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NeuralDEM -- Real-time Simulation of Industrial Particulate Flows

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read NeuralDEM claims that field-level neural operators can replace discrete-element simulations of 250k-particle hoppers and 500k-particle coupled CFD-DEM fluidized beds, with stable 28-second autoregressive rollouts.

desk verdict A genuinely useful surrogate framework for granular flows, with a solid hopper study and a fluidized-bed long-rollout claim that currently outruns the evidence. read the letter →

arxiv 2411.09678 v2 pith:H25WYSTT submitted 2024-11-14 cs.LG cs.AI

Benedikt Alkin , Tobias Kronlachner , Samuele Papa , Stefan Pirker , Thomas Lichtenegger , Johannes Brandstetter This is my paper · ORCID
classification cs.LGcs.AI
keywords neuraloperatorsdiscreteelementmethodCFD-DEMfluidizedbedhopperflowfield-basedsimulationautoregressivesurrogatereal-time
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

NeuralDEM sets out to replace the discrete element method (DEM), the standard but computationally expensive way to simulate granular and particulate flows, with a deep-learning surrogate that runs in real time. Its central claim is that a transformer-based neural operator, trained on smoothed field-level quantities rather than individual particle trajectories, can reproduce the macroscopic physics of industrial-scale hoppers and coupled CFD-DEM fluidized bed reactors. In the largest demonstration, a model with 850M parameters rolls out 28 seconds (2,800 machine-learning timesteps) of a reactor with 500k particles and 160k CFD cells, matching time-averaged solid fraction, fluid velocity, and Lacey mixing index statistics of the numerical ground truth. If this holds, engineers could bypass the costly calibration of microscopic DEM parameters, condition directly on measurable macroscopic material properties, and explore parameter spaces much faster than with current solvers.

What carries the argument

The carrying mechanism is the multi-branch neural operator, a transformer-based architecture with two kinds of branches. Main branches model the core physics, one for particle displacement and another for fluid velocity, and exchange tokens through concatenated attention before each block, so the phases are tightly coupled. Off branches, one per macroscopic field such as occupancy, transport, residence time, or mixing concentration, cross-attend to the main-branch tokens as keys and values but never send gradients back, so they read the microscopic state without perturbing it. Scalar conditioning, including timestep, hopper angle, friction, inlet velocity, or shear-cell-measured friction angle and flow function coefficient, enters every block through learned scale-shift-gate modulations. Decoding uses a query-based neural-field decoder that evaluates the latent state at arbitrary spatial coordinates, which is what lets the model output fields on any mesh resolution after training.

What would settle it

Run the largest fluidized-bed model on a 28-second trajectory at an inlet velocity above the 0.842 m/s maximum used in training, and compare time-averaged solid fraction and fluid velocity against a fresh CFD-DEM reference; if those averaged fields drift outside the validation-set error band, the claimed generalization across inlet velocities fails.

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Extended reading notes

Core claim

NeuralDEM's central discovery is that the Lagrangian information in a DEM simulation, the positions and displacements of every particle, can be discarded in favor of learned continuous fields, and that this compressed representation is enough for accurate long-horizon predictions when macroscopic quantities are added as auxiliary fields. The model is trained to make one prediction per machine-learning timestep, which is at least 1000 DEM timesteps, and then rolled out autoregressively. On hoppers, it predicts occupancy, transport, and residence-time fields for 250k-particle systems over 40 s trajectories and reproduces mass-flow and funnel-flow regimes, outflow rates, drainage times, and residual volumes. On fluidized beds, two coupled main branches, one for particle displacement and one for fluid velocity, plus an off-branch for particle mixing, reproduce bubble structures, time-averaged solid fraction and fluid velocity, and Lacey mixing indices for 500k particles and 160k CFD cells over 28 s, with total mass conserved almost exactly. The same framework generalizes to unseen hopper angles, friction angles, and inlet velocities, and can be conditioned on macroscopic shear-cell measurements instead of microscopic friction parameters.

Load-bearing premise

The load-bearing premise is that a smoothed, field-level description of the particle system, occupancy, transport, and residence time instead of individual particle positions and contacts, contains enough information to predict the next field state, and that autoregressive rollout keeps the model on the distribution it saw during training.

Editorial extensions

If this is right

  • If the central claim holds, engineers can skip microscopic DEM parameter calibration: conditioning on shear-cell-measured internal friction angle and flow function coefficient yields usable hopper predictions, so any material characterized in a shear cell can be simulated directly.
  • Real-time rollouts at industrial scale become feasible: a 40 s hopper trajectory runs in 1.4 s on a GPU, and a 3 s fluidized-bed trajectory in 11 s, versus six hours on 64 CPU cores.
  • The field representation allows evaluation at arbitrary output locations, such as an 80k-cell tetrahedral grid, without retraining, enabling variable-resolution visualization and analysis.
  • Long-horizon stability is a direct corollary: the largest model shows no stability problems up to 100 s and preserves total mass almost perfectly over 28 s rollouts.
  • Generalization to unseen conditions is part of the claim: drainage-time predictions remain reasonable when hopper angle and friction angle lie outside the training range by a substantial margin.

Reading between the lines

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

  • Because the cost of the neural operator scales with the number of latent tokens and output query points rather than the number of particles, the same architecture should extend to reactors with millions of particles if the field assumption holds, a testable claim the paper does not make.
  • The off-branch design, where macroscopic fields read from but never feed back into the dynamics, could be transferred to other coupled problems such as heat transfer or chemical species concentration, as a way to predict coarse observables without destabilizing the rollout.
  • The reported CPU inference time of 41 s for a 40 s hopper trajectory shows that the real-time claim currently depends on having a GPU, so the practical speedup for industrial users will depend on deployment hardware and output resolution.
  • A direct experimental check would be to take a material characterized only by shear-cell measurements, run NeuralDEM predictions for a hopper, and compare the predicted drainage time and residual mass against physical experiments rather than DEM ground truth.
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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 / 6 minor

Summary. The paper introduces NeuralDEM, a multi-branch transformer-based neural operator that replaces DEM and coupled CFD-DEM solvers with field-based surrogates. The method represents the Lagrangian particle configuration through continuous Eulerian fields (occupancy, transport, residence time) and adds a macroscopic auxiliary-field branch to predict quantities such as mixing or residence time directly. Experiments cover a 250k-particle hopper dataset (1000 simulations with varying hopper angle and friction, evaluated on outflow rate, drainage time, residual volume, residence time, and flow regime) and a 500k-particle, 160k-cell fluidized bed dataset (456 CFD-DEM trajectories with varying inlet velocity, evaluated on mixing index, time-averaged statistics, and rollout stability). The headline claim is that an 850M-parameter model produces physically correct 28 s (2800-step) rollouts of the fluidized bed, with real-time or near-real-time inference and generalization to unseen parameters.

