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arxiv: 2606.26421 · v1 · pith:KGLOT5OPnew · submitted 2026-06-24 · 💻 cs.LG · cs.CE

Otter Weather: Skillful and Computationally Efficient Medium-Range Weather Forecasting

Cristiana Diaconu , Jonas Scholz , Aliaksandra Shysheya , Stratis Markou , Payel Mukhopadhyay , Miles Cranmer , Richard E. Turner This is my paper

Pith reviewed 2026-06-26 01:17 UTC · model grok-4.3

classification 💻 cs.LG cs.CE
keywords weather forecastingmachine learningmedium-range predictioncomputational efficiencyspatiotemporal modelsprobabilistic forecastingnumerical weather predictionERA5
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The pith

Otter Weather outperforms the best NWP baseline by 9.6 percent at 24-hour lead time after training on fewer than 3.5 A100-days.

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

The paper introduces Otter Weather, a spatiotemporal forecasting model built for high efficiency in medium-range weather prediction. It shows that the deterministic version reaches higher skill than traditional numerical methods while using dramatically less training compute than prior AI approaches. These gains carry over to probabilistic forecasts trained with CRPS and appear when the same model is applied to an unrelated acoustic scattering problem. The work targets the barrier that massive compute requirements have placed on access to accurate forecasting tools.

Core claim

Otter Weather is a highly efficient spatiotemporal forecasting model that advances the skill-compute Pareto frontier. The deterministic version outperforms the best NWP baseline by 9.6 percent at 24-hour lead time while requiring fewer than 3.5 A100-days for training. It delivers a 2x efficiency gain over lightweight AI models and a 100-fold reduction relative to resource-intensive frontier architectures. Scaling to Otter-XL with CRPS training produces a 9.7 percent CRPS improvement over the IFS ENS baseline and outperforms GenCast by over 2 percent while using an order of magnitude less compute. The same model applied out-of-the-box to a complex acoustic scattering PDE task outperforms a st

What carries the argument

The Otter family of spatiotemporal forecasting models, which advance the skill-compute Pareto frontier through efficiency-focused design for weather prediction.

If this is right

  • High-performance medium-range forecasts become feasible for groups with limited compute resources.
  • Model development cycles for weather prediction shorten because training budgets drop by one to two orders of magnitude.
  • Probabilistic forecasting skill improves at comparable compute budgets when models are trained directly with CRPS.
  • The same efficiency-oriented design transfers to other scientific spatiotemporal tasks such as PDE modeling.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the reported efficiency scales with resolution, ensembles of Otter models could run on modest hardware for operational use.
  • The out-of-distribution success on an acoustic scattering task suggests the architecture may apply to other physical simulation domains without domain-specific redesign.
  • Real-world deployment would still require separate verification that reanalysis skill carries over to live data streams and model drift.

Load-bearing premise

That performance measured on ERA5 reanalysis at 1.5 degree resolution with standard WeatherBench protocols will translate to operational forecasting skill.

What would settle it

Evaluating Otter forecasts on live operational weather observations over multiple seasons and comparing accuracy and reliability directly against current NWP systems.

Figures

Figures reproduced from arXiv: 2606.26421 by Aliaksandra Shysheya, Cristiana Diaconu, Jonas Scholz, Miles Cranmer, Payel Mukhopadhyay, Richard E. Turner, Stratis Markou.

