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REVIEW 4 major objections 5 minor 78 references

High-throughput digital twin framework for predicting neurite deterioration using MetaFormer attention

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Pith's one-line read The paper claims that a MetaFormer-based digital twin turns 10 neuron-culture frames into 20 predicted frames of neurite deterioration, with mean relative errors of 1.9641% (synthetic) and 6.0339% (experimental).

desk verdict A useful, honest application of an existing video-prediction model to neurite deterioration with a new synthetic dataset, but the headline error numbers rest on an undefined, likely background-dominated metric and no baseline comparison. read the letter →

arxiv 2501.08334 v1 pith:W2TMWQBO submitted 2024-12-18 q-bio.NC cs.CVcs.LG

classification q-bio.NCcs.CVcs.LG
keywords NeurodevelopmentaldisordersNeuritedeteriorationDigitaltwinMetaFormerGatedspatiotemporalattentionPhasefieldmodelVideopredictionIsogeometricanalysis
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that a digital twin framework can turn ten microscopy frames of a neuron culture into twenty predicted frames of neurite deterioration, by linking an isogeometric-analysis phase-field simulator, experimental images, and a MetaFormer-based gated spatiotemporal attention model. The reported result is an average error of 1.9641% on synthetic deterioration and 6.0339% on experimental deterioration, with inference taking a fraction of a second per sequence. If that holds, researchers could cheaply preview how cultures will retract, atrophy, or fragment before running long, expensive experiments, and use the forecasts to guide experimental design for neurodevelopmental disorder studies. The paper additionally claims that the synthetic generator compensates for scarce experimental data and that adding VGG16-based perceptual loss to mean squared error preserves thin neurite structure.

What carries the argument

The load-bearing machinery is the MetaFormer framework -- a Transformer generalization in which the token-mixing operation can be any module -- instantiated with the gated spatiotemporal attention (gSTA) module: depth-wise convolution for local spatial features, dilated convolution for distant pixels, and a $1\times1$ channel-wise convolution whose gating modulates temporal information flow. This module sits between a convolutional encoder and decoder, expanding the temporal dimension from 10 frames to 20 frames. On the data side, the IGA-based phase field model supplies synthetic deterioration videos by coupling a phase-field equation, tubulin transport, synaptogenesis, and a driving force, generating patterns of retraction, atrophy, and fragmentation. The combined MSE and VGG16 perceptual loss is what the paper credits with keeping thin neurite structures coherent.

What would settle it

Mask each frame to neurite pixels only, using the ground-truth phase-field threshold, and recompute the reported error on those pixels; if the whole-frame error stays near 1.96% and 6.03% while the neurite-only error is much larger, the reported accuracy does not establish that deterioration was predicted.

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Extended reading notes

Core claim

The paper's central claim is that a MetaFormer-based gated spatiotemporal attention (gSTA) model, configured as an encoder-translator-decoder, can predict the next 20 frames of neurite deterioration from 10 input frames, capturing long-range temporal dependencies and morphological transformations such as retraction, atrophy, and fragmentation. On the synthetic dataset produced by the IGA-based phase field model, the average test error is reported as 1.9641%; on experimental neuron-culture videos, it is reported as 6.0339%. The model is trained separately on each dataset with a combined MSE and VGG16 perceptual loss, and the paper presents absolute error maps and error plots showing that errors grow as predictions extend further into the future, with maximum experimental errors near 24%.

Load-bearing premise

The load-bearing premise is that the pixel-by-pixel average percentage error over a full $256\times256$ frame actually measures whether retraction, atrophy, and fragmentation were predicted, and that the 70/15/15 split separates whole culture videos rather than $256\times256$ patches cut from the same video.

Editorial extensions

If this is right

  • A researcher with 10 frames of time-lapse microscopy can get 20 future frames of deterioration in under a second, letting culture experiments be triaged before they run.
  • The synthetic IGA phase-field dataset can stand in for scarce experimental data during model development and hyperparameter tuning.
  • Because errors grow with forecast horizon, with experimental maxima near 24%, the framework is most trustworthy for near-term predictions and long-horizon forecasts should be treated as less reliable.
  • The gSTA model produces all 20 output frames in one pass, which the paper gives as the reason it avoids the cumulative error of step-by-step recurrent predictors.
  • Combining perceptual loss with MSE should keep thin neurite structures visually coherent, which pure pixel-wise loss tends to blur.