Significance. If substantiated, the work is significant: it demonstrates that a coarse Eulerian field representation plus auxiliary macroscopic fields can replace per-particle DEM at industrially relevant scales (500k particles, 160k CFD cells), with large runtime speedups, conditioning on macroscopic material parameters, and some generalization to unseen conditions. The hopper results are quantified and largely credible: drainage time average error 0.19 s, residual volume error 0.41%, and outflow average error 17.3 on a roughly 800-1800 scale, with a held-out 20-degree parameter band test. The main weakness is that the central fluidized-bed long-rollout claim is supported only by time-averaged statistics and qualitative visual comparisons, with no quantitative long-rollout error metric. The paper also explicitly concedes (Section 5.2) that rollout success requires the output distribution to match the training input distribution, but it never tests this condition for the 2800-step rollouts. These gaps make the abstract's 'faithfully models ... trajectories of 28 s' claim currently unsupported, although it is plausibly fixable with additional evaluation.

major comments (4)
  1. [Section 4.3.3, Figures 15-16] The central claim of 28 s / 2800-step physically correct fluidized bed rollouts is not quantitatively supported. The evidence is the domain-averaged solid fraction over time (Figure 16) and qualitative mean/std slices (Figure 15), while Section 4.3.2 explicitly disclaims pointwise comparison. Time-averaged statistics and a single global scalar are insensitive to trajectory-level errors: a model that drifts into a plausible but wrong attractor, or that dissipates bubble dynamics, can match these diagnostics. I request a local or error-growth metric on the four long test sequences, for example cellwise mean-field MAE, bubble size/frequency statistics, or an error-versus-rollout-length curve comparing errors at 300 and 2800 steps. Without such a metric, the abstract's 'faithfully models ... trajectories of 28 s' is not established.
  2. [Section 5.2] The paper itself identifies the key failure mode: 'a requirement for the demonstrated success of the autoregressive rollout is that the output distribution during rollout should match the input distribution observed during training.' No experiment verifies this condition for the 2800-step fluidized bed rollouts, and no diagnostic of distributional drift is reported. Adding a quantitative distribution-match check (for example, evolving statistics of the solid fraction and fluid velocity fields over the rollout horizon, or comparing one-step prediction error at step 1 versus step 2800) would directly test this load-bearing assumption of the framework.
  3. [Section 4.2.5, Figure 11] The generalization claim for unseen hopper parameters is only qualitatively supported. The held-out 20-degree band is evaluated only through drainage time, and the text reports no average error for the held-out set; the 0.19 s figure refers to the random split in Figure 9b. To support the abstract's generalization claim, the authors should report quantitative errors on the held-out band for all reported macroscopic quantities (outflow, residual volume, residence time), not only drainage time.
  4. [Section 4.3.3, Figure 16] The mass-conservation claim is supported only visually. Figure 16 plots the domain-averaged solid fraction on a deliberately zoomed y-axis (0.15 to 0.25), and no numerical error is reported. Since mass conservation is presented as 'the most crucial property of a physics simulation,' the paper should report the maximum or mean absolute deviation of total solid fraction over the 2800-step rollout.
minor comments (6)
  1. [Section 2.1] The phrase 'from Blais et al.' is grammatically awkward; it should read 'by Blais et al.' or 'of Blais et al.'.
  2. [Section 4.3.5] The reported 11 s inference time for a 3 s fluidized bed trajectory is not real-time; the text should explicitly distinguish 'faster than the classical solver' from 'real-time' to avoid overstating the title's real-time claim.
  3. [Section 4.2.6, Table 3] The statement that the shear-cell parameters 'provide no additional information' is consistent with the near-identical errors in the last two rows, but the row with all four scalars shows slightly worse drainage error (0.23 s versus 0.19 s); the text should note that this difference is within noise or address it explicitly.
  4. [Section 4.3.1] The parameter count is not transparent: 12 blocks with hidden dimension 768 and three ViT-Base-equivalent branches would be about 258M parameters before DiT modulation, yet the model is reported as 850M. A short parameter breakdown would help readers judge the claim of scalability.
  5. [Section 4.3.3] The claim that the model 'did not show any stability problem up to 100 s' is not supported by any figure, table, or metric in the paper; either add evidence or soften the claim.
  6. [General] No data or code availability statement is provided; for reproducibility, the authors should state whether the datasets, trained models, and inference code will be released.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; the predicted macroscopic observables are read out from supervised fields and tested against held-out CFD-DEM data, and self-citations are motivational rather than load-bearing.

full rationale

The paper's macroscopic predictions (outflow rate, drainage time, residual volume, residence time, mixing index, and time-averaged statistics) are all computed from neural-network-predicted fields that were supervised on DEM/CFD-DEM training data. For example, Section 4.2.3 states: 'The occupancy field allows us to calculate an outflow rate by evaluating the occupancy field with the particle positions of the initial packing and subtracting the number of occupied positions from tML and tML+∆tML.' This is a legitimate readout from a predicted field, not a parameter fitted to the target quantity; the comparison is made against held-out DEM simulations (Figures 8, 9, 15, 16). The field-based physics representation is introduced as an explicit modeling assumption (Section 3.1: 'we assume that there exists some underlying field that describes the particle displacements in a DEM simulation'), and its success is tested empirically, so the central claims do not reduce to their inputs by construction. The paper does rely on self-citations for motivation and architecture choices: the UPT framework [3] (Alkin et al., sharing two authors) is used to justify the multi-branch transformer design, and [59] (Lichtenegger, a co-author) supports the low-effective-dimensionality premise. However, these citations are not invoked to forbid alternatives or to force a particular mathematical result; the framework's validity is demonstrated by the held-out experiments. Section 5.2 honestly concedes the distribution-match requirement for autoregressive rollouts and the difficulty of modeling particle-attached quantities, which is a limitation rather than a circular step. The 28 s fluidized-bed claim is supported by time-averaged statistics and stability plots rather than pointwise error, which is a matter of evidence strength, not circularity. Accordingly, no specific circular reduction can be exhibited from the paper's own equations, and the appropriate finding is no significant circularity.

