and forward-velocity window are hand-chosen; double Gaussian smoothing further affects velocity error scores.
  • DDIM sampling steps = 25
    Appendix A.2; reduces 200 training timesteps to 25 inference steps; affects refinement quality and all reported metrics.
  • Window blending overlap Δ = not specified
    Equations (3)-(5) use an overlap Δ for linear blending between autoregressive windows, but the paper never states its value; it affects rollout stability and all reported metrics.
assumptions (5)
  • domain assumption ANSYS Fluent VOF simulations of axisymmetric, viscous, incompressible droplets faithfully represent real inkjet droplet evolution
    Section 4.1; all training/testing data are synthetic; paper acknowledges transferability unvalidated in Section 6.
  • domain assumption The 212 curated videos span the relevant regimes (ligament thinning, pinch-off, satellite formation) and the 70/10/20 split is representative
    Sections 4.2 and 5.1; no external or experimental dataset is used.
  • domain assumption A learned operator and diffusion corrector can approximate the droplet-evolution solution operator from a 50-frame context
    Section 3; relies on empirical generalization of neural operators and diffusion models.
  • domain assumption Autoregressive sliding windows with linear blending produce sequences consistent with the true dynamics
    Equations (2)-(5); no error-propagation bound or physical consistency check beyond qualitative inspection.
  • domain assumption Randomness in the ten training runs is sufficient to quantify uncertainty of the reported gains
    Section 5.1; tables report means/stds but no hypothesis tests; velocity table has no std.

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Cite this review

Pith. "Pith review of Diffusion-corrected Autoregressive Fourier Neural Operator for Droplet Evolution Prediction." pith.science (2026). https://pith.science/paper/PQQLOYUO

@misc{pith2026260716238,
  author       = {Pith},
  title        = {Pith review of: Diffusion-corrected Autoregressive Fourier Neural Operator for Droplet Evolution Prediction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PQQLOYUO}},
  note         = {Machine review of arXiv:2607.16238}
}
read the original abstract

Predicting droplet evolution in material jetting, or Inkjet Printing (IJP), is essential for maintaining printing quality. However, long-horizon forecasts remain challenging due to error accumulation and the complex coupling of process variables. In this work, we introduce the Diffusion-corrected Auto-Regressive Fourier Neural Operator (DiffARFNO), a two-stage framework that combines an autoregressive Fourier-MIONet with a conditional Denoising Diffusion Implicit Model (DDIM) corrector. Fourier-MIONet is trained as a coarse predictor and deployed autoregressively for long-horizon forecasting. In the second stage, a DDIM-based conditional corrector refines the coarse prediction within each sliding window through efficient iterative denoising. By combining coarse predictions from Fourier-MIONet with a DDIM corrector that restores fine details, DiffARFNO aims to provide high-fidelity predictions for long-horizon forecasts. Extensive experiments on droplet datasets from ANSYS Fluent demonstrate that DiffARFNO significantly outperforms existing state-of-the-art models.

Figures

Figures reproduced from arXiv: 2607.16238 by the authors.

Figure 1
Figure 1. Overview of the proposed DiffARFNO framework. In [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Simulated droplet evolution dataset and final training samples. (a) ANSYS Flu [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. RGB predictions of ligament thinning regime. 5.3.1 Ligament Thinning [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: The error map of binary masks for ligament thinning regime. The error map is calculated between the prediction mask and the ground truth mask. however, mild smoothing becomes evident as the neck thins, resulting in less clear bound￾aries. PIANO produces visually plausi…
Figure 5
Figure 5. Figure 5: RGB predictions of pinch-off dynamics regime. based on the predicted and ground truth masks. Accurately resolving this process requires capturing severe neck thinning, the localization of the pinch-off point, and the temporal consistency of the droplet morphology. Diff…
Figure 6
Figure 6. Figure 6: The error map of binary masks for pinch-off dynamics regime. The error map is calculated between the prediction mask and the ground truth mask [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]
Figure 7
Figure 7. Figure 7: RGB predictions of satellite droplet evolution. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]
Figure 8
Figure 8. Figure 8: The error map of binary masks for satellite droplet evolution. The error map is calculated between the prediction mask and the ground truth mask. DiffARFNO provides the closest visual agreement with the ground truth in this regime. It better preserves the main droplet …
Figure 9
Figure 9. Figure 9: Frame-wise IoU trajectories for three representative test samples corresponding [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]
Figure 10
Figure 10. Figure 10: Illustration of droplet head positions used for velocity calculation. The droplet [PITH_FULL_IMAGE:figures/full_fig_p024_10.png]
Figure 11
Figure 11. Figure 11: Ligament thinning regime. Binary mask predictions for a representative case with an increasingly thinning ligament. DiffARFNO preserves the ligament thinning structure and boundary more accurately than the compared benchmarks. B Binary Mask Predictions To further show…
Figure 12
Figure 12. Figure 12: Pinch-off dynamics regime. Binary mask predictions for a representative topology-changing case. DiffARFNO better captures the pinch-off dynamics, whereas the benchmarks show errors such as missed pinch-off and neck morphology errors. close to the reference in both the…
Figure 13
Figure 13. Figure 13: Satellite droplet formation regime. Binary mask predictions for a repre￾sentative case involving small detached droplets. DiffARFNO more accurately recovers the satellite droplets and the main ligament morphology, while the benchmarks fail to detect the small droplets…

