Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

5D Neural Surrogates for Nonlinear Gyrokinetic Simulations of Plasma Turbulence

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

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

Pith's one-line read A 5D neural surrogate matches gyrokinetic turbulence fields and heat flux at roughly 200 times lower cost than the solver.

desk verdict A genuinely new 5D surrogate architecture with an honest but under-evidenced evaluation; the heat-flux claim hinges on an unspecified normalization inversion. read the letter →

arxiv 2502.07469 v1 pith:UQRZGYUQ submitted 2025-02-11 physics.plasm-ph cs.AIcs.LGstat.ML

Gianluca Galletti , Fabian Paischer , Paul Setinek , William Hornsby , Lorenzo Zanisi , Naomi Carey , Stanislas Pamela , Johannes Brandstetter This is my paper · ORCID
classification physics.plasm-phcs.AIcs.LGstat.ML PACS 52.35.Ra52.65.-y
keywords gyrokineticsimulationsplasmaturbulenceneuralsurrogate5DdistributionfunctionvisiontransformerSwin-UNetheatfluxfusionenergy
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

Plasma turbulence in fusion devices is modelled by evolving a five-dimensional distribution function describing the ions, and a single numerical simulation can take weeks. This paper tries to show that a neural network trained on the full 5D field can replace one expensive step of that evolution. The model, a five-dimensional hierarchical vision transformer called 5D Swin-UNet, is trained on gyrokinetic simulations with adiabatic electrons—a simplified case where electrons respond instantly and only the ion distribution is evolved—and tested on a trajectory with an ion temperature gradient it never saw. The authors report single-step predictions whose heat-flux time trace and non-zonal parts of the electrostatic potentials align with the solver, at roughly two orders of magnitude lower cost per step. If that stands, turbulence modelling becomes fast enough for iterative design and control studies that full gyrokinetic runs cannot support.

What carries the argument

The load-bearing object is 5D Swin-UNet, a hierarchical vision transformer extended to five dimensions. It partitions the 5D field into tokens through linear patch embedding, applies local shifted-window multi-head self-attention in all five dimensions to keep attention cost manageable, and reconstructs the next snapshot through a UNet-style encoder-decoder with patch merging and expansion. The same integration used in the numerical pipeline turns the predicted field into electrostatic potentials and heat flux, which is why the evaluation can claim physical fidelity rather than only pixel-level similarity. Because patch operations are linear rather than convolutional, the design avoids the high cost of high-dimensional convolutions without a dedicated implementation.

What would settle it

Train the same model with one global scaling factor instead of per-sample normalization and compare the absolute heat flux predicted for the holdout trajectory against GKW: agreement would support the claim, while divergence would show that the current match depends on per-sample scaling. A complementary check is to run the model autoregressively and measure how many steps the heat-flux trace survives before the overestimated zonal mode damps it.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that a neural surrogate can evolve the full 5D perturbed ion distribution function $\delta f$ for one time step and still produce physically meaningful transport diagnostics. The surrogate is trained on trajectories from the GKW solver with adiabatic electrons and ion temperature gradient values in the range $[4.9, 8.9]$, then applied to the held-out trajectory at ITG $=6.9$. From the predicted distribution the authors compute electrostatic potentials and the heat flux time trace; the non-zonal potential structure and the heat flux align with ground truth, while the zonal-flow mode—the large-scale flow that regulates turbulence—is overestimated, particularly in the linear phase. They measure 360 ms per step on an A100 GPU versus roughly 80 seconds for GKW on 64 CPU cores, which they describe as about two orders of magnitude faster. The claim is scoped to single-step prediction in the adiabatic-electron approximation; autoregressive rollouts, where the model's own outputs become the next input, are left as future work.

Load-bearing premise

The load-bearing premise is that the per-sample normalization used before training preserves the absolute amplitude of the distribution function; if it removes true scale, the matching heat-flux trace could be a shape artifact rather than a physically valid prediction.

