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REVIEW 3 major objections 5 minor 49 references

A joint voxel flow-phase field framework for ultra-long microstructure evolution prediction with physical regularization

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Coupling a voxel-flow video predictor with short phase-field simulations extends reliable microstructure forecasts from 2 to 82 frames, keeping normalized average-grain-area error at 1.64%.

desk verdict A hybrid VFN+PF acceleration scheme with a plausible core but an overstated image-data interface claim that needs testing. read the letter →

arxiv 2601.04898 v2 pith:UTX6BNHE submitted 2026-01-08 physics.comp-ph cond-mat.mtrl-sci

Ao Zhou , Salma Zahran , Chi Chen , Zhengyang Zhang , Yanming Wang This is my paper
classification physics.comp-phcond-mat.mtrl-sci
keywords phase-fieldmodelingvoxelflownetworkvideopredictiongraingrowthspinodaldecompositionphysicalregularizationmicrostructureevolutionmachinelearningacceleration
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 claims that a fast, image-only video prediction network—trained to warp two consecutive snapshots into the next frame—can be turned into a reliable ultra-long-horizon microstructure forecaster by periodically inserting short phase-field simulations that reset accumulated error. The central demonstration is a grain-growth run that starts from two images of a 600-grain microstructure and predicts 82 frames (82,000 phase-field time steps) while the grain count falls to 29; the normalized mean-square error of the average grain area over the whole run is 1.64%. The same architecture also predicts 18 frames of spinodal decomposition with 3.79% MSE and captures the characteristic coarsening wavelength. The practical stakes are speed and flexibility: the authors report roughly 10^2–10^3× faster predictions than full phase-field simulation, and the image-based interface means no governing PDEs need to be specified in advance. If correct, this is a path from raw image sequences—simulation or experimental—to long-time materials forecasting.

What carries the argument

The voxel flow network (VFN)—a nine-block, multi-scale optical-flow predictor that estimates backward per-pixel motion between two input frames and a learned blending mask, then warps the inputs to synthesize the next frame. The forward–reverse colormap mapping is the bridge that bijectively links turbo-colormap RGB pixels to phase-field order-parameter values, letting predicted images become initial conditions for the phase-field solver and letting simulation output become images again. The alternating schedule itself—10–18 VFN steps followed by a two-frame phase-field burst—acts as the physical regularizer and is what the paper calls the 'error reset.'

What would settle it

Count the distinct RGB triples among grain interiors in a predicted frame of the 600-grain test and compare with the 600 grain labels; if the number of distinct colors is less than the number of grains, or if a pixel-by-pixel nearest-color lookup against the turbo colormap assigns any interior pixel to the wrong grain index, the reconstructed phase-field state fed into the corrective phase-field run is corrupted and the claimed NMSE does not measure physical state. That check can be done offline from the stored predictions.

Watch

Extended reading notes

Core claim

Autoregressive video prediction can track phase-field evolution over long horizons if the learned predictor is periodically handed back to the physics: after every 10–18 voxel-flow predictions, the predicted image is converted into phase-field variables and used to initialize a short phase-field simulation, whose last two frames restart the network. On the 82-frame/600-grain grain-growth test this alternating scheme holds the normalized error of the average grain area to 1.64% even as grain count drops from 600 to 29, and it cuts error roughly threefold on a 38-frame test versus the network alone (MSE 9.32% vs 31.89%). The inserted simulations act as physical regularization that suppresses n

Load-bearing premise

The load-bearing premise is that the reverse colormap lookup is a faithful bijection between RGB colors and grain identities, so a predicted image can be converted back into a physically valid phase-field state; if two grains receive similar colors and the nearest-color match confuses them, the 'error reset' is fed a nonphysical state and the reported 1.64% error is not measuring the true microstructure.