Reading between the lines

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

  • A fairer test would restrict the error metric to pixels within a few micrometers of a neurite; because neurites occupy a small fraction of the frame, whole-frame MRE can stay low even if the model only predicts a static background.
  • The paper trains synthetic and experimental data separately; a direct next step would be to pretrain on synthetic and fine-tune on experimental, which the paper describes as ideal but does not demonstrate.
  • The known failure mode of missing neurons that enter the frame suggests an object-centric or detection-augmented variant could improve generalization beyond the current convolutional attention.
  • The gSTA's convolutional inductive bias handles small translations but not the large translations, scaling, and deformations in experimental videos, so an explicit registration or alignment preprocessing step is a testable extension.
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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 a digital twin framework for predicting neurite deterioration by combining an IGA-based phase field synthetic data generator, experimental neuron culture videos, and a MetaFormer-based gated spatiotemporal attention (gSTA) video prediction model adapted from SimVP/OpenSTL. The model takes 10 input frames and predicts the next 20 frames of neurite deterioration, trained separately on synthetic and experimental datasets with a combined MSE and VGG16 perceptual loss. The central quantitative claims are average errors of 1.9641% for synthetic and 6.0339% for experimental predictions, with inference at a fraction of a second. The paper also documents qualitative results on single- and multi-neuron synthetic cases and on experimental cases including soma shrinkage and neurite degeneration, while acknowledging limitations such as unpredictable neuron entry and the lack of a unified synthetic-experimental training pipeline.

Significance. If the reported accuracy is validated, this work would be a useful contribution at the intersection of computational biomechanics and machine learning, providing a plausible high-throughput pipeline for generating synthetic neurite deterioration data and predicting future morphological changes. The paper has several concrete strengths: the IGA-based phase field model is grounded in prior work and presented with explicit governing equations; the architectural details (encoder, MetaFormer layers, decoder dimensions, gSTA equations) are specified; the loss function in Eq. (10) is defined with its perceptual-weight parameter; the code and datasets are made available with a DOI; and the authors identify important limitations, including the separation of synthetic and experimental training and the questionable transferability of ImageNet-based perceptual features. These strengths make the paper a reasonable basis for further work, provided the evaluation metrics and experimental protocol are made rigorous enough to support the headline error numbers.

major comments (4)
  1. [Abstract, Sections 5.1 and 5.3] The mean relative error (MRE) is never defined with a formula. Section 5.1 states that "Mean Relative Error (MRE) values quantified for keyframes" and cites [27,23], but no definition or formula appears in the manuscript. This is a load-bearing issue because the paper's entire quantitative claim (1.9641% synthetic, 6.0339% experimental) rests on MRE. Neurites occupy only a small fraction of each 256x256 frame, so if MRE is computed over all pixels, a model that predicts near-static backgrounds could achieve low MRE while failing to predict retraction, atrophy, and fragmentation. The authors should define MRE precisely, report a foreground-only metric (e.g., error restricted to neurite masks or morphological distance), and compare against simple baselines such as repeating the last input frame.
  2. [Section 4.1 and Section 5, first paragraph] The data split is not specified as being performed before or after the 4x4 patchification described in Section 4.1. The experimental dataset consists of 10 videos, each segmented into nine samples, and each 30-frame sample is divided into sixteen 256x256 sections. If the 70/15/15 split is applied to these patches rather than to whole videos or whole samples, adjacent patches from the same culture share background and neurite content, causing train/test leakage and inflating the reported accuracy. The authors must state explicitly that the split is at the video level (or sample level, before patchification) for the experimental data and at the simulation-case level for the synthetic data, and they should report results separately for each split type if both are used.
  3. [Sections 4.3 and 5] No baseline comparison is reported. The paper claims that the MetaFormer gSTA architecture outperforms the prior CNN-based surrogate model [27] and that it captures long-range temporal dependencies better than convolutional recurrent methods, but Section 5 provides no quantitative comparison against [27], ConvLSTM, SimVP variants, or even trivial baselines. Without such comparisons, the headline MRE values cannot be interpreted: a low MRE on a sparse-background video prediction task may simply reflect the difficulty of the metric rather than the quality of the model. I request a table comparing the proposed model against at least the prior CNN [27], a frame-repetition baseline, and one standard video prediction baseline on the same data splits and with the same metric.
  4. [Sections 2, 3, and 5.3] The synthetic-to-synthetic evaluation is partly a self-consistency check of the authors' own IGA phase field simulator, and the paper does not demonstrate that the simulator's outputs match real neurite morphometrics. The synthetic test set is generated by the same code that generated the training set, and Section 5.3 explicitly states that the current framework handles synthetic and experimental datasets separately, with no transfer learning or fine-tuning. Therefore, the abstract's claim that the framework "seamlessly integrates simulations, experiments, and ML" is not supported by the experiments as reported. The authors should either add a synthetic-to-experimental transfer experiment (pre-train on synthetic, fine-tune on real images) or temper the integration claim and present the two tracks as separate validation studies.
minor comments (5)
  1. [Figure 3 caption] The caption says "Depth-wise convolution convolution" and appears to have a duplicated word; it should be "Depth-wise convolution."
  2. [Section 5.3] The text says "the sudden entrance of another neuron highlighted by the magenta dashed circles in Figure 6," but Figure 6's caption and the corresponding description in Section 5.2 use red dashed circles. This color inconsistency should be corrected.
  3. [Figure 8 and Section 5.3] The maximum experimental error is reported as approximately 24%, while the average is 6.0339%; the paper does not explain the distribution or the outliers. Reporting the median, quartiles, or error bars across the test samples would help readers assess whether the average is representative.
  4. [Section 4.1] The experimental dataset is described as "10 neuron culture videos, each approximately 11 seconds long at 25 frames per second, segmented into nine sequential segments." It would be helpful to state the original video dimensions and how the 4x4 split interacts with the frame size, since the patch size must be exactly 256x256 everywhere.
  5. [Section 5.3] The discussion of why synthetic and experimental data are processed separately is informative, but it also reveals that the claimed "digital twin" integration is currently only a future goal. The authors should either present the separate processing as an explicit limitation in the abstract or remove the word "seamlessly" from the abstract's integration claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the experimental results are independent held-out validation, and synthetic self-consistency is not presented as a derivation from the ML losses.