Editorial extensions

If this is right

  • If the central claim holds, one gyrokinetic step costs about 360 ms on a single GPU instead of about 80 seconds on 64 CPU cores, making parameter scans and control-loop studies practical.
  • If the central claim holds, the surrogate outputs the full 5D field, so heat flux and electrostatic potentials can be computed from the prediction at the next time step through the same integrals used by the numerical pipeline.
  • If the central claim holds, a trajectory driven by an unseen ion temperature gradient (ITG=6.9) yields heat-flux predictions that track the solver, indicating transfer across turbulence drive strength.
  • The paper's stated next step is to correct the zonal-mode overestimation, which does not affect single-step heat flux but is expected to damp autoregressive rollouts.

Reading between the lines

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

  • A reader may infer that the per-sample normalization is the key confound to test next: if a global scaling factor destroys the heat-flux match, the current result could be shape-matching rather than absolute transport prediction.
  • Because the shifted-window attention is dimension-agnostic, the same architecture could in principle be lifted to 6D kinetic-electron or electromagnetic gyrokinetics, but the fixed-resolution patch embedding would first need a neural-operator-style upgrade.
  • A cheap experiment the paper does not run is to reweight the loss toward the zonal mode; the paper's own diagnosis predicts this should improve single-step potential accuracy and make autoregressive rollouts more stable.
  • With only one holdout trajectory evaluated, the strongest generality test would be a multi-ITG holdout set with error bars, which the current dataset cannot support.
Share X Bluesky LinkedIn Reddit HN

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 5D Swin-UNet, a hierarchical vision transformer extended to five dimensions, as a neural surrogate for nonlinear gyrokinetic simulations under the adiabatic-electron approximation. The model is trained on next-step prediction of the 5D ion distribution function from GKW simulations across five ion-temperature-gradient (ITG) values, with one ITG held out. The authors evaluate the surrogate by visualizing the predicted distribution function, electrostatic potentials, and the heat-flux time trace, and report a two-orders-of-magnitude speedup over GKW for single-step predictions. The central claim is that the surrogate accurately infers downstream physical quantities such as heat flux and electrostatic potentials.

Significance. If the central claim holds, this is an important proof-of-concept: it is the first attempt to directly evolve the 5D gyrokinetic distribution function with a neural network rather than operating on reduced input spaces, and the proposed n-dimensional shifted-window attention is a general architectural contribution. The paper also provides a useful visualization scheme for 5D fields and a clearly stated speed advantage for single-step prediction. However, the current evidence for the accuracy claim is weakened by the unspecified inverse-normalization protocol, the use of the holdout trajectory for model selection, and the absence of quantitative error metrics. These issues are fixable and the underlying approach is promising, but the manuscript in its present form does not fully substantiate the abstract's broad accuracy claims.

major comments (4)
  1. [Section 4, Experiments; Figure 5] Section 4 states that 'Each sample of a trajectory is normalized on a per-sample basis,' but the paper never specifies how the model output is mapped back to physical units before computing the heat flux and electrostatic potentials. If the per-sample mean and standard deviation of the ground-truth target snapshot are used for the inverse transformation, then the absolute amplitude of the predicted heat flux is partly supplied by the target, making the agreement in Figure 5 an artifact of the evaluation protocol. Please state the exact inverse normalization and provide an evaluation that does not use target-snapshot statistics (e.g., denormalizing with the input snapshot's statistics or with a fixed reference normalization). Without this, the central claim of accurately inferring the heat flux time trace is not substantiated.
  2. [Section 4 and Appendix C] The holdout trajectory is used for model selection: Section 4 says the model is 'evaluat[ed] every 20 epochs on the holdout trajectory' and Appendix C says 'Model selection is performed every 20 training epochs based on the mean squared error on the holdout trajectory.' Consequently, the ITG=6.9 trajectory is not a fully unseen test case; it influences the selected checkpoint. The claim of generalization to an ITG never observed during training should be reframed as validation performance, or a separate test trajectory should be held out from all selection decisions.
  3. [Section 4, Figures 3-5] The central accuracy claims are supported only by qualitative visual comparisons; no quantitative error metrics (e.g., relative L2 error of the distribution function, relative error or correlation of the heat flux trace, or mode-resolved potential errors) are reported for any figure. Please report numbers, preferably with error bars over multiple training runs, so that 'accurately infer' has an operational meaning and the reader can judge the magnitude of the zonal-mode overestimation.
  4. [Abstract and Section 4, Figure 4a] The abstract claims accurate inference of electrostatic potentials without qualification, but Figure 4a shows that the zonal mode is 'strongly overestimated' in the linear phase (the paper's own description). This is a qualitative contradiction of the abstract's broad claim. The claim should be qualified to exclude or explicitly quantify the zonal-mode error, and the impact of this error on autoregressive rollout stability should be discussed as a known limitation.
minor comments (5)
  1. [Section 3.3] The sentence 'Potentials are computed by an integral over the velocities V|| and Vµ of the 5D distribution function. on the predictions of our surrogate model.' contains a grammatical error and a sentence fragment; it should be rewritten.
  2. [Section 4] The phrase 'euqal colour scale' should be 'equal color scale', and the phrase 'the the vertical wave vector' contains a duplicated article.
  3. [Conclusions] The word 'distributon' in the first sentence is a typo and should be 'distribution'.
  4. [Figure 5 caption] The notation 'Heat flux time trace (R δf)' is unclear; please define the integral operator R or use the standard heat-flux definition, and specify the units or normalization used in the plot.
  5. [Appendix B] Appendix B first lists ITG values {5.9, 7.9, 10, 15} for flux-trace discussion and then the dataset ITG values {4.9, 5.9, 6.9, 7.9, 8.9}; the relationship between these sets and the final training choices should be clarified.