Assumptions & free parameters 2 free parameters · 4 assumptions · 3 invented entities

The central contribution is an empirical ML surrogate: it introduces no new physical parameters, but it does rely on several domain assumptions about field smoothness, locality, and distribution match, and its reported macroscopic quantities are defined through hand-set evaluation thresholds. The auxiliary fields are model outputs, not independently evidenced physical entities.

free parameters (2)
  • Occupancy radius = not reported, chosen larger than particle radius
    Defines which positions count as occupied, directly affecting outflow rate, drainage time, and residual volume. Introduced by hand in Section 4.2.3.
  • Drainage threshold = 64 particles above outlet
    Evaluation definition for when a hopper is considered drained; the paper notes 32 and 128 give similar behavior, but the threshold is still a hand-set scalar.
assumptions (4)
  • domain assumption Effective degrees of freedom of a DEM system are much smaller than the microscopic particle count, so a compressed field can represent the dynamics.
    Invoked in Section 3.1 to justify modeling Lagrangian DEM output as a continuous field.
  • domain assumption Over an ML timestep of 0.1s in the hopper and 0.01s in the fluidized bed, the evolution at each point is determined by a nearby bounded subdomain.
    Stated in Section 3.1 to justify the locality of attention; the model would fail if long-range correlations dominate at these timesteps.
  • domain assumption Autoregressive rollout remains valid when the output distribution matches the training input distribution.
    Explicitly listed as a modeling limitation in Section 5.2; it is load-bearing for the 28s and 100s rollout claims.
  • domain assumption The LIGGGHTS and OpenFOAM simulations define the ground truth for all training and evaluation.
    All reported errors are distances to these simulations; no experimental validation is provided, so any systematic bias in the DEM solver is inherited.
invented entities (3)
  • Occupancy field
    purpose: Classifies whether a spatial location is occupied so outflow, drainage, and residual mass can be computed.
    An internal, learned field derived from particle positions; not independently measured or validated outside the DEM data.
  • Transport field
    purpose: Represents cumulative particle displacement over long horizons, used for flow regime visualization and refilling mode.
    A learned auxiliary field; no independent physical observable is linked to it outside the simulation data.
  • Residence time field
    purpose: Directly predicts how long particles at a location stay in the hopper.
    A learned macroscopic target, not a new physical quantity with independent measurement.

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Cite this review

Pith. "Pith review of NeuralDEM -- Real-time Simulation of Industrial Particulate Flows." pith.science (2026). https://pith.science/paper/H25WYSTT

@misc{pith2026241109678,
  author       = {Pith},
  title        = {Pith review of: NeuralDEM -- Real-time Simulation of Industrial Particulate Flows},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H25WYSTT}},
  note         = {Machine review of arXiv:2411.09678}
}
read the original abstract

Advancements in computing power have made it possible to numerically simulate large-scale fluid-mechanical and/or particulate systems, many of which are integral to core industrial processes. Among the different numerical methods available, the discrete element method (DEM) provides one of the most accurate representations of a wide range of physical systems involving granular and discontinuous materials. Consequently, DEM has become a widely accepted approach for tackling engineering problems connected to granular flows and powder mechanics. Additionally, DEM can be integrated with grid-based computational fluid dynamics (CFD) methods, enabling the simulation of chemical processes taking place, e.g., in fluidized beds. However, DEM is computationally intensive because of the intrinsic multiscale nature of particulate systems, restricting simulation duration or number of particles. Towards this end, NeuralDEM presents an end-to-end approach to replace slow numerical DEM routines with fast, adaptable deep learning surrogates. NeuralDEM is capable of picturing long-term transport processes across different regimes using macroscopic observables without any reference to microscopic model parameters. First, NeuralDEM treats the Lagrangian discretization of DEM as an underlying continuous field, while simultaneously modeling macroscopic behavior directly as additional auxiliary fields. Second, NeuralDEM introduces multi-branch neural operators scalable to real-time modeling of industrially-sized scenarios - from slow and pseudo-steady to fast and transient. Such scenarios have previously posed insurmountable challenges for deep learning models. Notably, NeuralDEM faithfully models coupled CFD-DEM fluidized bed reactors of 160k CFD cells and 500k DEM particles for trajectories of 28s. NeuralDEM will open many new doors to advanced engineering and much faster process cycles.

Figures

Figures reproduced from arXiv: 2411.09678 by the authors.

Figure 1
Figure 1. NeuralDEM presents an end-to-end approach to replace discrete element method (DEM) routines and coupled multiphysics simulations with deep learning surrogates. Top: Hopper simu￾lations. NeuralDEM treats inputs and outputs as continuous fields, while modeling macroscopic behavior directly as additional auxiliary fields. Bottom: Fluidized bed reactors. NeuralDEM is built to model complex multiphysics simulations, i.e.… view at source ↗
Figure 2
Figure 2. Discrete element method. The force on a particle consists of particle-particle contacts F (pc) i , the external force F (ext) i , and the interaction with a surrounding fluid phase F (pf) i . In a system of solid particles with masses mi , radii ri , positions ri , and velocities vi , each of them has to obey Newton’s second law d dt mivi = F (ext) i + F (pc) i + F (pf) i . (1) Particle i experiences forces of exter… view at source ↗
Figure 3
Figure 3. Neural operator learning. Neural operators aim to learn a mapping between function [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (15 more)
Figure 4
Figure 4. Figure 4: In our physics representation we model the Lagrangian discretization of DEM as an as￾sumed underlying continuous field. The approximator maps the encoded representation to one that can be decoded at any specified spatial location j ′ . The multi-branch neural operator …
Figure 5
Figure 5. Figure 5: Schematic architecture of a multi-branch transformer block. DiT [77] modulation is applied to each attention and MLP block but is omitted for visual clarity. 3.3 Scalar parameter conditioning Physical simulations often require various scalar parameters such as material…
Figure 6
Figure 6. Figure 6: Schematic of the two numerical experimental cases and the associated dimensions. [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: Visualization of a NeuralDEM generated trajectory vs the DEM simulation. Different [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Distribution of macroscopic measurements over the whole DEM generated hopper dataset. [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]
Figure 9
Figure 9. Figure 9: Macroscopic simulation insights from the predicted occupancy field. The NeuralDEM [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Visualization of a NeuralDEM generated material residence time vs the DEM simulation [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]
Figure 11
Figure 11. Figure 11: Generalization to DEM simulation settings that are outside the range seen during training. [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]
Figure 12
Figure 12. Figure 12: NeuralDEM transport field prediction using microscopic simulation parameters vs [PITH_FULL_IMAGE:figures/full_fig_p019_12.png]
Figure 13
Figure 13. Figure 13: NeuralDEM transport field prediction for the hopper case in refilling operation mode vs [PITH_FULL_IMAGE:figures/full_fig_p020_13.png]
Figure 14
Figure 14. Figure 14: Visualization of three snapshots taken at [PITH_FULL_IMAGE:figures/full_fig_p022_14.png]
Figure 15
Figure 15. Figure 15: Comparison of long term temporal averaging statistics for two fluid inlet velocities. [PITH_FULL_IMAGE:figures/full_fig_p023_15.png]
Figure 16
Figure 16. Figure 16: The average solid fraction predicted by the NeuralDEM model is stable over extremely [PITH_FULL_IMAGE:figures/full_fig_p024_16.png]
Figure 17
Figure 17. Figure 17: (a) Particle-based mix￾ing where the dark particles started from the right half of the reactor. (b) Field-based concentration ob￾tained using a Gaussian kernel on a mesh. Particle mixing by definition is a particle-associated quantity where each particle either belong…
Figure 18
Figure 18. Figure 18: Comparison of the temporal evolution of the Lacey mixing index for three different inlet [PITH_FULL_IMAGE:figures/full_fig_p025_18.png]