full rationale

The paper's central numerical claims (1.9641% synthetic and 6.0339% experimental MRE) come from evaluating a MetaFormer/gSTA model on held-out test splits (Section 5), not from fitting parameters to the test data and re-reporting them. The ML loss (Eq. 10) is a standard MSE plus VGG16 perceptual loss and is not derived from the reported error metric; MRE is not even defined in the manuscript, which is a reporting gap but not a circular reduction. Synthetic training data are generated by the authors' earlier IGA phase-field model [31], so synthetic-to-synthetic agreement is partly a self-consistency check of that simulator; however, the paper also evaluates on real neuron-culture videos in Section 5.2, which provides independent evidence not entailed by the simulator. Citations to prior work [27, 31, 45, 66] are legitimate reuse of computational models and architecture, not an imported uniqueness theorem that forces the conclusion. No equation or construction in the paper equates a fitted quantity with the quantity it claims to predict, and no prediction is shown to be the definitional output of its own input. The main weaknesses are undefined MRE, absence of baseline comparisons, and possible patch-level data leakage, all of which are correctness and reporting concerns rather than circularity.

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

The reported accuracy rests on parameters inherited from earlier IGA phase-field work, on hand-chosen ML hyperparameters, and on domain assumptions about simulation realism, the error metric, and dataset splitting. No new physical entities are introduced. The ledger shows that the novel contribution is mostly application and data engineering rather than new theory; several assumptions are acknowledged in the paper's Section 5.3 limitations.

free parameters (3)
  • Perceptual loss weight lambda (Eq. 10) = not reported
    The combined loss's weight lambda controls the balance between MSE and VGG16 perceptual loss; its value affects all reported error numbers but is never stated.
  • Model hyperparameters = hidS=64, hidT=256, Ns=4, Nt=16, lr=0.001, batch size=16
    Chosen by hand from prior configurations; no sensitivity analysis or ablation is reported, and the central accuracy claim depends on them.
  • Synthetic data generation parameters inherited from IGA phase-field model = not re-calibrated here
    The realism of the synthetic dataset rests on parameters from earlier work, such as the copti time profile, mobility, and anisotropy; they are inputs for this paper but are not validated against experimental neurite morphometrics here.
assumptions (5)
  • domain assumption The IGA-based phase field model generates deterioration patterns that are representative of real neurite deterioration in neurodevelopmental disorders.
    Invoked in Sections 2, 3, and 4.1 as the foundation of the synthetic dataset; if the simulation morphology is unrealistic, the low synthetic error says little about biology.
  • domain assumption Pixel-level mean relative error is an adequate measure of neurite morphology prediction quality.
    MRE is used in Sections 5.1 to 5.3 with no formula or segmentation-based metric; because neurites occupy few pixels, low MRE can coexist with poor structural prediction.
  • domain assumption The 2D time-lapse microscope frames capture neurite deterioration rather than imaging artifacts, translation, scaling, and unintended cell entry.
    The paper lists these confounds in Section 5.3 and Figure 6; the model's experimental accuracy depends on how much of the image change is true biological deterioration.
  • domain assumption The 70/15/15 split avoids leakage between training and test patches from the same culture video.
    Section 5 says only that the dataset is divided into three subsets; if the split is at the 256x256 patch level rather than the video level, adjacent spatial or temporal patches from the same video can appear in both training and test.
  • domain assumption ImageNet-pretrained VGG16 features are a useful perceptual loss for neurite images.
    The paper acknowledges in Section 6 that VGG16 is pretrained on ImageNet and may not align with neuron image features, yet it uses this loss for the reported results.