Circularity Check

1 steps flagged · score 6.0 of 10

Per-sample normalization may inject ground-truth amplitude into the heat-flux trace, making the central quantitative claim partly circular.

  1. fitted input called prediction [Section 4 (Experiments), 'Heat flux time trace' and Figure 5; see also Section 3.3 Evaluation]
    "Each sample of a trajectory is normalized on a per-sample basis. ... The heat flux is a scalar value that oscillates along an average in the saturated phase, and it is computed as a function of the 5D distribution function and the electrostatic potential. ... Heat flux time trace ( R δf ) for ground-truth (GT) and single-step prediction of 5D Swin-UNet (pred) for the holdout trajectory (ITG=6.9)."

    A per-sample z-score removes each snapshot's own mean and variance, so the model output is a normalized shape rather than a physical field. To compute a physical heat flux, one must de-normalize the prediction, but the paper never specifies this step. If the inversion uses the ground-truth sample's mean and standard deviation—the natural way to plot a normalized prediction on GKW's physical flux axis—then the amplitude of the predicted distribution function, and hence of its integral ∫δf, is exactly the target sample's amplitude. The close agreement in Figure 5 is then forced by construction at the amplitude level; the model only contributes the normalized shape.

full rationale

This is an empirical machine-learning paper rather than a first-principles derivation, so most of the claimed chain is architectural and data-driven, not circular. The extension of Swin Transformer to five dimensions is a straightforward generalization with no hidden ansatz smuggled in via citation, and the authors' prior neural-operator papers are contextual rather than load-bearing. The one serious circularity risk is preprocessing and evaluation: every sample is normalized with its own per-sample statistics, while the headline validation is the heat flux time trace, which is an integral of the predicted 5D distribution function. Because no de-normalization or restoration of physical units is described, the reported match in Figure 5 is consistent with the model only predicting a normalized shape whose absolute amplitude is supplied by the ground-truth sample's mean and standard deviation. Under that reading, the physically meaningful part of the downstream quantity—its amplitude—is equal by construction to the target, making the abstract's claim of accurate heat-flux inference partially circular. A secondary concern is that the holdout trajectory is used for model selection every 20 epochs, so the reported numbers are not a clean out-of-sample estimate; this is evaluation leakage rather than circularity by construction. The zonal-mode overestimation reported in Figure 4a confirms that amplitude errors do occur, which makes the unspecified normalization protocol consequential. Overall, one central evaluation step is vulnerable to reduction by construction, while the rest of the paper is self-contained empirical modeling.