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Reference graph

Works this paper leans on

106 extracted references · 64 canonical work pages · cited by 1 Pith paper

  1. [1]

    J., Bambrick, J., et al

    Abramson, J., Adler, J., Dunger, J., Evans, R., Green, T., Pritzel, A., Ronneberger, O., Will- more, L., Ballard, A. J., Bambrick, J., et al. Accurate structure prediction of biomolecular interactions with alphafold 3. Nature, pp. 1–3, 2024

    2024

  2. [2]

    Ali, Z., Biglari, R., Denil, J., Mertens, J., Poursoltan, M., and Traor ´e, M. K. From modeling and simulation to digital twin: evolution or revolution? SIMULATION: Transactions of The Society for Modeling and Simulation International, 100(7):751–769, 2024

    2024

  3. [3]

    Universal physics transformers

    Alkin, B., F ¨urst, A., Schmid, S., Gruber, L., Holzleitner, M., and Brandstetter, J. Universal physics transformers. arXiv preprint arXiv:2402.12365, 2024

    arXiv 2024

  4. [4]

    K., Moraveji, M

    Amani, H., Alamdari, E. K., Moraveji, M. K., and Peters, B. Experimental and numerical investigation of iron ore pellet firing using coupled CFD-DEM method. Particuology, 2024. 26

    2024

  5. [5]

    H., Besseron, X., and Peters, B

    Aminnia, N., Adhav, P., Darlik, F., Mashhood, M., Saraei, S. H., Besseron, X., and Peters, B. Three-dimensional CFD-DEM simulation of raceway transport phenomena in a blast furnace. Fuel, 334:126574, 2023

    2023

  6. [6]

    Anderson, T. B. and Jackson, R. O. Y . A fluid mechanical description of fluidized beds. Ind. Eng. Chem. Fundam., 6(4):527–539, 1967

    1967

  7. [7]

    Andr ´e, F. P. and Tavares, L. M. Simulating a laboratory-scale cone crusher in DEM using polyhedral particles. Powder Technol., 372:362–371, 2020

    2020

  8. [8]

    and Auli, M

    Baevski, A. and Auli, M. Adaptive input representations for neural language modeling. In ICLR, 2019

    2019

Show all 106 references
  1. [9]

    P., Simm, G., Ortner, C., and Cs´anyi, G

    Batatia, I., Kovacs, D. P., Simm, G., Ortner, C., and Cs´anyi, G. Mace: Higher order equivari- ant message passing neural networks for fast and accurate force fields. Advances in Neural Information Processing Systems, 35:11423–11436, 2022

    2022

  2. [10]

    P., Kornbluth, M., Molinari, N., Smidt, T

    Batzner, S., Musaelian, A., Sun, L., Geiger, M., Mailoa, J. P., Kornbluth, M., Molinari, N., Smidt, T. E., and Kozinsky, B. E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nature communications, 13(1):2453, 2022

    2022

  3. [11]

    Improvement of a pharmaceutical powder mixing process in a tote blender via DEM simula- tions

    Benque, B., Orefice, L., Forgber, T., Habeler, M., Schmid, B., Remmelgas, J., and Khinast, J. Improvement of a pharmaceutical powder mixing process in a tote blender via DEM simula- tions. Int. J. Pharm., 658:124224, 2024

    2024

  4. [12]

    Accurate medium-range global weather forecasting with 3d neural networks

    Bi, K., Xie, L., Zhang, H., Chen, X., Gu, X., and Tian, Q. Accurate medium-range global weather forecasting with 3d neural networks. Nature, 619(7970):533–538, 2023

    2023

  5. [13]

    Three-dimensional discrete element models for the granular statics and dynamics of powders in cavity filling

    Bierwisch, C., Kraft, T., Riedel, H., and Moseler, M. Three-dimensional discrete element models for the granular statics and dynamics of powders in cavity filling. J. Mech. Phys. Solids, 57(1):10–31, 2009

    2009

  6. [14]

    S., and Chaouki, J

    Blais, B., Vidal, D., Bertrand, F., Patience, G. S., and Chaouki, J. Experimental methods in chemical engineering: Discrete element method—DEM. Can. J. Chem. Eng. , 97(7):1964– 1973, 2019

    1964

  7. [15]

    P., Lucic, A., Stanley, M., Brandstetter, J., Garvan, P., Riechert, M., Weyn, J., Dong, H., Vaughan, A., et al

    Bodnar, C., Bruinsma, W. P., Lucic, A., Stanley, M., Brandstetter, J., Garvan, P., Riechert, M., Weyn, J., Dong, H., Vaughan, A., et al. Aurora: A foundation model of the atmosphere. arXiv preprint arXiv:2405.13063, 2024

    2024 arXiv

  8. [16]

    E., and Welling, M

    Brandstetter, J., Worrall, D. E., and Welling, M. Message passing neural PDE solvers. In ICLR, 2022

    2022

  9. [17]

    A review on discrete element method simulation in laser powder bed fusion additive manufacturing

    Chen, H., Sun, Y ., Yuan, W., Pang, S., Yan, W., and Shi, Y . A review on discrete element method simulation in laser powder bed fusion additive manufacturing. Chin. J. Mech. Eng. Addit. Manuf. Front., 1(1):100017, 2022