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Cite this review

Pith. "Pith review of High-throughput digital twin framework for predicting neurite deterioration using MetaFormer attention." pith.science (2026). https://pith.science/paper/W2TMWQBO

@misc{pith2026250108334,
  author       = {Pith},
  title        = {Pith review of: High-throughput digital twin framework for predicting neurite deterioration using MetaFormer attention},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W2TMWQBO}},
  note         = {Machine review of arXiv:2501.08334}
}
read the original abstract

Neurodevelopmental disorders (NDDs) cover a variety of conditions, including autism spectrum disorder, attention-deficit/hyperactivity disorder, and epilepsy, which impair the central and peripheral nervous systems. Their high comorbidity and complex etiologies present significant challenges for accurate diagnosis and effective treatments. Conventional clinical and experimental studies are time-intensive, burdening research progress considerably. This paper introduces a high-throughput digital twin framework for modeling neurite deteriorations associated with NDDs, integrating synthetic data generation, experimental images, and machine learning (ML) models. The synthetic data generator utilizes an isogeometric analysis (IGA)-based phase field model to capture diverse neurite deterioration patterns such as neurite retraction, atrophy, and fragmentation while mitigating the limitations of scarce experimental data. The ML model utilizes MetaFormer-based gated spatiotemporal attention architecture with deep temporal layers and provides fast predictions. The framework effectively captures long-range temporal dependencies and intricate morphological transformations with average errors of 1.9641% and 6.0339% for synthetic and experimental neurite deterioration, respectively. Seamlessly integrating simulations, experiments, and ML, the digital twin framework can guide researchers to make informed experimental decisions by predicting potential experimental outcomes, significantly reducing costs and saving valuable time. It can also advance our understanding of neurite deterioration and provide a scalable solution for exploring complex neurological mechanisms, contributing to the development of targeted treatments.

Figures

Figures reproduced from arXiv: 2501.08334 by the authors.

Figure 1
Figure 1. Overview of the proposed digital twin framework for predicting neurite deterioration. The framework combines an IGA-based synthetic [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. MetaFormer-based architecture overview. The proposed model predicts future neurite growth frames from input sequences via a spatial [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. gSTA for learning temporal characteristics [66]. (A) Depth-wise convolution convolution to collect information from the local reception [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: (A&B) Prediction for single and 2-neuron synthetic neurite deterioration. The input sequence (top row) consists of frames from time steps [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: (A&B) Prediction for 3-neuron synthetic neurite deterioration. The layout follows the same structure as Figure 4. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: (A&B): Predictions of experimental neurite transformations using a model trained on the experimental dataset. The layout follows the [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: (A&B) Prediction for neurite shrinking and deterioration given experimental input. The layout follows the same structure as Figure 4. [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: Comparison of error plots for (A) synthetic and (B) experimental datasets predictions. [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

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Reference graph

Works this paper leans on

78 extracted references · 63 canonical work pages

  1. [27]

    K. Qian, A. S. Liao, S. Gu, V . A. Webster-Wood, Y . J. Zhang, Biomimetic IGA neuron growth modeling with neurite morphometric features and CNN-based prediction, Computer Methods in Applied Mechanics and Engineering 417 (2023) 116213

  2. [1]

    Thapar, M

    A. Thapar, M. Cooper, M. Rutter, Neurodevelopmental disorders, The Lancet Psychiatry 4 (4) (2017) 339–346

  3. [2]

    Straub, B

    L. Straub, B. T. Bateman, S. Hernandez-Diaz, C. York, B. Lester, K. L. Wisner, C. J. McDougle, P. B. Pennell, K. J. Gray, Y . Zhu, et al., Neurodevelopmental disorders among publicly or privately insured children in the United States, JAMA Psychiatry 79 (3) (2022) 232–242

  4. [3]

    D. J. Morris-Rosendahl, M.-A. Crocq, Neurodevelopmental disorders–the history and future of a diagnostic concept, Dialogues in Clinical Neuroscience 22 (1) (2020) 65–72