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

This is an empirical machine learning paper; the central claim rests on trained network weights and several modeling choices. No new physical entities are introduced. The free parameters are the network parameters and hand-chosen training hyperparameters, while the axioms are the domain assumptions underlying the data generation and evaluation.

free parameters (5)
  • 5D Swin-UNet weights = learned from training data (not reported)
    The central claim depends entirely on the trained model weights, which are fitted to GKW data via mean squared error loss.
  • peak learning rate = 1e-3
    Hyperparameter chosen by hand (Appendix C) and part of the training recipe.
  • weight decay = 1e-5
    Hyperparameter chosen by hand (Appendix C).
  • number of training epochs = 100
    Chosen by hand; model selection every 20 epochs on the holdout trajectory (Appendix C).
  • ITG training values = [4.9, 5.9, 7.9, 8.9]
    The drive parameter is sampled in the range [4,10]; the holdout is 6.9, an interpolation between training values (Appendix B).
assumptions (5)
  • domain assumption The gyrokinetic equation with δf splitting (Eq. 1) accurately models plasma turbulence.
    The surrogate is trained on GKW solutions of this equation; if the equation is not a valid model, the surrogate learns incorrect physics.
  • domain assumption The adiabatic electron approximation is sufficient for the target physics.
    Only the ion distribution function is evolved; electrons are assumed Boltzmann-like (Section 3.1). This excludes kinetic electron effects relevant in many reactor scenarios.
  • ad hoc to paper Per-sample normalization preserves the information needed for heat flux inference.
    Each sample is normalized on a per-sample basis (Section 4); this may remove absolute amplitude information that determines transport levels.
  • domain assumption Four training trajectories in the ITG range [4.9, 8.9] are sufficient to generalize to the unseen ITG 6.9.
    A single holdout trajectory at ITG 6.9 is interpolated between training values; no evidence is provided for extrapolation to other parameters or geometries.
  • domain assumption Single-step prediction accuracy implies usefulness for downstream physical inference.
    The paper evaluates only single-step predictions and acknowledges that autoregressive rollouts fail due to zonal flow overestimation (Section 4).

how reviews work

0 comments
Cite this review

Pith. "Pith review of 5D Neural Surrogates for Nonlinear Gyrokinetic Simulations of Plasma Turbulence." pith.science (2026). https://pith.science/paper/UQRZGYUQ

@misc{pith2026250207469,
  author       = {Pith},
  title        = {Pith review of: 5D Neural Surrogates for Nonlinear Gyrokinetic Simulations of Plasma Turbulence},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UQRZGYUQ}},
  note         = {Machine review of arXiv:2502.07469}
}
read the original abstract

Nuclear fusion plays a pivotal role in the quest for reliable and sustainable energy production. A major roadblock to achieving commercially viable fusion power is understanding plasma turbulence, which can significantly degrade plasma confinement. Modelling turbulence is crucial to design performing plasma scenarios for next-generation reactor-class devices and current experimental machines. The nonlinear gyrokinetic equation underpinning turbulence modelling evolves a 5D distribution function over time. Solving this equation numerically is extremely expensive, requiring up to weeks for a single run to converge, making it unfeasible for iterative optimisation and control studies. In this work, we propose a method for training neural surrogates for 5D gyrokinetic simulations. Our method extends a hierarchical vision transformer to five dimensions and is trained on the 5D distribution function for the adiabatic electron approximation. We demonstrate that our model can accurately infer downstream physical quantities such as heat flux time trace and electrostatic potentials for single-step predictions two orders of magnitude faster than numerical codes. Our work paves the way towards neural surrogates for plasma turbulence simulations to accelerate deployment of commercial energy production via nuclear fusion.

Figures

Figures reproduced from arXiv: 2502.07469 by the authors.

Figure 1
Figure 1. Overview of the model architecture and n-dimensional attention. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Left: 5D distribution function with an ITG of 7.9 in the linear phase (t = 1.9). Right: 5D distribution function with an ITG of 7.9 in the saturated phase (t = 50.6). in 660 training samples and one unseen trajectory (165 samples). Appendix B provides a detailed discussion on the choice of ITGs used for data generation. To visually inspect the data, we slice trajectories according to timesteps and visualize the 5D d… view at source ↗
Figure 3
Figure 3. 5D Swin-UNet can accurately predict the distribution functon in five dimensions. We [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Visualization and comparison of the electrostatic potentials for model predictions [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Heat flux time trace (R δf) for ground￾truth (GT) and single-step prediction of 5D Swin￾UNet (pred) for the holdout trajectory (ITG=6.9). Heat flux time trace. We assess whether the model correctly infers the heat flux time trace of the holdout simulation (ITG=6.9) [P…
Figure 6
Figure 6. Figure 6: Flux trace over time (left) and averaged (right) for selected ITG values. [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Distribution function δf with an ITG of 7.9 at time t = 1.9 (Linear Phase). 12 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Distribution function δf with an ITG of 7.9 at time t = 50.6 (Saturated Phase). 13 [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. NeuroQD: A Learning-Based Simulation Framework For Quantum Dot Devices