Figure 1
Figure 1. Figure 1: Skill score over IFS HRES/ENS on the headline variables. (a) RMSE at 24h. (b) CRPS averaged over 1-10 days. Circles (◦) represent models trained at lower resolutions (1°/1.4°/1.5°), while stars (⋆) indicate higher-resolution training (0.25°/0.7°). The models in the Otter Weather family advance both the deterministic and probabilistic the Pareto frontiers of skill versus compute. mentary ways. First, it ena… view at source ↗
Figure 2
Figure 2. Figure 2: Otter Weather architecture. A 2D Swin Transformer predicts the future state Xt+δ from recent history Xt−(L−1)×δ, . . . , Xt. Atmospheric variables across 13 pressure levels, surface variables, and time embeddings (Etime) are concatenated channel-wise at a spatial resolution of H × W = 121 × 240. Within the shifted-window attention (SW-MHSA) blocks, we employ RoPE and omit attention masks to enable cross-bo… view at source ↗
Figure 3
Figure 3. Figure 3: Architectural and training ablations. Bars show the relative percentage change in predictive skill (6–24h RMSE average of non-RFT models) versus the base model (black zero-line). Blue indicates improvement; orange denotes degradation. Multipliers above each bar reflect the relative computational cost. Deviations from the base configuration either degrade performance or incur disproportionate computational … view at source ↗
Figure 4
Figure 4. Figure 4: Performance of Probabilistic Training Strategies. Average CRPS improvement over the IFS ensemble (a) and SSR (b) across 1–10 day lead times for three Otter CRPS variants: fine-tuning with MC Dropout, from-scratch training, and fine-tuning with AdaLN injection. For each base config￾uration, employing a Deep Ensemble (Deep Ens) consistently enhances skill and improves the spread. Otter Otter + Deep Ens Otter… view at source ↗
Figure 5
Figure 5. Figure 5: Scaling behavior of probabilistic Otter models. Side-by-side comparison of CRPS improvement against IFS ENS (%) (left) and Spread-Skill Ratio (right) across 1–10 day lead times for single-model and Deep Ensemble (Deep Ens) configurations of Otter and Otter-XL. Compute costs are annotated inside the bars in A100 days. At approximately 3.5× the computational cost, the Otter-XL models yield over a 55% relativ… view at source ↗
Figure 6
Figure 6. Figure 6: Ablation study on the acoustic scattering PDE task. We report the one-step VRMSE over [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Overview of the training pipeline for Otter CRPS models, detailing the computational cost [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Overview of the training pipeline for Otter CRPS (scratch) models, detailing the computa [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: RMSE skill over IFS HRES comparison for lead times up to 10 days for Otter, Otter-XL, [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: RMSE comparison for lead times up to 10 days. Lines represent IFS HRES (NWP [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Evolution of the ’fair’ CRPS with lead time for different number of ensemble members: [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Skill improvement over 1–3 day lead times (left) and Spread-Skill Ratio (right) for three [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Skill improvement over 1–3 day lead times (left) and Spread-Skill Ratio (right) for [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: CRPS skill over IFS ENS comparison for lead times up to 10 days for Otter CRPS, [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: SSR over IFS ENS comparison for lead times up to 10 days for Otter CRPS, Otter CRPS [PITH_FULL_IMAGE:figures/full_fig_p026_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: CRPS skill over IFS ENS comparison for lead times up to 10 days for Otter CRPS, Otter [PITH_FULL_IMAGE:figures/full_fig_p027_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: SSR over IFS ENS comparison for lead times up to 10 days for Otter CRPS, Otter CRPS [PITH_FULL_IMAGE:figures/full_fig_p027_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Visualization of Q700 at 12h lead time. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Visualization of SP at 3 days lead time. [PITH_FULL_IMAGE:figures/full_fig_p029_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Visualization of T2M at 10 days lead time. [PITH_FULL_IMAGE:figures/full_fig_p030_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Visualization of T850 at 12h lead time. 31 [PITH_FULL_IMAGE:figures/full_fig_p031_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Visualization of U10m at 3 days lead time. [PITH_FULL_IMAGE:figures/full_fig_p032_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Visualization of U850 at 10 days lead time. [PITH_FULL_IMAGE:figures/full_fig_p033_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Visualization of V10m at 12 hours lead time. [PITH_FULL_IMAGE:figures/full_fig_p034_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Visualization of V850 at 3 days lead time. [PITH_FULL_IMAGE:figures/full_fig_p035_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Visualization of Z500 at 10 days lead time. [PITH_FULL_IMAGE:figures/full_fig_p036_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Ablation study on the acoustic scattering PDE task. We report the rollout VRMSE (over [PITH_FULL_IMAGE:figures/full_fig_p038_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Example ground truth (GT) (top, predictions, and errors (prediction - GT) for an acoustic [PITH_FULL_IMAGE:figures/full_fig_p039_28.png] view at source ↗
read the original abstract