  5. [4]

    D’Souza, A

    H. D’Souza, A. Karmilo ff-Smith, Neurodevelopmental disorders, Wiley Interdisciplinary Reviews: Cognitive Science 8 (1-2) (2017) e1398

  6. [5]

    Kawatani, G

    K. Kawatani, G. O. Suarez, R. B. Perkerson, E. E. Parent, T. Nambara, J. A. Knight, T. M. Parsons, K. Gupta, F. Shue, A. Alnobani, et al., Human iPSC-derived MSCs induce neurotrophic e ffects and improve metabolic activity in acute neuronal injury models, Journal of Neuroscience (2024)

  7. [6]

    Khodosevich, C

    K. Khodosevich, C. M. Sellgren, Neurodevelopmental disorders-high-resolution rethinking of disease modeling, Molecular Psychiatry 28 (1) (2023) 34–43

  8. [7]

    T. Copf, Impairments in dendrite morphogenesis as etiology for neurodevelopmental disorders and implications for therapeutic treatments, Neuroscience & Biobehavioral Reviews 68 (2016) 946–978

Show all 78 references
  1. [8]

    L. H. Myers, Morphological variants in neurodevelopmental disorders, Karolinska Institutet, Stockholm, Sweden, 2019

  2. [9]

    A. S. Liao, W. Cui, Y . J. Zhang, V . A. Webster-Wood, Semi-automated quantitative evaluation of neuron developmental morphologyin vitro using the change-point test, Neuroinformatics 21 (1) (2023) 163–176

  3. [10]

    A. S. Liao, V . Webster-Wood, Y . Zhang, Quantification of neuron morphological development using the change-point test, in: Summer Biomechanics, Bioengineering and Biotransport Conference, 2021

  4. [11]

    Isomura, K

    T. Isomura, K. Kotani, Y . Jimbo, K. J. Friston, Experimental validation of the free-energy principle with in vitro neural networks, Nature Communications 14 (1) (2023) 4547

  5. [12]

    Soriano, Neuronal cultures: exploring biophysics, complex systems, and medicine in a dish, Biophysica 3 (1) (2023) 181–202

    J. Soriano, Neuronal cultures: exploring biophysics, complex systems, and medicine in a dish, Biophysica 3 (1) (2023) 181–202

  6. [13]

    H. G. E. Hentschel, A. Fine, Instabilities in cellular dendritic morphogenesis, Physical Review Letters 73 (1994) 3592–3595

  7. [14]

    J. K. Krottje, A. Van Ooyen, A mathematical framework for modeling axon guidance, Bulletin of Mathematical Biology 69 (2007) 3–31

  8. [15]

    Y . E. Pearson, E. Castronovo, T. A. Lindsley, D. A. Drew, Mathematical modeling of axonal formation Part I: geometry, Bulletin of Mathe- matical Biology 73 (2011) 2837–2864

  9. [16]

    Aeschlimann, L

    M. Aeschlimann, L. Tettoni, Biophysical model of axonal pathfinding, Neurocomputing 38-40 (2001) 87–92. 15

  10. [17]

    Cuntz, F

    H. Cuntz, F. Forstner, A. Borst, M. H ¨ausser, One rule to grow them all: a general theory of neuronal branching and its practical application, PLoS Computational Biology 6 (8) (2010) e1000877

  11. [18]

    Torben-Nielsen, E

    B. Torben-Nielsen, E. De Schutter, Context-aware modeling of neuronal morphologies, Frontiers in Neuroanatomy 8 (2014) 92

  12. [19]

    J. P. Eberhard, A. Wanner, G. Wittum, NeuGen: a tool for the generation of realistic morphology of cortical neurons and neural networks in 3D, Neurocomputing 70 (1-3) (2006) 327–342

  13. [20]

    van Ooyen, A

    A. van Ooyen, A. Carnell, S. de Ridder, B. Tarigan, H. D. Mansvelder, F. Bijma, M. de Gunst, J. van Pelt, Independently outgrowing neurons and geometry-based synapse formation produce networks with realistic synaptic connectivity, PLOS ONE 9 (1) (2014) e85858

  14. [21]

    A. Li, A. Barati Farimani, Y . J. Zhang, Deep learning of material transport in complex neurite networks, Scientific Reports 11 (2021) 11280

  15. [22]

    A. Li, Y . J. Zhang, Modeling intracellular transport and traffic jam in 3D neurons using PDE-constrained optimization, Journal of Mechanics 38 (2022) 44–59

  16. [23]