Editorial extensions

If this is right

  • Ultra-long microstructure forecasting becomes feasible from image data alone: two snapshots in, no PDEs, no hand-specified physical model.
  • The error-reset schedule turns any autoregressive video model into a long-horizon emulator, with the phase-field insertion interval as a controllable speed–accuracy knob.
  • Because grains keep their color/identity through the mapping, quantitative post-processing (grain counts, area distributions, characteristic length) can be applied directly to predictions.
  • The method generalizes across at least two physically distinct phase-field models using the same network architecture and training procedure.
  • A joint run at 82,000 phase-field steps costs roughly 14.6% of a full simulation, making long coarsening studies practical at large scale.

Reading between the lines

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

  • Editorial inference: the 'error reset' idea is not specific to phase fields; any dissipative PDE with a cheap accurate solver could be interleaved with a learned fast predictor to bound trajectory drift, so the scheme may transfer to fluid or climate emulators.
  • Editorial inference: the colormap interface is the fragile link; real experimental images (EBSD/SEM) do not carry clean grain-identity labels, so applying the method to experiment would require an additional segmentation/registration step that the current benchmark does not test.
  • Editorial inference: the reported NMSE is on the average grain area, a coarsened statistic; a per-grain identity-tracking metric would be a sharper test and might degrade faster than the average-area error suggests.
  • Editorial inference: since error growth slows as grains coarsen, the optimal phase-field insertion frequency likely scales with interface density; an adaptive scheduler using predicted boundary content could cut the 14.6% cost further.
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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

3 major / 5 minor

Summary. The paper proposes a joint prediction framework that alternates a voxel-flow network (VFN) with short, periodically inserted phase-field (PF) simulations. The VFN predicts the next microstructure image from two previous images using learned optical flow and a blending mask; PF insertions are used to reset accumulated error. The method is demonstrated on two PF models: grain growth (multi-order-parameter Allen–Cahn) and spinodal decomposition (Cahn–Hilliard). Reported results include 18-frame predictions with 6.76% pixel-mismatch and SSIM 0.911 for grain growth, and an 82-frame joint prediction for a 600-grain initial state with NMSE of average grain area of 1.64%. The authors also report computational speedups of 10^2–10^3 relative to full PF simulation.

Significance. If the central claim is valid, the framework offers a practical means of extending machine-learning-based microstructure prediction to time horizons that pure video-prediction models cannot reach, by periodically re-anchoring the prediction with a physics simulator. The paper is honest in several respects: the comparison with ConvLSTM and SimVP uses a deliberately harder input–output setting for VFN, and the visualization of learned flow fields and masks gives useful interpretability. The main contribution is therefore a hybrid surrogate scheme rather than a new physical model. However, the credibility of the 'physical regularization' claim rests entirely on the faithfulness of the image–data mapping used to reconstruct PF states from predicted images, and that mapping is not adequately validated.