State-of-the-art medium-range AI weather models can outperform traditional Numerical Weather Prediction (NWP) but require massive training budgets. This restricts usage for under-resourced groups and severely limits fast model iteration. Here we develop Otter Weather, a highly efficient spatiotemporal forecasting model designed to democratise high-performance weather prediction with AI. Evaluated on ERA5 reanalysis data at 1.5{\deg} resolution using standard WeatherBench protocols, the Otter family significantly advances the skill-compute Pareto frontier. The deterministic version outperforms the best NWP baseline by 9.6% at a 24-hour lead time while requiring fewer than 3.5 A100-days for training. It provides a 2x efficiency gain over lightweight AI models and a 100-fold reduction in compute compared to resource-intensive frontier architectures. We extend these efficiency gains into probabilistic forecasting by training via the Continuous Ranked Probability Score (CRPS). Scaling to a larger architecture, Otter-XL achieves a 9.7% CRPS improvement over the IFS ENS baseline. This yields an almost two-fold increase in predictive skill over comparable lightweight models at similar compute budgets. Otter-XL also outperforms frontier architectures like GenCast by over 2%, while using an order of magnitude less compute. Finally, Otter is applied out-of-the-box to a complex acoustic scattering PDE task where it outperforms a state-of-the-art foundation modelling approach, suggesting that the advances made here might apply across a range of scientific domains.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces Otter Weather, a spatiotemporal AI model for medium-range weather forecasting. Evaluated on ERA5 reanalysis at 1.5° resolution with WeatherBench protocols, the deterministic version is claimed to outperform the best NWP baseline by 9.6% at 24-hour lead time while using fewer than 3.5 A100-days for training; a 2x efficiency gain over lightweight AI models and 100-fold reduction versus frontier models is reported. The work extends the approach to probabilistic forecasting via CRPS (Otter-XL achieving 9.7% improvement over IFS ENS), and demonstrates out-of-the-box application to an acoustic scattering PDE task.

Significance. If the performance and compute claims hold under full verification, the work would meaningfully advance the skill-compute Pareto frontier for AI weather models, lowering barriers for under-resourced groups and enabling faster iteration. The cross-domain PDE result provides additional evidence of broader applicability. The emphasis on reproducible low-compute training is a positive contribution if the end-to-end accounting is complete.

major comments (3)
  1. [§4] §4 (Results, deterministic model): The 9.6% outperformance claim at 24 h versus the best NWP baseline is load-bearing for the central efficiency claim but lacks explicit identification of the baseline (IFS deterministic vs. ensemble), the precise metric (RMSE vs. ACC), the variable set, and vertical levels; any mismatch with standard WeatherBench NWP comparisons would invalidate the percentage.
  2. [§5] §5 (Training and compute): The <3.5 A100-day training budget is central to the efficiency advantage but is presented without a full accounting of data staging, hyper-parameter sweeps, checkpointing, and validation passes; without this breakdown the quoted figure cannot be confirmed as the complete reproducible cost.
  3. [§3] §3 (Methods): No ablation studies, error bars, or sensitivity analyses on architecture or training choices are referenced in support of the reported gains; this omission prevents assessment of whether improvements are robust or attributable to post-hoc tuning.
minor comments (2)
  1. [Figure 2] Figure 2: Axis labels and legend entries for the Pareto frontier plot should explicitly state the exact metric and lead time used for each point to avoid ambiguity in cross-model comparisons.
  2. Notation: The definition of the spatiotemporal architecture (e.g., any custom convolution or attention blocks) should be given in a single equation block rather than scattered across text for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their detailed and constructive comments on our manuscript. We address each major comment point by point below, providing clarifications and committing to revisions where appropriate to strengthen the paper.

read point-by-point responses

  1. Referee: [§4] §4 (Results, deterministic model): The 9.6% outperformance claim at 24 h versus the best NWP baseline is load-bearing for the central efficiency claim but lacks explicit identification of the baseline (IFS deterministic vs. ensemble), the precise metric (RMSE vs. ACC), the variable set, and vertical levels; any mismatch with standard WeatherBench NWP comparisons would invalidate the percentage.

    Authors: We appreciate the referee's attention to this detail. The 9.6% improvement is calculated as the relative reduction in RMSE for the deterministic Otter model compared to the IFS deterministic forecast (not ensemble) at 24-hour lead time, using the standard set of WeatherBench variables (2m temperature, 10m wind components, geopotential, specific humidity, etc.) at 1.5° resolution across all vertical levels where applicable. This aligns with WeatherBench protocols. To eliminate any potential for misinterpretation, we will revise §4 to explicitly state these parameters and include a supplementary table detailing the comparison. revision: yes

  2. Referee: [§5] §5 (Training and compute): The <3.5 A100-day training budget is central to the efficiency advantage but is presented without a full accounting of data staging, hyper-parameter sweeps, checkpointing, and validation passes; without this breakdown the quoted figure cannot be confirmed as the complete reproducible cost.