    cond-mat.mes-hall 2025-09 conditional novelty 6.0 of 10

    A U-Net trained on one small quantum dot device predicts electrostatic potentials for devices up to 99 dots, giving a 1000x faster simulator that reproduces real-device tuning features.

Reference graph

Works this paper leans on

31 extracted references · 6 canonical work pages · cited by 1 Pith paper

  1. [3]

    C Bourdelle, J Citrin, B Baiocchi, A Casati, P Cottier, X Garbet, and F Imbeaux and

    doi: 10.48550/ARXIV .2405.13063. C Bourdelle, J Citrin, B Baiocchi, A Casati, P Cottier, X Garbet, and F Imbeaux and. Core turbulent transport in tokamak plasmas: bridging theory and experiment with QuaLiKiz. Plasma Physics and Controlled Fusion, 58(1):014036, December

    arXiv doi:10.48550/arxiv.2405.13063

  2. [5]

    Brunton, Bernd R

    Steven L. Brunton, Bernd R. Noack, and Petros Koumoutsakos. Machine learning for fluid mechan- ics. Annual Review of Fluid Mechanics, 52(V olume 52, 2020):477–508,

    work page 2020

  3. [6]

    Those figures show all 10 pairwise combinations of axes

    in the linear and saturated phases, respectively. Those figures show all 10 pairwise combinations of axes. To repre- sent the remaining 3 axes in a 2D image, we compress them by taking the average (see Figures 7a and 8a), computing the standard deviation (see Figures 7b and 8b), or extracting slices at specific positions mainly at the start (see Figures 7...

    work page 2021

  4. [8]

    doi: 10.1063/5.0136752. Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszko- reit, and Neil Houlsby. An image is worth 16x16 words: Transformers for image recognition at scale. In 9th International Conference on Learning Re...

    doi:10.1063/5.0136752

  5. [9]

    doi: https://doi.org/10.1002/ctpp.202200137. W. A Hornsby, A. Gray, J. Buchanan, B. S. Patel, D. Kennedy, F. J. Casson, C. M. Roach, M. B. Lykkegaard, H. Nguyen, N. Papadimas, B. Fourcin, and J. Hart. Gaussian process regression models for the properties of micro-tearing modes in spherical tokamaks. Physics of Plasmas, 31 (1), jan

    doi:10.1002/ctpp.202200137

  6. [10]

    doi: 10.1063/5.0174478

    ISSN 1089-7674. doi: 10.1063/5.0174478. K. Itoh, S.-I. Itoh, P. H. Diamond, T. S. Hahm, A. Fujisawa, G. R. Tynan, M. Yagi, and Y . Nagashima. Physics of zonal flowsa). Physics of Plasmas, 13(5):055502, 05

    doi:10.1063/5.0174478

  7. [12]

    Kingma and Jimmy Ba

    Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In Yoshua Bengio and Yann LeCun (eds.), 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings,

    work page 2015

  8. [13]

    ISBN 9798400701900

    Association for Computing Machinery. ISBN 9798400701900. doi: 10.1145/3592979. 3593412. Remi Lam, Alvaro Sanchez-Gonzalez, Matthew Willson, Peter Wirnsberger, Meire Fortunato, Fer- ran Alet, Suman Ravuri, Timo Ewalds, Zach Eaton-Rosen, Weihua Hu, Alexander Merose, Stephan Hoyer, George Holland, Oriol Vinyals, Jacklynn Stott, Alexander Pritzel, Shakir Mo- ...

    doi:10.1145/3592979

Show all 31 references
  1. [14]

    Zongyi Li, Nikola B

    doi: 10.1126/science.adi2336. Zongyi Li, Nikola B. Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, and Anima Anandkumar. Neural operator: Graph kernel network for partial differential equations. CoRR, abs/2003.03485,

    arXiv

  2. [15]

    Swin transformer: Hierarchical vision transformer using shifted windows

    Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin transformer: Hierarchical vision transformer using shifted windows. In 2021 IEEE/CVF International Conference on Computer Vision, ICCV 2021, Montreal, QC, Canada, October 10-17, 20...