    A. Li, Y . J. Zhang, Isogeometric analysis-based physics-informed graph neural network for studying traffic jam in neurons, Computer Methods in Applied Mechanics and Engineering 403 (2023) 115757

  17. [24]

    A. Li, Y . J. Zhang, Modeling material transport regulation and traffic jam in neurons using PDE-constrained optimization, Scientific Reports 12 (1) (2022) 3902

  18. [25]

    Takaki, K

    T. Takaki, K. Nakagawa, Y . Morita, E. Nakamachi, Phase-field modeling for axonal extension of nerve cells, Mechanical Engineering Journal 2 (3) (2015) 15–00063

  19. [26]

    K. Qian, A. Pawar, A. S. Liao, C. Anitescu, V . A. Webster-Wood, A. W. Feinberg, T. Rabczuk, Y . J. Zhang, Modeling neuron growth using isogeometric collocation based phase field method, Scientific Reports 12 (2022) 8120

  20. [28]

    Y . J. Zhang, Challenges and advances in image-based geometric modeling and mesh generation, in: Image-Based Geometric Modeling and Mesh Generation, Springer, Dordrecht, Netherlands, 2013

  21. [29]

    Y . J. Zhang, Geometric Modeling and Mesh Generation from Scanned Images, Chapman and Hall/CRC, New York, US, 2016

  22. [30]

    Zhang, Y

    Y . Zhang, Y . Bazilevs, S. Goswami, C. L. Bajaj, T. J. Hughes, Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow, Computer Methods in Applied Mechanics and Engineering 196 (29-30) (2007) 2943–2959

  23. [31]

    K. Qian, G. O. Suarez, T. Nambara, T. Kanekiyo, A. S. Liao, V . A. Webster-Wood, Y . J. Zhang, Neurodevelopmental disorders modeling using isogeometric analysis, dynamic domain expansion and local refinement, Computer Methods in Applied Mechanics and Engineering 433 (2025) 117534

  24. [32]

    Singh, E

    M. Singh, E. Fuenmayor, E. P. Hinchy, Y . Qiao, N. Murray, D. Devine, Digital twin: origin to future, Applied System Innovation 4 (2) (2021) 36

  25. [33]

    Jones, C

    D. Jones, C. Snider, A. Nassehi, J. Yon, B. Hicks, Characterising the digital twin: a systematic literature review, CIRP Journal of Manufac- turing Science and Technology 29 (2020) 36–52

  26. [34]

    F. Tao, H. Zhang, A. Liu, A. Y . Nee, Digital twin in industry: state-of-the-art, IEEE Transactions on Industrial Informatics 15 (4) (2018) 2405–2415

  27. [35]

    M. Liu, S. Fang, H. Dong, C. Xu, Review of digital twin about concepts, technologies, and industrial applications, Journal of Manufacturing Systems 58 (2021) 346–361

  28. [36]

    M. M. Rathore, S. A. Shah, D. Shukla, E. Bentafat, S. Bakiras, The role of AI, machine learning, and big data in digital twinning: a systematic literature review, challenges, and opportunities, IEEE Access 9 (2021) 32030–32052

  29. [37]

    Oprea, P

    S. Oprea, P. Martinez-Gonzalez, A. Garcia-Garcia, J. A. Castro-Vargas, S. Orts-Escolano, J. Garcia-Rodriguez, A. Argyros, A review on deep learning techniques for video prediction, IEEE Transactions on Pattern Analysis and Machine Intelligence 44 (6) (2020) 2806–2826

  30. [38]

    W. Yan, Y . Zhang, P. Abbeel, A. Srinivas, VideoGPT: video generation using VQ-V AE and transformers, arXiv Preprint arXiv:2104.10157 (2021)

  31. [39]

    Neimark, O

    D. Neimark, O. Bar, M. Zohar, D. Asselmann, Video transformer network, in: Proceedings of the IEEE /CVF International Conference on Computer Vision, 2021, pp. 3163–3172

  32. [40]

    Ye, G.-A

    X. Ye, G.-A. Bilodeau, Video prediction by e fficient transformers, Image and Vision Computing 130 (2023) 104612

  33. [41]

    Y . Tang, L. Qi, F. Xie, X. Li, C. Ma, M.-H. Yang, PredFormer: transformers are effective spatial-temporal predictive learners, arXiv Preprint arXiv:2410.04733 (2024)

  34. [42]

    W. Yu, M. Luo, P. Zhou, C. Si, Y . Zhou, X. Wang, J. Feng, S. Yan, Metaformer is actually what you need for vision, in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022, pp. 10819–10829