    Authors: The reported figure of fewer than 3.5 A100-days corresponds to the compute required for training the final Otter model after architecture selection. We recognize that a transparent end-to-end accounting is essential. In the revised manuscript, we will provide a comprehensive breakdown in §5, including estimates for data preparation, hyperparameter exploration (noting that sweeps were limited), checkpointing, and validation, to allow full verification of the total cost. revision: yes

  3. Referee: [§3] §3 (Methods): No ablation studies, error bars, or sensitivity analyses on architecture or training choices are referenced in support of the reported gains; this omission prevents assessment of whether improvements are robust or attributable to post-hoc tuning.

    Authors: We agree that ablations and sensitivity analyses would strengthen the claims. Although the primary results show consistent outperformance across multiple lead times and variables, we will incorporate additional analyses in the revised version, including sensitivity to key architectural choices (e.g., spatiotemporal attention mechanisms) and training hyperparameters, along with error bars from repeated training runs with different seeds where computationally feasible. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical results are direct comparisons to external baselines

full rationale

The paper reports an ML model's performance on ERA5 reanalysis at 1.5° using WeatherBench protocols, with gains stated as direct numerical comparisons to external NWP baselines (IFS deterministic and ENS). No equations, derivations, or first-principles claims appear in the abstract or description. Efficiency figures are presented as measured training budgets versus other published models, not as quantities fitted from or defined by the target metrics. No self-citations, ansatzes, or uniqueness theorems are invoked as load-bearing steps. The derivation chain is therefore self-contained empirical evaluation against independent external references.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no information on free parameters, background axioms, or new entities; all ledger fields left empty.

pith-pipeline@v0.9.1-grok · 5824 in / 1101 out tokens · 29188 ms · 2026-06-26T01:17:22.662333+00:00 · methodology

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Reference graph

Works this paper leans on

46 extracted references · 8 canonical work pages

  1. [1]

    Anna Allen, Stratis Markou, Will Tebbutt, Wessel P

    URL https://arxiv.org/ abs/2506.10772. Anna Allen, Stratis Markou, Will Tebbutt, Wessel P. Bruinsma, Tom R. Andersson, Michael Herzog, Nicholas D. Lane, Matthew Chantry, J. Scott Hosking, and Richard E. Turner. End-to-end data- driven weather prediction.Nature,

    arXiv

  2. [2]

    URL https: //www.nature.com/articles/s41586-025-08897-0

    doi: 10.1038/s41586-025-08897-0. URL https: //www.nature.com/articles/s41586-025-08897-0. Zied Ben Bouallegue, Mihai Alexe, Matthew Chantry, Mariana Clare, Jesper Dramsch, Simon Lang, Christian Lessig, Linus Magnusson, Ana Prieto Nemesio, Florian Pinault, Baudouin Raoult, and Steffen Tietsche. New ml model on ecmwf web charts,

    work page doi:10.1038/s41586-025-08897-0

  3. [3]

    AIFS Blog

    URL https://www.ecmwf.int/ en/about/media-centre/aifs-blog/2023/new-ml-model-ecmwf-web-charts . AIFS Blog. Kaifeng Bi, Lingxi Xie, Hengheng Zhang, Xin Chen, Xiaotao Gu, and Qi Tian. Pangu-weather: A 3d high-resolution model for fast and accurate global weather forecast,

    2023

  4. [4]

    Cristian Bodnar, Wessel P

    URL https: //arxiv.org/abs/2211.02556. Cristian Bodnar, Wessel P. Bruinsma, Ana Lucic, Megan Stanley, Anna Allen, Johannes Brandstetter, Patrick Garvan, Maik Riechert, Jonathan A. Weyn, Haiyu Dong, Jayesh K. Gupta, Kit Thambirat- nam, Alexander T. Archibald, Chun-Chieh Wu, Elizabeth Heider, Max Welling, Richard E. Turner, and Paris Perdikaris. A foundatio...

    arXiv

  5. [5]

    doi: 10.1038/s41586-025-09005-y

    ISSN 1476-4687. doi: 10.1038/s41586-025-09005-y. URL https://doi.org/10.1038/s41586-025-09005-y . Boris Bonev, Thorsten Kurth, Ankur Mahesh, Mauro Bisson, Jean Kossaifi, Karthik Kashinath, Anima Anandkumar, William D. Collins, Michael S. Pritchard, and Alexander Keller. Fourcastnet 3: A geometric approach to probabilistic machine-learning weather forecast...

    work page doi:10.1038/s41586-025-09005-y

  6. [6]