major comments (3)
  1. [§2.1, Fig. 1(d)] The paper claims a 'bijective correspondence' between images and phase-field data. For grain growth, the reverse mapping recovers only a discrete grain index per pixel (0 for boundary, 1..N_g for grains). The continuous order parameters η_i, including interface widths and multi-order-parameter overlaps, are discarded. Initializing the PF solver from a binarized label field is nonphysical. No experiment compares PF evolution from the true continuous state vs the reconstructed label state over the same 2,000-step PF segment. This is load-bearing because the PF insertion is the mechanism described as 'physical regularization.' Please provide such a test, or revise the claim to describe the insertion as a label-map smoothing/denoising step rather than a physically consistent correction.
  2. [§3.1.1, Eqs. (5)–(6)] The quantity called MSE is actually a pixel-wise misclassification rate (δ_ij), i.e., a 0–1 loss, not a mean squared error in phase-field variables. Reporting 6.76% as 'MSE' is misleading. Similarly, the NMSE in Eq. (8) is computed on the scalar average grain area, which is insensitive to per-pixel or morphological errors and cannot by itself substantiate the claim that 'grain morphology and area distribution are well preserved.' Please report additional metrics such as per-grain area distributions, boundary-length error, or a topology metric.
  3. [§3.2.3, Fig. 6] The ultra-long 82-frame experiment appears to be a single initial condition. It is not stated how many independent validation runs are used or whether the reported NMSE is an average over runs. With one trajectory, the 1.64% figure has no uncertainty. In addition, the periodic PF insertions use the exact ground-truth simulator that generated the training data; this is a hybrid acceleration scheme, not a pure 'prediction' of unseen dynamics. The abstract and conclusion should state this explicitly and avoid implying that the method is a standalone forecaster.
minor comments (5)
  1. [Abstract/conclusion vs §3.2.2] Speedup claims are inconsistent: the abstract says 'about 1,000 times faster,' §3.2.2 says direct PF simulation is 'about 100 times slower' than a VFN sequence, and the conclusion says '10^2 to 10^3 times faster.' Please unify these numbers and define the baseline precisely.
  2. [Table 1] The table caption refers to the '20th image,' while the text in §3.1.1 and §3.1.2 reports predictions of 18 frames from 2 inputs. The MSE for VFN is listed as 6.3% in Table 1 but 6.76% in §3.1.1. Please clarify the frame indexing and reconcile the numbers.
  3. [§2.4] The spinodal decomposition model is attributed to 'A. Cahn'; the reference [6] is J.W. Cahn. Please correct.
  4. [Eq. (4)] Typo: 'the sun of them' should be 'the sum of them.'
  5. [General] No code or data availability statement is provided. For reproducibility of a deep-learning paper, providing code and trained-model weights would be valuable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the VFN is trained on PF snapshots, tested on held-out PF snapshots, and corrected by the PF simulator itself; no prediction reduces to its input by construction.

full rationale

The paper's derivation chain is an empirical surrogate-modeling pipeline, not a circular one. The VFN is trained end-to-end on phase-field simulation snapshots and validated on held-out simulations from the same physical models; this is standard supervised evaluation, not a fitted parameter being renamed as a prediction. The alternating PF corrections are produced by an independent numerical solver, and although the same solver generates the ground truth, using it as a corrector is an explicit algorithmic choice, not a hidden reuse of the target output. The image–data mapping is a preprocessing interface; even if the reverse mapping is lossy with respect to continuous order parameters, that is a validity or accuracy limitation rather than a logical reduction of the central claim to its inputs. No load-bearing self-citation chain appears: the VFN architecture is attributed to an external CVPR work [41], and comparisons use an external OpenSTL benchmark [49]. Accordingly, no step in the claimed derivation is equivalent to its own inputs by definition, and the paper should receive a no-circularity finding.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the accuracy of the PF simulators, the fidelity of the image mapping, and the representational power of voxel flow; none of these are derived, they are assumed or empirically validated on two test cases.

free parameters (1)
  • PF insertion schedule = 38-frame: 11 VFN - 2 PF - 11 VFN - 2 PF - 12 VFN; 82-frame: ~11 VFN per PF segment
    Manually chosen to balance error and runtime (Fig. 5c); reported error/cost numbers depend on this schedule.
assumptions (4)
  • domain assumption Phase-field simulations (Allen–Cahn for grain growth, Cahn–Hilliard for spinodal) are accurate ground truth
    The paper treats its own PF simulations as ground truth for training and validation; no experimental validation is provided (Sec 2.4, Sec 3).
  • ad hoc to paper The turbo-colormap mapping is bijective between grain-index matrices and RGB images
    Section 2.1 states a bijective correspondence, but no error analysis is given; with 600 grains, RGB colors are densely sampled and nearest-neighbor matching may misassign.
  • ad hoc to paper Microstructure evolution over 1,000-step intervals can be represented by two-frame optical flow with a fusion mask
    Eq. (1) assumes future frames are a mask-weighted warp of two past frames; this excludes genuine creation/destruction of structure except via the mask, which is untested for annihilation events.
  • domain assumption Snapshots at 1,000-step intervals contain sufficient temporal resolution for the network to learn dynamics
    Data are generated at this interval (Sec 2.4); if dynamics on shorter timescales matter, the network cannot see them.