    2022

  10. [18]

    and Wang, J

    Chen, X. and Wang, J. A comparison of two-fluid model, dense discrete particle model and CFD-DEM method for modeling impinging gas–solid flows. Powder Technol., 254:94–102, 2014

    2014

  11. [19]

    Chen, X., Liang, C., Huang, D., Real, E., Wang, K., Pham, H., Dong, X., Luong, T., Hsieh, C., Lu, Y ., and Le, Q. V . Symbolic discovery of optimization algorithms.Advances in Neural Information Processing Systems, 36:49205–49233, 2023

    2023

  12. [20]

    Digital twins in pharmaceutical and biopharmaceutical manufacturing: A literature review

    Chen, Y ., Yang, O., Sampat, C., Bhalode, P., Ramachandran, R., and Ierapetritou, M. Digital twins in pharmaceutical and biopharmaceutical manufacturing: A literature review. Pro- cesses, 8(9), 2020. ISSN 2227-9717

    2020

  13. [21]

    and Wang, J

    Cheng, Z. and Wang, J. Estimation of contact forces of granular materials under uniaxial compression based on a machine learning model. Granular Matter, 24:1–14, 2022

    2022

  14. [22]

    Coetzee, C. J. Calibration of the discrete element method. Powder Technol., 310:104–142, 2017. 27

    2017

  15. [23]

    Cundall, P. A. and Strack, O. D. L. A discrete numerical model for granular assemblies. G´eotechnique, 29(1):47–65, 1979

    1979

  16. [24]

    Fluidized bed gas-solid heat transfer using a CFD- DEM coarse-graining technique

    de Munck, M., Peters, E., and Kuipers, J. Fluidized bed gas-solid heat transfer using a CFD- DEM coarse-graining technique. Chem. Eng. Sci., 280:119048, 2023. ISSN 0009-2509

    2023

  17. [25]

    Particle dynamics in a multi-staged fluidized bed: Particle transport behavior on micro-scale by discrete particle modelling

    Diez, E., Kieckhefen, P., Meyer, K., B¨uck, A., Tsotsas, E., and Heinrich, S. Particle dynamics in a multi-staged fluidized bed: Particle transport behavior on micro-scale by discrete particle modelling. Adv. Powder Technol., 30(10):2014–2031, 2019. ISSN 0921-8831

    2014

  18. [26]

    An image is worth 16x16 words: Transformers for image recognition at scale

    Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., De- hghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., and Houlsby, N. An image is worth 16x16 words: Transformers for image recognition at scale. In ICLR, 2021

    2021

  19. [27]

    Scaling rectified flow transformers for high-resolution image synthesis

    Esser, P., Kulal, S., Blattmann, A., Entezari, R., M ¨uller, J., Saini, H., Levi, Y ., Lorenz, D., Sauer, A., Boesel, F., Podell, D., Dockhorn, T., English, Z., and Rombach, R. Scaling rectified flow transformers for high-resolution image synthesis. In ICML, volume 235 of Proc...

    2024

  20. [28]

    Application of GPU-DEM simulation on large-scale granular handling and processing in ironmaking related industries

    Gan, J., Evans, T., and Yu, A. Application of GPU-DEM simulation on large-scale granular handling and processing in ironmaking related industries. Powder Technol., 361:258–273,

  21. [29]

    H., and Kwade, A

    Giannis, K., Schilde, C., Finke, J. H., and Kwade, A. Modeling of high-density compaction of pharmaceutical tablets using multi-contact discrete element method. Pharmaceutics, 13 (12):2194, 2021

    2021

  22. [30]

    Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descrip- tions

    Gidaspow, D. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descrip- tions. Elsevier Science, 1994. ISBN 9780122824708

    1994

  23. [31]

    G., Kuipers, J

    Goniva, C., Kloss, C., Deen, N. G., Kuipers, J. A. M., and Pirker, S. Influence of rolling friction on single spout fluidized bed simulation. Particuology, 10:582–591, 2012

    2012

  24. [32]

    K., Kok, S., and Wilke, D

    Govender, N., Rajamani, R. K., Kok, S., and Wilke, D. N. Discrete element simulation of mill charge in 3D using the BLAZE-DEM GPU framework. Miner. Eng., 79:152–168, 2015. ISSN 0892-6875

    2015

  25. [33]

    CFD-DEM simulation of a coating process in a fluidized bed rotor granulator

    Grohn, P., Lawall, M., Oesau, T., Heinrich, S., and Antonyuk, S. CFD-DEM simulation of a coating process in a fluidized bed rotor granulator. Processes, 8(9):1090, 2020

    2020

  26. [34]

    O., Teninge, A., Hariri, A

    Guillaud, X., Faruque, M. O., Teninge, A., Hariri, A. H., Vanfretti, L., Paolone, M., Dinavahi, V ., Mitra, P., Lauss, G., Dufour, C., Forsyth, P., Srivastava, A. K., Strunz, K., Strasser, T., and Davoudi, A. Applications of real-time simulation technologies in power and energ...

    2015

  27. [35]

    Convolutional neural networks for steady flow approximation

    Guo, X., Li, W., and Iorio, F. Convolutional neural networks for steady flow approximation. In Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pp. 481–490, 2016

    2016

  28. [36]

    Gupta, J. K. and Brandstetter, J. Towards multi-spatiotemporal-scale generalized PDE mod- eling. Trans. Mach. Learn. Res., 2023, 2023

    2023

  29. [37]

    Gnot: A general neural operator transformer for operator learning

    Hao, Z., Wang, Z., Su, H., Ying, C., Dong, Y ., Liu, S., Cheng, Z., Song, J., and Zhu, J. Gnot: A general neural operator transformer for operator learning. In ICML, volume 202 of Proceedings of Machine Learning Research, pp. 12556–12569. PMLR, 2023

    2023

  30. [38]

    and Farimani, A

    Hemmasian, A. and Farimani, A. B. Pretraining a neural operator in lower dimensions. arXiv preprint arXiv:2407.17616, 2024

    2024 arXiv

  31. [39]

    Poseidon: Efficient foundation models for pdes

    Herde, M., Raoni ´c, B., Rohner, T., K¨appeli, R., Molinaro, R., de B´ezenac, E., and Mishra, S. Poseidon: Efficient foundation models for pdes. arXiv preprint arXiv:2405.19101, 2024

    2024 arXiv

  32. [40]

    Perceiver: General perception with iterative attention

    Jaegle, A., Gimeno, F., Brock, A., Vinyals, O., Zisserman, A., and Carreira, J. Perceiver: General perception with iterative attention. In ICML, volume 139 of Proceedings of Machine Learning Research, pp. 4651–4664. PMLR, 2021. 28