    Salva Rühling Cachay, Miika Aittala, Hailey James, and Rose Yu

    URLhttps://arxiv.org/abs/2507.12144. Salva Rühling Cachay, Miika Aittala, Hailey James, and Rose Yu. Elucidated rolling diffusion models for probabilistic forecasting of complex dynamics. InNeurIPS 2025,

    arXiv 2025

  7. [7]

    Salva Ruhling Cachay, Duncan Watson-Parris, and Rose Yu

    URL https: //arxiv.org/abs/2506.20024. Salva Ruhling Cachay, Duncan Watson-Parris, and Rose Yu. U-cast: A surprisingly simple and efficient frontier probabilistic ai weather forecaster.arXiv preprint arXiv:2604.09041,

    arXiv

  8. [8]

    Cristiana Diaconu, Miles Cranmer, Richard E

    URLhttps://arxiv.org/abs/2412.12971. Cristiana Diaconu, Miles Cranmer, Richard E. Turner, Tanya Marwah, and Payel Mukhopadhyay. Probabilistic retrofitting of learned simulators,

    arXiv

  9. [9]

    org/abs/1802.10026

    URL https://arxiv. org/abs/1802.10026. Tilmann Gneiting and Adrian E. Raftery. Strictly proper scoring rules, prediction, and es- timation.Journal of the American Statistical Association, 102(477):359–378,

    Pith/arXiv arXiv

  10. [10]

    Ali Hassani, Steven Walton, Jiachen Li, Shen Li, and Humphrey Shi

    doi: 10.1198/016214506000001437. Ali Hassani, Steven Walton, Jiachen Li, Shen Li, and Humphrey Shi. Neighborhood attention transformer,

    work page doi:10.1198/016214506000001437

  11. [11]

    12 Kaiming He, Xinlei Chen, Saining Xie, Yanghao Li, Piotr Dollár, and Ross Girshick

    URLhttps://arxiv.org/abs/2204.07143. 12 Kaiming He, Xinlei Chen, Saining Xie, Yanghao Li, Piotr Dollár, and Ross Girshick. Masked autoencoders are scalable vision learners,

    arXiv

  12. [12]

    URLhttps://arxiv.org/abs/2111.06377. Hans Hersbach, Bill Bell, Paul Berrisford, Gionata Biavati, András Horányi, Joaquín Muñoz Sabater, Julien Nicolas, Carole Peubey, Raluca Radu, Iryna Rozum, Dinand Schepers, Adrian Simmons, Cornel Soci, Dick Dee, and Jean-Noël Thépaut. The ERA5 global reanalysis.Quarterly Journal of the Royal Meteorological Society, 146...

    Pith/arXiv arXiv 1999

  13. [13]

    Keller Jordan, Yuchen Jin, Vlado Boza, You Jiacheng, Franz Cesista, Laker Newhouse, and Jeremy Bernstein

    doi: https://doi.org/10.1002/qj.3803. Keller Jordan, Yuchen Jin, Vlado Boza, You Jiacheng, Franz Cesista, Laker Newhouse, and Jeremy Bernstein. Muon: An optimizer for hidden layers in neural networks. https://kellerjordan. github.io/posts/muon/,

    work page doi:10.1002/qj.3803

  14. [14]

    Ryan Keisler

    Accessed: 2026-02-03. Ryan Keisler. Forecasting global weather with graph neural networks,

    2026

  15. [15]

    org/abs/2202.07575

    URL https://arxiv. org/abs/2202.07575. Dmitrii Kochkov, J. Yuval, I. Langmore, P. Norgaard, J. Smith, G. Mooers, M. K. Klöwer, et al. Neural general circulation models for weather and climate.Nature, 632(8027):1060– 1066,

    arXiv

  16. [16]

    URL https://www.nature.com/articles/ s41586-024-07744-y

    doi: 10.1038/s41586-024-07744-y. URL https://www.nature.com/articles/ s41586-024-07744-y. Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles,

    work page doi:10.1038/s41586-024-07744-y

  17. [17]

    Simon Lang, Mihai Alexe, Matthew Chantry, Jesper Dramsch, Florian Pinault, Baudouin Raoult, Mariana C

    URLhttps://arxiv.org/abs/2212.12794. Simon Lang, Mihai Alexe, Matthew Chantry, Jesper Dramsch, Florian Pinault, Baudouin Raoult, Mariana C. A. Clare, Christian Lessig, Michael Maier-Gerber, Linus Magnusson, Zied Ben Bouallègue, Ana Prieto Nemesio, Peter D. Dueben, Andrew Brown, Florian Pappenberger, and Florence Rabier. Aifs – ecmwf’s data-driven forecast...