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Cite this review

Pith. "Pith review of A joint voxel flow-phase field framework for ultra-long microstructure evolution prediction with physical regularization." pith.science (2026). https://pith.science/paper/UTX6BNHE

@misc{pith2026260104898,
  author       = {Pith},
  title        = {Pith review of: A joint voxel flow-phase field framework for ultra-long microstructure evolution prediction with physical regularization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UTX6BNHE}},
  note         = {Machine review of arXiv:2601.04898}
}
read the original abstract

Phase-field (PF) modeling is a powerful tool for simulating microstructure evolution. To accelerate the simulation of PF models governed by complex PDEs, machine learning methods such as PINNs and ConvLSTM have been introduced. However, current machine-learning-based approaches still suffer from limited flexibility, poor generalization, and short prediction horizons. To address these challenges, we present a joint framework that couples a voxel-flow network (VFN) with PF simulations in an alternating manner for long-horizon prediction of microstructure evolution with substantial computational acceleration. The VFN iteratively predicts future evolution by generating the next snapshot from the previous two snapshots. Periodic PF simulations suppress nonphysical artifacts, reduce accumulated error, and extend the reliable prediction horizon. The VFN was validated using a grain-growth example, and its accuracy outperforms that of similar prediction methods while preserving topological grain details. For an ultra-long grain-growth prediction of 82 frames from 2 input frames, the grain number decreases from 600 to 29 while the NMSE of the average grain area remains 1.64%. The framework also exhibits good generalizability across different PF models. Overall, this joint framework enables rapid, flexible, generalizable, and physically consistent microstructure forecasting from image-based data over ultra-long time scales.

Figures

Figures reproduced from arXiv: 2601.04898 by the authors.

Figure 1
Figure 1. Method diagram of this work. (a) Voxel flow network with padding–cropping [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Visualization of intermediate voxel flow variable values. In the predicting of [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Voxel flow network prediction results. (a) Input images, ground truth and pre [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Comparison of the 20th snapshot between different predicting methods. VFN [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]
Figure 5
Figure 5. Figure 5: Joint prediction of grain growth. (a) Comparison of phase-field ground truth (red [PITH_FULL_IMAGE:figures/full_fig_p023_5.png]
Figure 6
Figure 6. Figure 6: Long-term joint prediction for large grain microstructure. (a) Comparison of [PITH_FULL_IMAGE:figures/full_fig_p025_6.png]

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Works this paper leans on

49 extracted references · 1 linked inside Pith

  1. [1]

    Steinbach, Phase-field models in materials science, Modelling and sim- ulation in materials science and engineering 17 (7) (2009) 073001

    I. Steinbach, Phase-field models in materials science, Modelling and sim- ulation in materials science and engineering 17 (7) (2009) 073001

    2009

  2. [2]

    Hötzer, M

    J. Hötzer, M. Seiz, M. Kellner, W. Rheinheimer, B. Nestler, Phase-field simulation of solid state sintering, Acta Materialia 164 (2019) 184–195

    2019

  3. [3]

    L.-Q. Chen, W. Yang, Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: The grain-growth kinetics, Physical Review B 50 (21) (1994) 15752

    1994

  4. [4]

    L. Chen, H. W. Zhang, L. Y. Liang, Z. Liu, Y. Qi, P. Lu, J. Chen, L.-Q. Chen, Modulation of dendritic patterns during electrodeposition: A nonlinear phase-field model, Journal of Power Sources 300 (2015) 376–385

    2015

  5. [5]

    Shibuta, Y

    Y. Shibuta, Y. Okajima, T. Suzuki, Phase-field modeling for electrode- position process, Science and Technology of Advanced Materials 8 (6) (2007) 511

    2007

  6. [6]

    J. W. Cahn, On spinodal decomposition, Acta metallurgica 9 (9) (1961) 795–801

    1961

  7. [7]