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Works this paper leans on

77 extracted references · 5 canonical work pages

  1. [1]

    Chemistry of Materials , volume =

    Calvert, Paul , title =. Chemistry of Materials , volume =. 2001 , doi =

    2001

  2. [2]

    A Threshold Selection Method from Gray-Level Histograms , year=

    Otsu, Nobuyuki , journal=. A Threshold Selection Method from Gray-Level Histograms , year=

  3. [3]

    Reliability Engineering & System Safety , volume=

    Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration , author=. Reliability Engineering & System Safety , volume=. 2024 , publisher=

    2024

  4. [4]

    Additive Manufacturing , volume=

    Unsupervised learning for the droplet evolution prediction and process dynamics understanding in inkjet printing , author=. Additive Manufacturing , volume=. 2020 , publisher=

    2020

  5. [5]

    Annual Review of Materials Research , volume=

    Inkjet printing of functional and structural materials: fluid property requirements, feature stability, and resolution , author=. Annual Review of Materials Research , volume=. 2010 , publisher=

    2010

  6. [6]

    Atomization and sprays , volume=

    Future, opportunities and challenges of inkjet technologies , author=. Atomization and sprays , volume=. 2013 , publisher=

    2013

  7. [7]

    2021 , issn =

    CFD-based numerical modeling to predict the dimensions of printed droplets in electrohydrodynamic inkjet printing , journal =. 2021 , issn =. doi:https://doi.org/10.1016/j.jmapro.2021.04.003 , url =

    work page doi:10.1016/j.jmapro.2021.04.003 2021

  8. [8]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=

    Predrnn: A recurrent neural network for spatiotemporal predictive learning , author=. IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=. 2022 , publisher=

    2022

Show all 77 references
  1. [9]

    IEEE Transactions on Multimedia , year=

    SimVPv2: Towards simple yet powerful spatiotemporal predictive learning , author=. IEEE Transactions on Multimedia , year=

  2. [10]

    Parallel Sampling of Diffusion Models , url =

    Shih, Andy and Belkhale, Suneel and Ermon, Stefano and Sadigh, Dorsa and Anari, Nima , booktitle =. Parallel Sampling of Diffusion Models , url =

  3. [11]

    Journal of Manufacturing Science and Engineering , volume =

    Wu, Dazhong and Xu, Changxue , title =. Journal of Manufacturing Science and Engineering , volume =. 2018 , month =. doi:10.1115/1.4040619 , url =

    2018 doi

  4. [12]

    2018 , issn =

    Additive manufacturing (3D printing): A review of materials, methods, applications and challenges , journal =. 2018 , issn =. doi:https://doi.org/10.1016/j.compositesb.2018.02.012 , url =

    2018 doi

  5. [13]

    Advances in neural information processing systems , volume=

    Denoising diffusion probabilistic models , author=. Advances in neural information processing systems , volume=

  6. [14]

    Advances in Neural Information Processing Systems (NeurIPS) , year =

    Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks , author =. Advances in Neural Information Processing Systems (NeurIPS) , year =. doi:10.48550/arXiv.1506.03099 , url =

    doi arXiv

  7. [15]

    Proceedings of the Computer Vision and Pattern Recognition Conference , pages=

    Progressive autoregressive video diffusion models , author=. Proceedings of the Computer Vision and Pattern Recognition Conference , pages=

  8. [16]