  35. [43]

    C. Tan, S. Li, Z. Gao, W. Guan, Z. Wang, Z. Liu, L. Wu, S. Z. Li, OpenSTL: a comprehensive benchmark of spatio-temporal predictive learning, Advances in Neural Information Processing Systems 36 (2023) 69819–69831

  36. [44]

    Simonyan, A

    K. Simonyan, A. Zisserman, Very deep convolutional networks for large-scale image recognition, arXiv Preprint arXiv:1409.1556 (2014)

  37. [45]

    Z. Gao, C. Tan, L. Wu, S. Z. Li, SimVP: simpler yet better video prediction, in: Proceedings of the IEEE /CVF Conference on Computer Vision and Pattern Recognition, 2022, pp. 3170–3180

  38. [46]

    Gomez, A

    H. Gomez, A. Reali, G. Sangalli, Accurate, e fficient, and (iso) geometrically flexible collocation methods for phase-field models, Journal of Computational Physics 262 (2014) 153–171

  39. [47]

    Schillinger, M

    D. Schillinger, M. J. Borden, H. K. Stolarski, Isogeometric collocation for phase-field fracture models, Computer Methods in Applied Mechanics and Engineering 284 (2015) 583–610

  40. [48]

    T. J. Hughes, J. A. Cottrell, Y . Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering 194 (39-41) (2005) 4135–4195

  41. [49]

    Takaki, Phase-field modeling and simulations of dendrite growth, ISIJ International 54 (2) (2014) 437–444

    T. Takaki, Phase-field modeling and simulations of dendrite growth, ISIJ International 54 (2) (2014) 437–444

  42. [50]

    D. R. McLean, B. P. Graham, Mathematical formulation and analysis of a continuum model for tubulin-driven neurite elongation, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 460 (2048) (2004) 2437–2456

  43. [51]

    D. R. McLean, A. van Ooyen, B. P. Graham, Continuum model for tubulin-driven neurite elongation, Neurocomputing 58 (2004) 511–516

  44. [52]

    van Ooyen, B

    A. van Ooyen, B. P. Graham, G. J. A. Ramakers, Competition for tubulin between growing neurites during development, Neurocomputing 16 38-40 (2001) 73–78

  45. [53]

    K. T. Nella, B. M. Norton, H.-T. Chang, R. A. Heuer, C. B. Roque, A. J. Matsuoka, Bridging the electrode–neuron gap: finite element modeling of in vitro neurotrophin gradients to optimize neuroelectronic interfaces in the inner ear, Acta Biomaterialia 151 (2022) 360–378

  46. [54]

    C. E. Krewson, W. M. Saltzman, Transport and elimination of recombinant human NGF during long-term delivery to the brain, Brain Research 727 (1-2) (1996) 169–181

  47. [55]

    X. Wei, Y . J. Zhang, L. Liu, T. J. Hughes, Truncated T-splines: fundamentals and methods, Computer Methods in Applied Mechanics and Engineering 316 (2017) 349–372

  48. [56]

    L. Liu, Y . J. Zhang, X. Wei, NURBS surface reparameterization using truncated T-splines, in: 23rd International Meshing Roundtable. London, UK. Oct. 12-15, 2014

  49. [57]

    Piegl, W

    L. Piegl, W. Tiller, The NURBS Book, Springer Science & Business Media, Dordrecht, Netherlands, 2012

  50. [58]

    X. Wei, Y . Zhang, T. J. Hughes, M. A. Scott, Truncated hierarchical Catmull-Clark subdivision with local refinement, Computer Methods in Applied Mechanics and Engineering 291 (2015) 1–20

  51. [59]

    X. Wei, Y . J. Zhang, T. J. Hughes, M. A. Scott, Extended truncated hierarchical Catmull-Clark subdivision, Computer Methods in Applied Mechanics and Engineering 299 (2016) 316–336

  52. [60]

    X. Wei, X. Li, K. Qian, T. J. Hughes, Y . J. Zhang, H. Casquero, Analysis-suitable unstructured T-splines: multiple extraordinary points per face, Computer Methods in Applied Mechanics and Engineering 391 (2022) 114494

  53. [61]

    Balay, S

    S. Balay, S. Abhyankar, M. F. Adams, S. Benson, J. Brown, P. Brune, K. Buschelman, E. Constantinescu, L. Dalcin, A. Dener, V . Eijkhout, J. Faibussowitsch, W. D. Gropp, V . Hapla, T. Isaac, P. Jolivet, D. Karpeev, D. Kaushik, M. G. Knepley, F. Kong, S. Kruger, D. A. May, L. C....