    arXiv

  18. [18]

    org/abs/2406.01465

    URL https://arxiv. org/abs/2406.01465. Simon Lang, Mihai Alexe, Matthew Chantry, Mariana Pinheiro, Peter Dueben, and Tim Palmer. Aifs-crps: Ensemble forecasting using a model trained with a loss function based on the continuous ranked probability score.npj Artificial Intelligence, 2(1),

    arXiv

  19. [19]

    Fanny Lehmann, Firat Ozdemir, Benedikt Soja, Torsten Hoefler, Siddhartha Mishra, and Sebastian Schemm

    doi: 10.1038/s44260-026-00045-z. Fanny Lehmann, Firat Ozdemir, Benedikt Soja, Torsten Hoefler, Siddhartha Mishra, and Sebastian Schemm. Finetuning a weather foundation model with lightweight decoders for unseen physical processes,

    work page doi:10.1038/s44260-026-00045-z

  20. [20]

    Jingyuan Liu, Jianlin Su, Xingcheng Yao, Zhejun Jiang, Guokun Lai, Yulun Du, Yidao Qin, Weixin Xu, Enzhe Lu, Junjie Yan, et al

    URLhttps://arxiv.org/abs/2506.19088. Jingyuan Liu, Jianlin Su, Xingcheng Yao, Zhejun Jiang, Guokun Lai, Yulun Du, Yidao Qin, Weixin Xu, Enzhe Lu, Junjie Yan, et al. Muon is scalable for llm training.arXiv preprint arXiv:2502.16982,

    arXiv

  21. [21]

    Ilya Loshchilov and Frank Hutter

    URL https://arxiv.org/abs/2103.14030. Ilya Loshchilov and Frank Hutter. Fixing weight decay regularization in adam.CoRR, abs/1711.05101,

    Pith/arXiv arXiv

  22. [22]

    URLhttp://arxiv.org/abs/1711.05101. Ankur Mahesh, William Collins, Boris Bonev, Noah Brenowitz, Yair Cohen, Joshua Elms, Peter Harrington, Karthik Kashinath, Thorsten Kurth, Joshua North, Travis OBrien, Michael Pritchard, David Pruitt, Mark Risser, Shashank Subramanian, and Jared Willard. Huge ensembles part i: Design of ensemble weather forecasts using s...

    Pith/arXiv arXiv

  23. [23]

    13 Michael McCabe, Payel Mukhopadhyay, Tanya Marwah, Bruno Regaldo-Saint Blancard, Francois Rozet, Cristiana Diaconu, Lucas Meyer, Kaze W

    URL https://arxiv.org/abs/2408.03100. 13 Michael McCabe, Payel Mukhopadhyay, Tanya Marwah, Bruno Regaldo-Saint Blancard, Francois Rozet, Cristiana Diaconu, Lucas Meyer, Kaze W. K. Wong, Hadi Sotoudeh, Alberto Bietti, Irina Espejo, Rio Fear, Siavash Golkar, Tom Hehir, Keiya Hirashima, Geraud Krawezik, Francois Lanusse, Rudy Morel, Ruben Ohana, Liam Parker,...

    arXiv

  24. [24]

    Tung Nguyen, Johannes Brandstetter, Ashish Kapoor, Jayesh K

    URLhttps://arxiv.org/abs/2511.15684. Tung Nguyen, Johannes Brandstetter, Ashish Kapoor, Jayesh K. Gupta, and Aditya Grover. Climax: A foundation model for weather and climate,

    arXiv

  25. [25]

    Tung Nguyen, Rohan Shah, Hritik Bansal, Troy Arcomano, Romit Maulik, Veerabhadra Kotamarthi, Ian Foster, Sandeep Madireddy, and Aditya Grover

    URL https://arxiv.org/abs/2301.10343. Tung Nguyen, Rohan Shah, Hritik Bansal, Troy Arcomano, Romit Maulik, Veerabhadra Kotamarthi, Ian Foster, Sandeep Madireddy, and Aditya Grover. Scaling transformer neural networks for skillful and reliable medium-range weather forecasting,

    arXiv

  26. [26]

    Ruben Ohana, Michael McCabe, Lucas Meyer, Rudy Morel, Fruzsina J

    URL https://arxiv.org/abs/ 2312.03876. Ruben Ohana, Michael McCabe, Lucas Meyer, Rudy Morel, Fruzsina J. Agocs, Miguel Beneitez, Mar- sha Berger, Blakesley Burkhart, Keaton Burns, Stuart B. Dalziel, Drummond B. Fielding, Daniel Fortunato, Jared A. Goldberg, Keiya Hirashima, Yan-Fei Jiang, Rich R. Kerswell, Suryanarayana Maddu, Jonah Miller, Payel Mukhopad...