    2018 , issn =

    Drop-on-demand satellite-free drop formation for precision fluid delivery , journal =. 2018 , issn =. doi:https://doi.org/10.1016/j.ces.2018.04.014 , url =

    2018 doi

  9. [17]

    Virtual and Physical Prototyping , volume =

    Haining Zhang and Lin Cui and Pil-Ho Lee and Yongrae Kim and Seung Ki Moon and Joon Phil Choi , title =. Virtual and Physical Prototyping , volume =. 2024 , publisher =. doi:10.1080/17452759.2024.2429530 , URL =

    2024

  10. [18]

    Procedia Manufacturing , volume=

    In-situ droplet monitoring of inkjet 3D printing process using image analysis and machine learning models , author=. Procedia Manufacturing , volume=. 2021 , publisher=

    2021

  11. [19]

    IEEE Access , year=

    Multi-Parameter Prediction of Inkjet Droplet Characteristics Based on Dual-Pulse Waveform and Ensemble Learning , author=. IEEE Access , year=

  12. [20]

    Annual Review of Fluid Mechanics , volume=

    Nonstandard inkjets , author=. Annual Review of Fluid Mechanics , volume=. 2013 , publisher=

    2013

  13. [21]

    Additive Manufacturing , volume=

    Droplet evolution prediction in material jetting via tensor time series analysis , author=. Additive Manufacturing , volume=. 2023 , publisher=

    2023

  14. [22]

    Scientific reports , volume=

    Mesh-based GNN surrogates for time-independent PDEs , author=. Scientific reports , volume=. 2024 , publisher=

    2024

  15. [23]

    Benchmarking autoregressive conditional diffusion models for turbulent flow simulation , journal =

    Georg Kohl and Li-Wei Chen and Nils Thuerey , keywords =. Benchmarking autoregressive conditional diffusion models for turbulent flow simulation , journal =. 2026 , issn =. doi:https://doi.org/10.1016/j.neunet.2026.108641 , url =

    2026

  16. [24]

    Journal of Manufacturing Science and Engineering , volume=

    Multiclass reinforced active learning for droplet pinch-off behaviors identification in inkjet printing , author=. Journal of Manufacturing Science and Engineering , volume=. 2023 , publisher=

    2023

  17. [25]

    Journal of computational physics , volume=

    Volume of fluid (VOF) method for the dynamics of free boundaries , author=. Journal of computational physics , volume=. 1981 , publisher=

    1981

  18. [26]

    Advances in Water Resources , volume=

    U-FNO—An enhanced Fourier neural operator-based deep-learning model for multiphase flow , author=. Advances in Water Resources , volume=. 2022 , publisher=

    2022

  19. [27]

    Journal of Machine Learning Research , volume=

    Fourier neural operator with learned deformations for pdes on general geometries , author=. Journal of Machine Learning Research , volume=

  20. [28]

    2025 , eprint=

    Physics-informed Attention-enhanced Fourier Neural Operator for Solar Magnetic Field Extrapolations , author=. 2025 , eprint=

    2025

  21. [29]

    Annual review of fluid mechanics , volume=

    Fundamental fluid dynamics challenges in inkjet printing , author=. Annual review of fluid mechanics , volume=. 2022 , publisher=

    2022

  22. [30]

    Advances in Neural Information Processing Systems , volume=

    Pde-refiner: Achieving accurate long rollouts with neural pde solvers , author=. Advances in Neural Information Processing Systems , volume=

  23. [31]

    arXiv preprint arXiv:2309.10714 , year=

    Reconstruct-and-generate diffusion model for detail-preserving image denoising , author=. arXiv preprint arXiv:2309.10714 , year=

    arXiv

  24. [32]

    Advances in Neural Information Processing Systems , volume=

    A unified conditional framework for diffusion-based image restoration , author=. Advances in Neural Information Processing Systems , volume=

  25. [33]

    Review of Scientific Instruments , volume=

    Visualization of drop-on-demand inkjet: Drop formation and deposition , author=. Review of Scientific Instruments , volume=. 2006 , publisher=

    2006

  26. [34]

    Data-driven stochastic closure modeling via conditional diffusion model and neural operator , journal =

    Xinghao Dong and Chuanqi Chen and Jin-Long Wu , keywords =. Data-driven stochastic closure modeling via conditional diffusion model and neural operator , journal =. 2025 , issn =. doi:https://doi.org/10.1016/j.jcp.2025.114005 , url =

    2025

  27. [35]