    2021

  33. [41]

    Digital twin applications toward industry 4.0: A review

    Javaid, M., Haleem, A., and Suman, R. Digital twin applications toward industry 4.0: A review. Cognitive Robotics, 3:71–92, 2023. ISSN 2667-2413

    2023

  34. [42]

    Johnson, K. L. Contact Mechanics. Cambridge University Press, Cambridge, UK, 1985

    1985

  35. [43]

    Highly accurate protein structure prediction with alphafold

    Jumper, J., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O., Tunyasuvu- nakool, K., Bates, R., ˇZ´ıdek, A., Potapenko, A., et al. Highly accurate protein structure prediction with alphafold. nature, 596(7873):583–589, 2021

    2021

  36. [44]

    Possibilities and limits of computa- tional fluid dynamics–discrete element method simulations in process engineering: a review of recent advancements and future trends

    Kieckhefen, P., Pietsch, S., Dosta, M., and Heinrich, S. Possibilities and limits of computa- tional fluid dynamics–discrete element method simulations in process engineering: a review of recent advancements and future trends. Annu. Rev. Chem. Biomol. Eng., 11(1):397–422, 2020

    2020

  37. [45]

    Kipf, T. N. and Welling, M. Semi-supervised classification with graph convolutional net- works. In ICLR, 2017

    2017

  38. [46]

    Models, algorithms and vali- dation for opensource DEM and CFD-DEM

    Kloss, C., Goniva, C., Hager, A., Amberger, S., and Pirker, S. Models, algorithms and vali- dation for opensource DEM and CFD-DEM. Prog. Comput. Fluid Dyn., 12:140–152, 2012

    2012

  39. [47]

    M., Wessels, D

    Knigge, D. M., Wessels, D. R., Valperga, R., Papa, S., Sonke, J.-J., Gavves, E., and Bekkers, E. J. Space-time continuous pde forecasting using equivariant neural fields. arXiv preprint arXiv:2406.06660, 2024

    2024 arXiv

  40. [48]

    A., Alieva, A., Wang, Q., Brenner, M

    Kochkov, D., Smith, J. A., Alieva, A., Wang, Q., Brenner, M. P., and Hoyer, S. Machine learning–accelerated computational fluid dynamics. Proceedings of the National Academy of Sciences, 118(21):e2101784118, 2021

    2021

  41. [49]

    M., Bekkers, E., Nagaraja, N., and Gavves, E

    Kofinas, M. M., Bekkers, E., Nagaraja, N., and Gavves, E. Latent field discovery in inter- acting dynamical systems with neural fields. Advances in Neural Information Processing Systems, 36, 2024

    2024

  42. [50]

    B., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A

    Kovachki, N. B., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A. M., and Anandkumar, A. Neural operator: Learning maps between function spaces with applications to pdes. J. Mach. Learn. Res., 24:89:1–89:97, 2023

    2023

  43. [51]

    Lacey, P. M. C. Developments in the theory of particle mixing.Journal of Applied Chemistry, 4(5):257–268, 1954

    1954

  44. [52]

    Learning skillful medium-range global weather forecasting

    Lam, R., Sanchez-Gonzalez, A., Willson, M., Wirnsberger, P., Fortunato, M., Alet, F., Ravuri, S., Ewalds, T., Eaton-Rosen, Z., Hu, W., et al. Learning skillful medium-range global weather forecasting. Science, 382(6677):1416–1421, 2023

    2023

  45. [53]

    Large-scale discrete element modeling for a gas–solid–liquid flow system

    Li, R., Duan, G., Yamada, D., and Sakai, M. Large-scale discrete element modeling for a gas–solid–liquid flow system. Ind. Eng. Chem. Res., 62(42):17008–17018, 2023

    2023

  46. [55]

    B., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A

    Li, Z., Kovachki, N. B., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A. M., and Anandkumar, A. Neural operator: Graph kernel network for partial differential equations. arXiv preprint arXiv:2003.03485, 2020

    2003 arXiv

  47. [56]

    B., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A

    Li, Z., Kovachki, N. B., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A. M., and Anandkumar, A. Fourier neural operator for parametric partial differential equations. In ICLR, 2021

    2021

  48. [57]

    B., Choy, C

    Li, Z., Kovachki, N. B., Choy, C. B., Li, B., Kossaifi, J., Otta, S. P., Nabian, M. A., Stadler, M., Hundt, C., Azizzadenesheli, K., and Anandkumar, A. Geometry-informed neural operator for large-scale 3d pdes. Advances in Neural Information Processing Systems, 36:35836–35854,...

    2023

  49. [58]

    The prediction of contact force networks in granular materials based on graph neural networks

    Li, Z., Li, X., Zhang, H., Huang, D., and Zhang, L. The prediction of contact force networks in granular materials based on graph neural networks. The Journal of Chemical Physics, 158 (5), 2023

    2023

  50. [59]

    Local and global recurrences in dynamic gas-solid flows

    Lichtenegger, T. Local and global recurrences in dynamic gas-solid flows. Int. J. Multiphase Flow, 106:125 – 137, 2018

    2018

  51. [60]

    Data-assisted, physics-informed propagators for recurrent flows

    Lichtenegger, T. Data-assisted, physics-informed propagators for recurrent flows. Phys. Rev. Fluids, 9:024401, Feb 2024

    2024

  52. [61]

    and Pirker, S

    Lichtenegger, T. and Pirker, S. Fast long-term simulations of hot, reacting, moving particle beds with a melting zone. Chem. Eng. Sci., 283:119402, 2024

    2024

  53. [62]

    Lichtenegger, T., Peters, E. A. J. F., Kuipers, J. A. M., and Pirker, S. A recurrence CFD study of heat transfer in a fluidized bed. Chem. Eng. Sci., 172:310–322, 2017

    2017

  54. [63]

    Pde-refiner: Achieving accurate long rollouts with neural pde solvers

    Lippe, P., Veeling, B., Perdikaris, P., Turner, R., and Brandstetter, J. Pde-refiner: Achieving accurate long rollouts with neural pde solvers. Advances in Neural Information Processing Systems, 36:67398–67433, 2023

    2023

  55. [64]

    Post-training quantization for vision transformer

    Liu, Z., Wang, Y ., Han, K., Zhang, W., Ma, S., and Gao, W. Post-training quantization for vision transformer. Advances in Neural Information Processing Systems , 34:28092–28103, 2021