    Tourret, H

    D. Tourret, H. Liu, J. LLorca, Phase-field modeling of microstructure evolution: Recent applications, perspectives and challenges, Progress in Materials Science 123 (2022) 100810

    2022

  8. [8]

    Shen, J.-J

    Z.-H. Shen, J.-J. Wang, J.-Y. Jiang, S. X. Huang, Y.-H. Lin, C.-W. Nan, L.-Q. Chen, Y. Shen, Phase-field modeling and machine learning of electric-thermal-mechanical breakdown of polymer-based dielectrics, Nature communications 10 (1) (2019) 1843

    2019

Show all 49 references
  1. [9]

    Z. Wang, W. Yang, L. Xiang, X. Wang, Y. Zhao, Y. Xiao, P. Liu, Y. Liu, M. Banu, O. Zikanov, et al., Multi-input convolutional network forultrafastsimulation offieldevolvement, Patterns3 (6)(2022)100494

    2022

  2. [10]

    Raissi, P

    M. Raissi, P. Perdikaris, G. Karniadakis, Physics-informed neural net- works: A deep learning framework for solving forward and inverse prob- lems involving nonlinear partial differential equations, Journal of Com- putational Physics 378 (2019) 686–707. 26

    2019

  3. [11]

    Lanzoni, A

    D. Lanzoni, A. Fantasia, R. Bergamaschini, O. Pierre-Louis, F. Montal- enti, Extreme time extrapolation capabilities and thermodynamic con- sistency of physics-inspired neural networks for the 3d microstructure evolution of materials via cahn–hilliard flow, Machine Learning: S...

    2024

  4. [12]

    Colby L, J

    W. Colby L, J. Zhao, Solving allen-cahn and cahn-hilliard equations using the adaptive physics informed neural networks, Communications in Computational Physics 29 (2021) 930–954

    2021

  5. [13]

    Haridasan, V

    N. Haridasan, V. S. Krishnaveni, S. Sandra, M. S. Abhijith, Physics Informed Neural Networks: Fundamentals and Application to Phase Field Models, Springer Nature Switzerland, Cham, 2025, pp. 103–153

    2025

  6. [14]

    P. Chen, B. Jiang, Physics-informed neural networks for learning allen- cahn equation using hard constraint representation, in: 2024 China Au- tomation Congress (CAC), 2024, pp. 6433–6438

    2024

  7. [15]

    N. Chen, S. Lucarini, R. Ma, A. Chen, C. Cui, Pf-pinns: Physics- informed neural networks for solving coupled allen-cahn and cahn- hilliard phase field equations, Journal of Computational Physics 529 (2025) 113843

    2025

  8. [16]

    R. Qiu, R. Huang, Y. Xiao, J. Wang, Z. Zhang, J. Yue, Z. Zeng, Y. Wang, Physics-informed neural networks for phase-field method in two-phase flow, Physics of Fluids 34 (5) (2022) 052109

    2022

  9. [17]

    Elfetni, R

    S. Elfetni, R. D. Kamachali, Pinns-mpf: A physics-informed neural net- work framework for multi-phase-field simulation of interface dynamics, Engineering Analysis with Boundary Elements 176 (2025) 106200

    2025

  10. [18]

    Elfetni, R

    S. Elfetni, R. Darvishi Kamachali, Pinn-phase: A physics- informed neural network hybrid framework for energy-based trans- fer learning in diffuse interface problems, Available at SSRN: https://ssrn.com/abstract=52070411 (2025)

    2025

  11. [19]

    W. Li, M. Z. Bazant, J. Zhu, Phase-field deeponet: Physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionals, Computer Meth- ods in Applied Mechanics and Engineering 416 (2023) 116299. 27

    2023

  12. [20]

    Gangmei, S

    G. Gangmei, S. Rana, B. Rolfe, K. Mitra, S. Bhattacharyya, Learning coupled allen-cahn and cahn-hilliard phase-field equations using physics- informed neural operator(pino) (2025). arXiv:2507.18731