    arXiv

  27. [27]

    URL https://arxiv.org/abs/2412.00568. Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopadhyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, Pedram Hassanzadeh, Karthik Kashinath, and Animashree Anandkumar. Fourcastnet: A global data- driven high-resolution weather model using adaptive f...

    arXiv

  28. [28]

    Ilan Price, Alvaro Sanchez-Gonzalez, Ferran Alet, Tom R

    URL https: //arxiv.org/abs/2202.11214. Ilan Price, Alvaro Sanchez-Gonzalez, Ferran Alet, Tom R. Andersson, Andrew El-Kadi, Dominic Masters, Timo Ewalds, Jacklynn Stott, Shakir Mohamed, Peter Battaglia, Remi Lam, and Matthew Willson. Gencast: Diffusion-based ensemble forecasting for medium-range weather,

    Pith/arXiv arXiv

  29. [29]

    Stephan Rasp, Stephan Hoyer, Aravind Merose, Johannes Langguth, Sebastian Deiser, et al

    URL https://arxiv.org/abs/2312.15796. Stephan Rasp, Stephan Hoyer, Aravind Merose, Johannes Langguth, Sebastian Deiser, et al. Weath- erbench 2: A benchmark for the next generation of data-driven global weather models.arXiv preprint arXiv:2308.15560 (Also published in Journal of Advances in Modeling Earth Systems), 2023/2024. doi: 10.1029/2023MS004019. Ma...

    work page doi:10.1029/2023ms004019 2023

  30. [30]

    Noam Shazeer

    URL https://arxiv.org/abs/2310.06743. Noam Shazeer. Glu variants improve transformer,

    arXiv

  31. [31]

    URL https://arxiv.org/abs/2002. 05202. Noam Shazeer, Azalia Mirhoseini, Krzysztof Maziarz, Andy Davis, Quoc Le, Geoffrey Hinton, and Jeff Dean. Outrageously large neural networks: The sparsely-gated mixture-of-experts layer,

    2002

  32. [32]

    Jianlin Su, Yu Lu, Shengfeng Pan, Ahmed Murtadha, Bo Wen, and Yunfeng Liu

    URLhttps://arxiv.org/abs/1701.06538. Jianlin Su, Yu Lu, Shengfeng Pan, Ahmed Murtadha, Bo Wen, and Yunfeng Liu. Roformer: Enhanced transformer with rotary position embedding,

    Pith/arXiv arXiv

  33. [33]

    Christopher Subich

    URL https://arxiv.org/abs/ 2104.09864. Christopher Subich. Efficient fine-tuning of 37-level graphcast with the canadian global deterministic analysis.Artificial Intelligence for the Earth Systems, 4(3), July

    Pith/arXiv arXiv

  34. [34]

    doi: 10.1175/aies-d-24-0101.1

    ISSN 2769-7525. doi: 10.1175/aies-d-24-0101.1. URLhttp://dx.doi.org/10.1175/AIES-D-24-0101.1. Xiuyu Sun, Xiaohui Zhong, Xiaoze Xu, Yuanqing Huang, Hao Li, J. David Neelin, Deliang Chen, Jie Feng, Wei Han, Libo Wu, and Yuan Qi. Fuxi weather: A data-to-forecast machine learning system for global weather,

    work page doi:10.1175/aies-d-24-0101.1

  35. [35]

    Defa Zhu, Hongzhi Huang, Zihao Huang, Yutao Zeng, Yunyao Mao, Banggu Wu, Qiyang Min, and Xun Zhou

    URLhttps://arxiv.org/abs/2408.05472. Defa Zhu, Hongzhi Huang, Zihao Huang, Yutao Zeng, Yunyao Mao, Banggu Wu, Qiyang Min, and Xun Zhou. Hyper-connections,

    arXiv

  36. [36]

    14 A Summary Table of Related Work We provide a comparative summary of deterministic weather models in table

    URLhttps://arxiv.org/abs/2409.19606. 14 A Summary Table of Related Work We provide a comparative summary of deterministic weather models in table

    arXiv

  37. [37]

    Otter-XL closely approaches the performance of the best high-resolution model (GraphCast) despite using two orders of magnitude less compute

    Despite operating with the lowest compute budget, Otter Weather achieves superior performance in the medium-resolution category and remains competitive with state-of-the-art models in the high-resolution regime. Otter-XL closely approaches the performance of the best high-resolution model (GraphCast) despite using two orders of magnitude less compute. Tab...