    2021

  3. [18]

    doi: 10.1038/S42256-021-00302-5. O. Meneghini, S.P. Smith, P.B. Snyder, G.M. Staebler, J. Candy, E. Belli, L. Lao, M. Kostuk, T. Luce, T. Luda, J.M. Park, and F. Poli. Self-consistent core-pedestal transport simulations with neural network accelerated models. Nuclear Fusion, 5...

    doi

  4. [19]

    Amil Merchant, Simon L

    doi: 10.1088/1741-4326/ aa7776. Amil Merchant, Simon L. Batzner, Samuel S. Schoenholz, Muratahan Aykol, Gowoon Cheon, and Ekin Dogus Cubuk. Scaling deep learning for materials discovery. Nat., 624(7990):80–85,

    doi

  5. [20]

    doi: 10.1038/S41586-023-06735-9. S. Van Mulders, F. Felici, O. Sauter, J. Citrin, A. Ho, M. Marin, and K.L. van de Plassche. Rapid optimization of stationary tokamak plasmas in RAPTOR: demonstration for the ITER hybrid scenario with neural network surrogate transport model QLK...

    doi

  6. [21]

    8 Preprint

    doi: 10.1088/1741-4326/ac0d12. 8 Preprint. E. Narita, M. Honda, S. Maeyama, and T.-H. Watanabe. Toward efficient runs of nonlinear gyroki- netic simulations assisted by a convolutional neural network model recognizing wavenumber- space images. Nuclear Fusion, 62(8):086037, jun

    doi

  7. [22]

    Tung Nguyen, Johannes Brandstetter, Ashish Kapoor, Jayesh K

    doi: 10.1088/1741-4326/ac70e8. Tung Nguyen, Johannes Brandstetter, Ashish Kapoor, Jayesh K. Gupta, and Aditya Grover. Climax: A foundation model for weather and climate. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (...

    doi

  8. [25]

    doi: 10.1007/978-3-319-24574-4\_28. Jacob H. Seidman, Georgios Kissas, Paris Perdikaris, and George J. Pappas. NOMAD: nonlin- ear manifold decoders for operator learning. In Sanmi Koyejo, S. Mohamed, A. Agarwal, Danielle Belgrave, K. Cho, and A. Oh (eds.),Advances in Neural In...

    doi

  9. [28]

    Mattersim: A deep learning atomistic model across elements, temperatures and pressures

    Han Yang, Chenxi Hu, Yichi Zhou, Xixian Liu, Yu Shi, Jielan Li, Guanzhi Li, Zekun Chen, Shuizhou Chen, Claudio Zeni, Matthew Horton, Robert Pinsler, Andrew Fowler, Daniel Zügner, Tian Xie, Jake Smith, Lixin Sun, Qian Wang, Lingyu Kong, Chang Liu, Hongxia Hao, and Ziheng Lu. Ma...

    arXiv

  10. [30]

    doi: 10.48550/ARXIV .2307.08423. SUPPLEMENTARY MATERIAL CONTENTS A Gyrokinetic framework 10 B Data Generation and Visualisation 10 C Implementation details 11 A G YROKINETIC FRAMEWORK Solved within GKW is the gyrokinetic set of equations. The full details can be found in Peete...

    2009 doi arXiv

  11. [2006]

    doi: 10.1063/1.2178779

    ISSN 1070-664X. doi: 10.1063/1.2178779. 7 Preprint. John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ronneberger, Kathryn Tunyasuvunakool, Russ Bates, Augustin Žídek, Anna Potapenko, et al. Highly accurate protein structure prediction with alpha...

    doi

  12. [2007]

    doi: 10.1063/1.2436852

    ISSN 1089-7674. doi: 10.1063/1.2436852. Nils Thuerey, Philipp Holl, Maximilian Müller, Patrick Schnell, Felix Trost, and Kiwon Um. Physics-based deep learning. CoRR, abs/2109.05237,

    arXiv

  13. [2009]

    doi: https://doi.org/10.1016/j.cpc.2009.07.001

    ISSN 0010-4655. doi: https://doi.org/10.1016/j.cpc.2009.07.001. 40 YEARS OF CPC: A celebratory issue focused on quality software for high performance, grid and novel computing architectures. G.V . Pereverzev and P.N. Yushmanov. Astra - automated system for transport analysis,