    Journal of fluid mechanics , volume=

    The retraction of jetted slender viscoelastic liquid filaments , author=. Journal of fluid mechanics , volume=. 2021 , publisher=

    2021

  28. [36]

    Reviews of modern physics , volume=

    Nonlinear dynamics and breakup of free-surface flows , author=. Reviews of modern physics , volume=. 1997 , publisher=

    1997

  29. [37]

    Proceedings of the Royal Society A , volume=

    Integrating neural operators with diffusion models improves spectral representation in turbulence modelling , author=. Proceedings of the Royal Society A , volume=. 2025 , publisher=

    2025

  30. [38]

    arXiv preprint arXiv:2010.02502 , year=

    Denoising diffusion implicit models , author=. arXiv preprint arXiv:2010.02502 , year=

    2010 arXiv

  31. [39]

    2024 , eprint=

    CoNFiLD: Conditional Neural Field Latent Diffusion Model Generating Spatiotemporal Turbulence , author=. 2024 , eprint=

    2024

  32. [40]

    Advances in neural information processing systems , volume=

    Dyffusion: A dynamics-informed diffusion model for spatiotemporal forecasting , author=. Advances in neural information processing systems , volume=

  33. [41]

    Advances in neural information processing systems , volume=

    Video diffusion models , author=. Advances in neural information processing systems , volume=

  34. [42]

    International Conference on Medical image computing and computer-assisted intervention , pages=

    U-net: Convolutional networks for biomedical image segmentation , author=. International Conference on Medical image computing and computer-assisted intervention , pages=. 2015 , organization=

    2015

  35. [43]

    Advances in Neural Information Processing Systems , volume=

    DiffusionPDE: Generative PDE-solving under partial observation , author=. Advances in Neural Information Processing Systems , volume=

  36. [44]

    Journal of Computational Physics , volume=

    A physics-informed diffusion model for high-fidelity flow field reconstruction , author=. Journal of Computational Physics , volume=. 2023 , publisher=

    2023

  37. [45]

    Forschungsbericht- Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt , year=

    A software package for sequential quadratic programming , author=. Forschungsbericht- Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt , year=

  38. [46]

    arXiv preprint arXiv:2011.13456 , year=

    Score-based generative modeling through stochastic differential equations , author=. arXiv preprint arXiv:2011.13456 , year=

    2011 arXiv

  39. [47]

    Nature Communications , volume =

    Drop impact printing , author =. Nature Communications , volume =. 2020 , doi =

    2020

  40. [48]

    Journal of Machine Learning Research , volume=

    Neural operator: Learning maps between function spaces with applications to pdes , author=. Journal of Machine Learning Research , volume=

  41. [49]

    Handbook of Numerical Analysis , volume=

    Operator learning: Algorithms and analysis , author=. Handbook of Numerical Analysis , volume=. 2024 , publisher=

    2024

  42. [50]

    Advances in Neural Information Processing Systems , volume=

    Understanding the Expressivity and Trainability of Fourier Neural Operator: A Mean-Field Perspective , author=. Advances in Neural Information Processing Systems , volume=

  43. [51]

    IEEE transactions on pattern analysis and machine intelligence , volume=

    Image super-resolution via iterative refinement , author=. IEEE transactions on pattern analysis and machine intelligence , volume=. 2022 , publisher=

    2022

  44. [52]

    Journal of Machine Learning Research , volume=

    On universal approximation and error bounds for Fourier neural operators , author=. Journal of Machine Learning Research , volume=

  45. [53]

    Langmuir , volume=

    Influence of fluid physical properties on ink-jet printability , author=. Langmuir , volume=. 2009 , publisher=

    2009

  46. [54]

    Transactions on Machine Learning Research , issn=

    Towards Stability of Autoregressive Neural Operators , author=. Transactions on Machine Learning Research , issn=. 2023 , url=

    2023

  47. [55]

    arXiv preprint arXiv:2202.00512 , year=

    Progressive distillation for fast sampling of diffusion models , author=. arXiv preprint arXiv:2202.00512 , year=

    arXiv

  48. [56]

    Advances in neural information processing systems , volume=

    Elucidating the design space of diffusion-based generative models , author=. Advances in neural information processing systems , volume=

  49. [57]

    arXiv preprint arXiv:2010.08895 , year=

    Fourier neural operator for parametric partial differential equations , author=. arXiv preprint arXiv:2010.08895 , year=

    2010 arXiv

  50. [58]