    2024

  38. [38]

    constant-width

    For every spatial location (h, w), we generate a dense feature vector containing all harmonic terms for degrees 0≤ℓ≤L max and orders −ℓ≤m≤ℓ . This results in (Lmax + 1)2 = 441 unique geometric features per pixel. These raw harmonic features are cached and passed through a learnable linear projection to match the token dimensionDbefore being added to the i...

    2023

  39. [39]

    The downsampling operations reduce the spatial resolution by a factor of 2 at each stage (via 2×2 strided convolution) while maintaining the channel dimension constant at D

    blocks. The downsampling operations reduce the spatial resolution by a factor of 2 at each stage (via 2×2 strided convolution) while maintaining the channel dimension constant at D. The skip connections use complex fusion (concatenation followed by a1×1convolution) rather than simple summation. B.2.4 Swin Transformer Block and Feed-Forward Network The fun...

    2021

  40. [40]

    The aggregated loss sums over all target variables and pressure levelsv, averaging over lead timest= 1,

    Mathematically, we can express the loss computed per variable v and at lead timetas: Lt v = vuut 1 HW HX i=1 WX j=1 w(ϕi), ˆX t i,j,v −X t i,j,v 2 (3) where w(ϕi) = cosϕ i 1 H PH k=1 cosϕ k downweights grid cells toward the poles, and ϕi is the latitude of row i over a uniform H×W grid. The aggregated loss sums over all target variables and pressure level...

    2024

  41. [41]

    To form a deep ensemble, the pipeline branches to train three independent models for the equivalent of 1-A100 days each, using varied learning rates (10−6, 2×10 −6, and 5×10 −6)

    In the final Rollout Fine-Tuning (RFT) phase (Stage 3), we restrict the dataset to the 2007–2019 period and apply the exact same curriculum learning strategy utilised for the deterministic model. To form a deep ensemble, the pipeline branches to train three independent models for the equivalent of 1-A100 days each, using varied learning rates (10−6, 2×10 ...

    2007

  42. [42]

    Probabilistic model: Otter CRPS (scratch)

    remains a promising avenue for future work. Probabilistic model: Otter CRPS (scratch). Stage 2: CRPS RFT Deep Ens ΔCRPS: 6.2% Stage 1: CRPS Training (Scratch) ΔCRPS: 1.2% Cost: 5 Days M1: LR=1e6 ΔCRPS: 4.5% Cost: 1.0 Days M2: LR=2e6 ΔCRPS: 4.8% Cost: 1.0 Days Initial CRPS Checkpoint M3: LR=5e6 ΔCRPS: 5.0% Cost: 1.0 Days Figure 8: Overview of the training ...

    1979

  43. [43]

    Stage 2 (CRPS fine-tuning) is executed for 5 epochs on the 1979–2019 ERA5 dataset. To obtain a single base model, we perform Rollout Fine-Tuning (RFT) for a single epoch on the 2007–2019 ERA5 data, employing the same curriculum learning strategy used for the deterministic model. To construct a deep ensemble version of the AdaLN model, we then independentl...

    1979

  44. [44]

    These lead to the following main observations: • Benefits of Deep Ensembling:Deep ensembling yields a consistent performance boost for the Otter CRPS models across all evaluated atmospheric variables. These gains are achieved at a minimal computational cost—in our case, the ensemble members were gen- erated by varying the learning rate during a standard h...

    2025

  45. [45]

    D.2 Base Deterministic Configuration

    we use the following definition for the VRMSE: VRMSE(u, v) = s ⟨(u−v) 2⟩ ⟨(u− ⟨u⟩) 2⟩+ϵ ,(6) where⟨·⟩denotes the spatial mean operator and we addϵ= 10 −6 for numerical stability. D.2 Base Deterministic Configuration. The base configuration for PDE task is: •Embedding Dimension:D= 384; •Depth Profile (U-Net):[2,8,4]blocks per stage; •Attention Heads:16; •F...

    2025

  46. [46]

    Consistent with our one-step findings, the majority of ablations degrade rollout performance. There are, however, some exceptions: models utilising AdamW, or a backbone configuration of D= 640 with a [1, 4, 1] depth profile, achieve superior rollout metrics at a comparable computational cost. Despite these nuances, we base our primary evaluation on one-st...

    2025