    2009 doi

  14. [2010]

    doi: 10.1063/1.3505308

    ISSN 1089-7674. doi: 10.1063/1.3505308. G. M. Staebler, J. E. Kinsey, and R. E. Waltz. A theory-based transport model with comprehensive physics. Physics of Plasmas, 14(5), may

    doi

  15. [2014]

    Olaf Ronneberger, Philipp Fischer, and Thomas Brox

    doi: 10.1585/pfr.9.3403023. Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedi- cal image segmentation. In Nassir Navab, Joachim Hornegger, William M. Wells III, and Alejan- dro F. Frangi (eds.), Medical Image Computing and Computer-A...

    doi

  16. [2015]

    Johannes Brandstetter

    doi: 10.1088/0741-3335/58/1/014036. Johannes Brandstetter. Envisioning better benchmarks for machine learning pde solvers. Nature Machine Intelligence, pp. 1–2,

    doi

  17. [2017]

    doi: 10.1088/1361-6587/aa8aeb. J. Citrin, P. Trochim, T. Goerler, D. Pfau, K. L. van de Plassche, and F. Jenko. Fast transport simulations with higher-fidelity surrogate models for ITER. Physics of Plasmas, 30(6), jun

    doi

  18. [2020]

    doi: https://doi.org/10.1146/annurev-fluid-010719-060214

    ISSN 1545-4479. doi: https://doi.org/10.1146/annurev-fluid-010719-060214. J Citrin, C Bourdelle, F J Casson, C Angioni, N Bonanomi, Y Camenen, X Garbet, L Garzotti, T Görler, O Gürcan, F Koechl, F Imbeaux, O Linder, K van de Plassche, P Strand, and G Szepesi and. Tractable flu...

    doi

  19. [2021]

    Ze Liu, Jia Ning, Yue Cao, Yixuan Wei, Zheng Zhang, Stephen Lin, and Han Hu

    doi: 10.1109/ICCV48922.2021.00986. Ze Liu, Jia Ning, Yue Cao, Yixuan Wei, Zheng Zhang, Stephen Lin, and Han Hu. Video swin transformer. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2022, New Orleans, LA, USA, June 18-24, 2022, pp. 3192–3201. IEEE,

    2021

  20. [2022]

    Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis

    doi: 10.1109/ CVPR52688.2022.00320. Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis. Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.Nat. Mach. Intell., 3(3):218–229,

    2022

  21. [2023]

    Cristian Bodnar, Wessel P

    doi: 10.1038/S41586-023-06185-3. Cristian Bodnar, Wessel P. Bruinsma, Ana Lucic, Megan Stanley, Johannes Brandstetter, Patrick Garvan, Maik Riechert, Jonathan A. Weyn, Haiyu Dong, Anna Vaughan, Jayesh K. Gupta, Kit Thambiratnam, Alex Archibald, Elizabeth Heider, Max Welling, R...

    arXiv

  22. [2024]

    Universal physics transformers

    Benedikt Alkin, Andreas Fürst, Simon Schmid, Lukas Gruber, Markus Holzleitner, and Johannes Brandstetter. Universal physics transformers. CoRR, abs/2402.12365, 2024a. doi: 10.48550/ ARXIV .2402.12365. Benedikt Alkin, Tobias Kronlachner, Samuele Papa, Stefan Pirker, Thomas Lich...

    doi arXiv

  23. [2025]

    Xuan Zhang, Limei Wang, Jacob Helwig, Youzhi Luo, Cong Fu, Yaochen Xie, Meng Liu, Yuchao Lin, Zhao Xu, Keqiang Yan, Keir Adams, Maurice Weiler, Xiner Li, Tianfan Fu, Yucheng Wang, 9 Preprint. Haiyang Yu, Yuqing Xie, Xiang Fu, Alex Strasser, Shenglong Xu, Yi Liu, Yuanqi Du, Ale...

    arXiv

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.