    2025 arXiv

  13. [21]

    Lin, S.-J

    L.-C. Lin, S.-J. Chen, H.-Y. Yu, Connecting structural characteristics and material properties in phase-separating polymer solutions: Phase- field modeling and physics-informed neural networks, Polymers 15 (24) (2023) 4711

    2023

  14. [22]

    A. A. K. Farizhandi, M. Mamivand, Spatiotemporal prediction of mi- crostructure evolution with predictive recurrent neural network, Com- putational Materials Science 223 (2023) 112110

    2023

  15. [23]

    C. Zhu, S. Liu, Z. Gao, L. Wang, J. Miao, Spatiotemporal evolution of grain microstructure: A cnn perspective, Materials Today Communica- tions 40 (2024) 110005

    2024

  16. [24]

    K. Yang, Y. Cao, Y. Zhang, S. Fan, M. Tang, D. Aberg, B. Sadigh, F. Zhou, Self-supervised learningand prediction of microstructureevolu- tion with convolutional recurrent neural networks, Patterns 2 (5) (2021) 100243

    2021

  17. [25]

    S. Fan, A. L. Hitt, M. Tang, B. Sadigh, F. Zhou, Accelerate microstruc- ture evolution simulation using graph neural networks with adaptive spatiotemporal resolution, Machine Learning: Science and Technology 5 (2) (2024) 025027

    2024

  18. [26]

    Y. Qin, S. DeWitt, B. Radhakrishnan, G. Biros, Graingnn: A dynamic graph neural network for predicting 3d grain microstructure, Journal of Computational Physics 510 (2024) 113061

    2024

  19. [27]

    P. Wu, A. S. Iquebal, K. Ankit, Emulating microstructural evolution during spinodal decomposition using a tensor decomposed convolutional and recurrent neural network, Computational Materials Science 224 (2023) 112187

    2023

  20. [28]

    H. Mao, C. Xie, J. Pan, Q. Cao, X. Zhang, Y. Luo, Y. Du, H. Ning, Spatiotemporal prediction of solidified dendrites based on convolutional long-short-term neural network, Materials Today Communications 41 (2024) 110634. 28

    2024

  21. [29]

    N. Wang, J. Zhou, G. Guo, Y. Zhang, W. Gao, J. Wang, L. Tang, Y. Zhang, Z. Zhang, Prediction and characterization of microstructure evolution based on deep learning method and in-situ scanning electron microscope, Materials Characterization 204 (2023) 113230

    2023

  22. [30]

    D. M. d. O. Zapiain, J. A. Stewart, R. Dingreville, Accelerating phase- field-based microstructure evolution predictions via surrogate models trained by machine learning methods, npj Computational Materials 7 (1) (2021) 3

    2021

  23. [31]

    C. Hu, S. Martin, R. Dingreville, Accelerating phase-field predictions via recurrent neural networks learning the microstructure evolution in latent space, Computer Methods in Applied Mechanics and Engineering 397 (2022) 115128

    2022

  24. [32]

    Oommen, K

    V. Oommen, K. Shukla, S. Goswami, R. Dingreville, G. E. Karniadakis, Learning two-phase microstructure evolution using neural operators and autoencoder architectures, npj Computational Materials 8 (1) (2022) 190

    2022

  25. [33]

    Ciesielski, Y

    D. Ciesielski, Y. Li, S. Hu, E. King, J. Corbey, P. Stinis, Deep operator network surrogate for phase-field modeling of metal grain growth during solidification, Computational Materials Science 246 (2025) 113417

    2025

  26. [34]

    Tseng, C.-W

    B.-Y. Tseng, C.-W. C. Guo, Y.-C. Chien, J.-P. Wang, C.-H. Yu, Deep learning model to predict ice crystal growth, Advanced Science 10 (21) (2023) 2207731

    2023

  27. [35]