  54. [62]

    Zhang, J

    J. Zhang, J. Brown, S. Balay, J. Faibussowitsch, M. Knepley, O. Marin, R. T. Mills, T. Munson, B. F. Smith, S. Zampini, The PetscSF scalable communication layer, IEEE Transactions on Parallel and Distributed Systems 33 (4) (2022) 842–853

  55. [63]

    Karypis, V

    G. Karypis, V . Kumar, A fast and high quality multilevel scheme for partitioning irregular graphs, SIAM Journal on Scientific Computing 20 (1) (1998) 359–392

  56. [64]

    A. Li, R. Chen, A. B. Farimani, Y . J. Zhang, Reaction diffusion system prediction based on convolutional neural network, Scientific Reports 10 (2020) 3894

  57. [65]

    X. Shi, Z. Chen, H. Wang, D.-Y . Yeung, W.-K. Wong, W.-C. Woo, Convolutional LSTM network: a machine learning approach for precipi- tation nowcasting, Advances in Neural Information Processing systems 28 (2015)

  58. [66]

    C. Tan, Z. Gao, S. Li, S. Z. Li, SimVP: towards simple yet powerful spatiotemporal predictive learning, arXiv Preprint arXiv:2211.12509 (2022)

  59. [67]

    J. L. Bentley, Multidimensional binary search trees used for associative searching, Communications of the ACM 18 (9) (1975) 509–517

  60. [68]

    J. Zhao, M. D. Davis, Y . A. Martens, M. Shinohara, N. R. Gra ff-Radford, S. G. Younkin, Z. K. Wszolek, T. Kanekiyo, G. Bu, APOE ε4/ε4 diminishes neurotrophic function of human iPSC-derived astrocytes, Human Molecular Genetics 26 (14) (2017) 2690–2700

  61. [69]

    Kawatani, M.-L

    K. Kawatani, M.-L. Holm, S. C. Starling, Y . A. Martens, J. Zhao, W. Lu, Y . Ren, Z. Li, P. Jiang, Y . Jiang, et al., Abca7 deficiency causes neuronal dysregulation by altering mitochondrial lipid metabolism, Molecular Psychiatry (2023) 1–11

  62. [70]

    Elfwing, E

    S. Elfwing, E. Uchibe, K. Doya, Sigmoid-weighted linear units for neural network function approximation in reinforcement learning, Neural Networks 107 (2018) 3–11

  63. [71]

    Nwankpa, W

    C. Nwankpa, W. Ijomah, A. Gachagan, S. Marshall, Activation functions: comparison of trends in practice and research for deep learning, arXiv Preprint arXiv:1811.03378 (2018)

  64. [72]

    W. Shi, J. Caballero, F. Husz ´ar, J. Totz, A. P. Aitken, R. Bishop, D. Rueckert, Z. Wang, Real-time single image and video super-resolution us- ing an efficient sub-pixel convolutional neural network, in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recog...

  65. [73]

    Vaswani, Attention is all you need, Advances in Neural Information Processing Systems (2017)

    A. Vaswani, Attention is all you need, Advances in Neural Information Processing Systems (2017)

  66. [74]

    Hendrycks, K

    D. Hendrycks, K. Gimpel, Gaussian error linear units (GELUs), arXiv Preprint arXiv:1606.08415 (2016)

  67. [75]

    Wilkins-Diehr, S

    N. Wilkins-Diehr, S. Sanielevici, J. Alameda, J. Cazes, L. Crosby, M. Pierce, R. Roskies, An overview of the XSEDE extended collaborative support program, in: High Performance Computer Applications - 6th International Conference, ISUM 2015, V ol. 595 of Communications in Compu...

  68. [76]

    Towns, T

    J. Towns, T. Cockerill, M. Dahan, I. Foster, K. Gaither, A. Grimshaw, V . Hazlewood, S. Lathrop, D. Lifka, G. D. Peterson, R. Roskies, J. R. Scott, N. Wilkins-Diehr, XSEDE: accelerating scientific discovery, Computing in Science & Engineering 16 (5) (2014) 62–74

  69. [77]

    Weiss, T

    K. Weiss, T. M. Khoshgoftaar, D. Wang, A survey of transfer learning, Journal of Big Data 3 (2016) 1–40

  70. [78]

    Y . Wang, Q. Yao, J. T. Kwok, L. M. Ni, Generalizing from a few examples: a survey on few-shot learning, ACM Computing Surveys (CSUR) 53 (3) (2020) 1–34. 17

Pith tools

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