    2021

  56. [65]

    GPU accelerated MFiX-DEM simulations of granular and multiphase flows

    Lu, L. GPU accelerated MFiX-DEM simulations of granular and multiphase flows. Partic- uology, 62:14–24, 2022. ISSN 1674-2001

    2022

  57. [66]

    Lu, L., Jin, P., Pang, G., Zhang, Z., and Karniadakis, G. E. Learning nonlinear operators via deeponet based on the universal approximation theorem of operators. Nature machine intelligence, 3(3):218–229, 2021

    2021

  58. [67]

    Boundary graph neural networks for 3d simulations

    Mayr, A., Lehner, S., Mayrhofer, A., Kloss, C., Hochreiter, S., and Brandstetter, J. Boundary graph neural networks for 3d simulations. Proceedings of the AAAI Conference on Artificial Intelligence, 37(8):9099–9107, 2023

    2023

  59. [68]

    R.-S., Parker, L

    McCabe, M., Blancard, B. R.-S., Parker, L. H., Ohana, R., Cranmer, M., Bietti, A., Eick- enberg, M., Golkar, S., Krawezik, G., Lanusse, F., et al. Multiple physics pretraining for physical surrogate models. arXiv preprint arXiv:2310.02994, 2023

    arXiv

  60. [69]

    S., Aykol, M., Cheon, G., and Cubuk, E

    Merchant, A., Batzner, S., Schoenholz, S. S., Aykol, M., Cheon, G., and Cubuk, E. D. Scaling deep learning for materials discovery. Nature, pp. 1–6, 2023

    2023

  61. [70]

    P., Tancik, M., Barron, J

    Mildenhall, B., Srinivasan, P. P., Tancik, M., Barron, J. T., Ramamoorthi, R., and Ng, R. Nerf: Representing scenes as neural radiance fields for view synthesis. Communications of the ACM, 65(1):99–106, 2021

    2021

  62. [71]

    Development of three-dimensional GPU DEM code–benchmarking, validation, and application in mineral processing

    Mittal, A., Mangadoddy, N., and Banerjee, R. Development of three-dimensional GPU DEM code–benchmarking, validation, and application in mineral processing. Comput. Part. Mech., 10(6):1533–1556, 2023

    2023

  63. [72]

    J., Kornbluth, M., and Kozinsky, B

    Musaelian, A., Batzner, S., Johansson, A., Sun, L., Owen, C. J., Kornbluth, M., and Kozinsky, B. Learning local equivariant representations for large-scale atomistic dynamics. Nature Communications, 14(1):579, 2023

    2023

  64. [73]

    Nasato, D. S. and P ¨oschel, T. Influence of particle shape in additive manufacturing: Discrete element simulations of polyamide 11 and polyamide 12. Addit. Manuf., 36:101421, 2020

    2020

  65. [74]

    K., and Grover, A

    Nguyen, T., Brandstetter, J., Kapoor, A., Gupta, J. K., and Grover, A. Climax: A foundation model for weather and climate. In ICML, volume 202 of Proceedings of Machine Learning Research, pp. 25904–25938. PMLR, 2023

    2023

  66. [75]

    R., Zarghami, R., Sotudeh-Gharebagh, R., and Mostoufi, N

    Norouzi, H. R., Zarghami, R., Sotudeh-Gharebagh, R., and Mostoufi, N. Coupled CFD-DEM modeling: formulation, implementation and application to multiphase flows . John Wiley & Sons, 2016. 30

    2016

  67. [76]

    Fourcastnet: A global data-driven high-resolution weather model using adaptive fourier neural operators

    Pathak, J., Subramanian, S., Harrington, P., Raja, S., Chattopadhyay, A., Mardani, M., Kurth, T., Hall, D., Li, Z., Azizzadenesheli, K., et al. Fourcastnet: A global data-driven high-resolution weather model using adaptive fourier neural operators. arXiv preprint arXiv:2202.11...

    2022 arXiv

  68. [77]

    and Xie, S

    Peebles, W. and Xie, S. Scalable diffusion models with transformers. In ICCV, pp. 4172–

  69. [78]

    Film: Visual reasoning with a general conditioning layer

    Perez, E., Strub, F., De Vries, H., Dumoulin, V ., and Courville, A. Film: Visual reasoning with a general conditioning layer. Proceedings of the AAAI conference on artificial intelli- gence, 32(1):3942–3951, 2018

    2018

  70. [79]

    Pfaff, T., Fortunato, M., Sanchez-Gonzalez, A., and Battaglia, P. W. Learning mesh-based simulation with graph networks. In ICLR, 2021

    2021

  71. [80]

    High-resolution image synthesis with latent diffusion models

    Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on com- puter vision and pattern recognition, pp. 10684–10695, 2022

    2022

  72. [81]

    and Koshizuka, S

    Sakai, M. and Koshizuka, S. Large-scale discrete element modeling in pneumatic conveying. Chem. Eng. Sci., 64(3):533–539, 2009

    2009

  73. [82]

    Learning to simulate complex physics with graph networks

    Sanchez-Gonzalez, A., Godwin, J., Pfaff, T., Ying, R., Leskovec, J., and Battaglia, P. Learning to simulate complex physics with graph networks. In ICML, volume 119 of Proceedings of Machine Learning Research, pp. 8459–8468. PMLR, 2020

    2020

  74. [83]

    C., Hagenbuchner, M., and Monfardini, G

    Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., and Monfardini, G. The graph neural network model. IEEE transactions on neural networks, 20(1):61–80, 2008

    2008

  75. [84]

    Seidman, J., Kissas, G., Perdikaris, P., and Pappas, G. J. Nomad: Nonlinear manifold de- coders for operator learning. Advances in Neural Information Processing Systems, 35:5601– 5613, 2022

    2022

  76. [85]

    Megatron-lm: Training multi-billion parameter language models using model parallelism

    Shoeybi, M., Patwary, M., Puri, R., LeGresley, P., Casper, J., and Catanzaro, B. Megatron-lm: Training multi-billion parameter language models using model parallelism. arXiv preprint arXiv:1909.08053, 2019

    1909 arXiv

  77. [86]

    N., Bergman, A

    Sitzmann, V ., Martel, J. N., Bergman, A. W., Lindell, D. B., and Wetzstein, G. Implicit neural representations with periodic activation functions. Advances in Neural Information Processing Systems, 33:7462–7473, 2020

    2020

  78. [87]

    Resiliency of deep neural networks under quantization

    Sung, W., Shin, S., and Hwang, K. Resiliency of deep neural networks under quantization. arXiv preprint arXiv:1511.06488, 2015