    Chen, H.-Y

    S.-J. Chen, H.-Y. Yu, L-mau: A multivariate time-series network for pre- dicting the cahn-hilliard microstructure evolutions via low-dimensional approaches, Computer Physics Communications 305 (2024) 109342

    2024

  28. [36]

    L. H. Rieger, K. Zelič, I. Mele, T. Katrašnik, A. Bhowmik, Setting the standard for machine learning in phase field prediction: a benchmark dataset and baseline metrics, Scientific data 11 (1) (2024) 1275

    2024

  29. [37]

    Peivaste, N

    I. Peivaste, N. H. Siboni, G. Alahyarizadeh, R. Ghaderi, B. Svendsen, D. Raabe, J. R. Mianroodi, Machine-learning-based surrogate modeling of microstructure evolution using phase-field, Computational Materials Science 214 (2022) 111750. 29

    2022

  30. [38]

    W. Yan, J. Melville, V. Yadav, K. Everett, L. Yang, M. S. Kesler, A. R. Krause, M. R. Tonks, J. B. Harley, A novel physics-regularized inter- pretable machine learning model for grain growth, Materials & Design 222 (2022) 111032

    2022

  31. [39]

    Z. Gao, C. Tan, L. Wu, S. Z. Li, Simvp: Simpler yet better video predic- tion, in: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022, p. 3170–3180

    2022

  32. [40]

    P. Wu, H. Huang, Q. Yang, B. Qian, Y. Gao, Y. Yang, H. Zhang, Q. Zhen, Simgate: A deep learning surrogate model for predicting mi- crostructure evolution using the phase-field method, Computational Ma- terials Science 256 (2025) 113883

    2025

  33. [41]

    X. Hu, Z. Huang, A. Huang, J. Xu, S. Zhou, A dynamic multi-scale voxel flow network for video prediction, in: Proceedings of the IEEE/CVF ConferenceonComputerVisionandPatternRecognition(CVPR),2023, pp. 6121–6131

    2023

  34. [42]

    H. X. Zhu, S. M. Thorpe, A. H. Windle, The geometrical properties of irregular two-dimensional voronoi tessellations, Philosophical Magazine A 81 (12) (2007) 2765–2783

    2007

  35. [43]

    Paszke, S

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, S. Chintala, Pytorch: An imperative style, high- perfor...

    2019

  36. [44]

    C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virta- nen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, R. Kern, M. Picus, S. Hoyer, M. H. van Kerkwijk, M. Brett, A. Haldane, J. F. del Río, M. Wiebe, P. Peterson, P. Gérard-Marchant, K. Sheppard, ...

    2020

  37. [45]

    Johnson, A

    J. Johnson, A. Alahi, L. Fei-Fei, Perceptual losses for real-time style transfer and super-resolution, in: B. Leibe, J. Matas, N. Sebe, 30 M. Welling (Eds.), Computer Vision – ECCV 2016, Springer Interna- tional Publishing, Cham, 2016, pp. 694–711

    2016

  38. [46]

    Z. Wang, A. Bovik, H. Sheikh, E. Simoncelli, Image quality assessment: fromerrorvisibilitytostructuralsimilarity, IEEETransactionsonImage Processing 13 (4) (2004) 600–612

    2004

  39. [47]

    van der Walt, J

    S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, T. Yu, the scikit-image contributors, scikit-image: image processing in Python, PeerJ 2 (2014) e453

    2014

  40. [48]

    X. Shi, Z. Chen, H. Wang, D.-Y. Yeung, W.-K. Wong, W.-c. Woo, Con- volutional lstm network: A machine learning approach for precipita- tion nowcasting, Advances in neural information processing systems 28 (2015)

    2015

  41. [49]

    C. Tan, S. Li, Z. Gao, W. Guan, Z. Wang, Z. Liu, L. Wu, S. Z. Li, Open- stl: A comprehensive benchmark of spatio-temporal predictive learning, in: Conference on Neural Information Processing Systems Datasets and Benchmarks Track, 2023. 31

    2023

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.