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

    Lu, Lu and Jin, Pengzhan and Pang, Guofei and Zhang, Zhongqiang and Karniadakis, George Em , year=. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators , volume=. Nature Machine Intelligence , publisher=. doi:10.1038/s42256-021-0...

    doi

  51. [59]

    International conference on medical image computing and computer-assisted intervention , pages=

    3D U-Net: learning dense volumetric segmentation from sparse annotation , author=. International conference on medical image computing and computer-assisted intervention , pages=. 2016 , organization=

    2016

  52. [60]

    Physics of Fluids , volume=

    Experimental study of the parameters for stable drop-on-demand inkjet performance , author=. Physics of Fluids , volume=. 2019 , publisher=

    2019

  53. [61]

    2023 , issn =

    A surrogate modelling strategy to improve the surface morphology quality of inkjet printing applications , journal =. 2023 , issn =. doi:https://doi.org/10.1016/j.jmapro.2023.01.078 , url =

    2023 doi

  54. [62]

    Physics of Fluids , volume=

    Analysis of drop-on-demand printing characteristics and stability driven by inertial forces , author=. Physics of Fluids , volume=. 2024 , publisher=

    2024

  55. [63]

    ChemEngineering , volume=

    Coupled CFD-Response Surface Method (RSM) Methodology for Optimizing Jettability Operating Conditions , author=. ChemEngineering , volume=. 2018 , doi=

    2018

  56. [64]

    2017 , issn =

    Optimizing inkjet printing process to fabricate thick ceramic coatings , journal =. 2017 , issn =. doi:https://doi.org/10.1016/j.ceramint.2016.12.103 , url =

    2017 doi

  57. [65]

    Segura, L. J. and Wang, T. and Zhou, C. and Sun, H. , title =. Additive Manufacturing , volume =

  58. [66]

    and Zhang, Z

    Xu, C. and Zhang, Z. and Fu, J. and Huang, Y. , title =. Langmuir , volume =

  59. [67]

    and Zhang, Z

    Xu, C. and Zhang, Z. and Huang, Y. and Xu, H. , title =. Journal of Manufacturing Science and Engineering , volume =

  60. [68]

    IISE Transactions , volume=

    Reinforcement learning for fuselage shape control during aircraft assembly , author=. IISE Transactions , volume=. 2026 , publisher=

    2026

  61. [69]

    arXiv preprint arXiv:2511.22090 , year=

    Quantum Bayesian Optimization for Quality Improvement in Fuselage Assembly , author=. arXiv preprint arXiv:2511.22090 , year=

    arXiv

  62. [70]

    IISE Transactions , volume=

    SmartFixture: Physics-guided reinforcement learning for automatic fixture layout design in manufacturing systems , author=. IISE Transactions , volume=. 2025 , publisher=

    2025

  63. [71]

    IEEE Transactions on Automation Science and Engineering , year=

    ADs: Active Data-selection for Data Quality Assurance in Data-sharing over Advanced Manufacturing Systems , author=. IEEE Transactions on Automation Science and Engineering , year=

  64. [72]

    Expert Systems with Applications , volume=

    Uni-3DAD: Gan-inversion aided universal 3D anomaly detection on model-free products , author=. Expert Systems with Applications , volume=. 2025 , publisher=

    2025

  65. [73]

    Journal of Manufacturing Science and Engineering , volume=

    MVGCN: Multi-view graph convolutional neural network for surface defect identification using three-dimensional point cloud , author=. Journal of Manufacturing Science and Engineering , volume=. 2023 , publisher=

    2023

  66. [74]

    IISE Transactions , volume=

    NP-ODE: Neural process aided ordinary differential equations for uncertainty quantification of finite element analysis , author=. IISE Transactions , volume=. 2022 , publisher=

    2022

  67. [75]

    Npj Materials Degradation , volume=

    StressNet-Deep learning to predict stress with fracture propagation in brittle materials , author=. Npj Materials Degradation , volume=. 2021 , publisher=

    2021

  68. [76]

    Journal of Manufacturing Systems , volume=

    Data science skills and domain knowledge requirements in the manufacturing industry: A gap analysis , author=. Journal of Manufacturing Systems , volume=. 2021 , publisher=

    2021

  69. [77]

    Journal of intelligent manufacturing , volume=

    Trends in intelligent manufacturing research: a keyword co-occurrence network based review , author=. Journal of intelligent manufacturing , volume=. 2022 , publisher=

    2022

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.