    2015 arXiv

  79. [88]

    P., Galletti, G., Brandstetter, J., Adami, S., and Adams, N

    Toshev, A. P., Galletti, G., Brandstetter, J., Adami, S., and Adams, N. A. Learning la- grangian fluid mechanics with e ( 3)-equivariant graph neural networks. arXiv preprint arXiv:2305.15603, 2023

    2023 arXiv

  80. [89]

    P., Erbesdobler, J

    Toshev, A. P., Erbesdobler, J. A., Adams, N. A., and Brandstetter, J. Neural SPH: improved neural modeling of lagrangian fluid dynamics. In ICML, volume 235 of Proceedings of Ma- chine Learning Research, pp. 48428–48452. PMLR, 2024

    2024

  81. [90]

    N., Kaiser, Ł., and Polosukhin, I

    Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., and Polosukhin, I. Attention is all you need. Advances in neural information processing systems, 30, 2017

    2017

  82. [91]

    and Brunton, S

    Vinuesa, R. and Brunton, S. L. Enhancing computational fluid dynamics with machine learn- ing. Nature Computational Science, 2(6):358–366, 2022

    2022

  83. [92]

    Study on the modeling method of sunflower seed particles based on the discrete element method

    Wang, S., Yu, Z., Zhang, W., et al. Study on the modeling method of sunflower seed particles based on the discrete element method. Comput. Electron. Agr, 198:107012, 2022

    2022

  84. [93]

    H., Sankaran, S., Wang, H., Pappas, G

    Wang, S., Seidman, J. H., Sankaran, S., Wang, H., Pappas, G. J., and Perdikaris, P. Bridg- ing operator learning and conditioned neural fields: A unifying perspective. arXiv preprint arXiv:2405.13998, 2024. 31

    2024 arXiv

  85. [94]

    and Wang, C

    Wang, T. and Wang, C. Latent neural operator for solving forward and inverse pde problems. arXiv preprint arXiv:2406.03923, 2024

    2024 arXiv

  86. [95]

    G., Tabor, G., Jasak, H., and Fureby, C

    Weller, H. G., Tabor, G., Jasak, H., and Fureby, C. A tensorial approach to computational continuum mechanics using object-oriented techniques. Computer in Physics , 12(6):620– 631, 11 1998. ISSN 0894-1866

    1998

  87. [96]

    Transolver: A fast transformer solver for pdes on general geometries

    Wu, H., Luo, H., Wang, H., Wang, J., and Long, M. Transolver: A fast transformer solver for pdes on general geometries. In ICML, volume 235 of Proceedings of Machine Learning Research, pp. 53681–53705. PMLR, 2024

    2024

  88. [97]

    Neural fields in visual computing and beyond

    Xie, Y ., Takikawa, T., Saito, S., Litany, O., Yan, S., Khan, N., Tombari, F., Tompkin, J., Sitzmann, V ., and Sridhar, S. Neural fields in visual computing and beyond. Computer Graphics Forum, 41(2):641–676, 2022

    2022

  89. [98]

    Gspmd: general and scalable parallelization for ml computation graphs

    Xu, Y ., Lee, H., Chen, D., Hechtman, B., Huang, Y ., Joshi, R., Krikun, M., Lepikhin, D., Ly, A., Maggioni, M., et al. Gspmd: general and scalable parallelization for ml computation graphs. arXiv preprint arXiv:2105.04663, 2021

    2021 arXiv

  90. [99]

    A review of the application of discrete element method in agricultural engineering: A case study of soybean

    Yan, D., Yu, J., Wang, Y ., Zhou, L., Sun, K., and Tian, Y . A review of the application of discrete element method in agricultural engineering: A case study of soybean. Processes, 10 (7):1305, 2022

    2022

  91. [100]

    A review of real-time fault diagnosis methods for industrial smart manufacturing

    Yan, W., Wang, J., Lu, S., Zhou, M., and Peng, X. A review of real-time fault diagnosis methods for industrial smart manufacturing. Processes, 11(2), 2023. ISSN 2227-9717

    2023

  92. [101]

    CFD-DEM modeling of dense gas-solid reacting flow in the framework of GPU

    Yu, J., Wang, S., Luo, K., and Fan, J. CFD-DEM modeling of dense gas-solid reacting flow in the framework of GPU. Chem. Eng. J, 484:149480, 2024. ISSN 1385-8947

    2024

  93. [102]

    Mattergen: a generative model for inorganic materials design

    Zeni, C., Pinsler, R., Z ¨ugner, D., Fowler, A., Horton, M., Fu, X., Shysheya, S., Crabb ´e, J., Sun, L., Smith, J., et al. Mattergen: a generative model for inorganic materials design. arXiv preprint arXiv:2312.03687, 2023

    2023 arXiv

  94. [103]

    Discrete element method simulation of granu- lar materials considering particle breakage in geotechnical and mining engineering: A short review

    Zhang, C., Chen, Y ., Wang, Y ., and Bai, Q. Discrete element method simulation of granu- lar materials considering particle breakage in geotechnical and mining engineering: A short review. Green and Smart Mining Engineering, 2024

    2024

  95. [104]

    Comparison of roller-spreading and blade-spreading processes in powder-bed additive manufacturing by DEM simulations

    Zhang, J., Tan, Y ., Xiao, X., and Jiang, S. Comparison of roller-spreading and blade-spreading processes in powder-bed additive manufacturing by DEM simulations. Particuology, 66:48– 58, 2022

    2022

  96. [105]

    Artificial intelligence for science in quantum, atomistic, and continuum systems

    Zhang, X., Wang, L., Helwig, J., Luo, Y ., Fu, C., Xie, Y ., Liu, M., Lin, Y ., Xu, Z., Yan, K., et al. Artificial intelligence for science in quantum, atomistic, and continuum systems. arXiv preprint arXiv:2307.08423, 2023

    2023 arXiv

  97. [106]

    Applications of discrete element method in the research of agricultural machinery: A review

    Zhao, H., Huang, Y ., Liu, Z., Liu, W., and Zheng, Z. Applications of discrete element method in the research of agricultural machinery: A review. Agriculture, 11(5):425, 2021

    2021

  98. [107]

    R., and Farimani, A

    Zhou, A., Li, Z., Schneier, M., Buchanan Jr, J. R., and Farimani, A. B. Text2pde: Latent diffusion models for accessible physics simulation. arXiv preprint arXiv:2410.01153, 2024. 32

    2024 arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.