Organizations: Nanjing University of Information Science and Technology · Nanyang Technological University · Harbin Institute of Technology · Princeton University · Karolinska Institutet
Machine learning-based weather prediction (MLWP) has achieved strong performance in global weather forecasting. Recent Hierarchical Equal Area isoLatitude Pixelation (HEALPix)-based methods use the HEALPix (HP) grid to avoid area distortion near the poles of conventional latitude-longitude (LL) grids. However, existing HP-based approaches often use pointwise mapping methods and process HP pixels within separate base faces or local windows. Consequently, the mapping may introduce reconstruction errors and cross-face communication depends on handcrafted boundary handling or shifted windows. We propose the Spherical Spiral Scanning Network (S3N) to address both limitations. First, L2Proj provides a bidirectional method for mapping atmospheric fields between the LL and HP grids through an L2 projection of their continuous finite-element representations. Second, the Attention-Guided Quad-Spiral State-Space Scanning (AQSS) block uses cross-latitude attention to guide selective state-space updates along four global pole-to-pole spiral paths. This design enables continuous information propagation across HP base-face boundaries without additional boundary-processing mechanisms. Experiments show that S3N achieves better results at 4-, 7-, and 10-day lead times, and exhibits slower error growth in long-range forecasting.
Figures & tables
Figure 1: Comparison of various methods. (a) The average error of L2Proj is much lower than that of bilinear interpolation. (b) We treat HEALPix pixels from the twelve base faces as a sequence rather than stacking the twelve base faces as patches, thereby avoiding handcrafted boundary handling.
Figure 2: Overview of our S 3 N framework. (a) The overall pipeline of our model, which follows an encoder-processor-decoder architecture. (b) Illustration of the L2Proj computation. We use L2Proj as the encoder and decoder for projecting atmospheric fields between the LL and the HP grids. (c) Details of the proposed AQSS block. Cross-latitude information is collected from eight cross-latitude neighbors to guide the Mamba updates and the weighted fusion of the four path features.
Method
Bilinear Interpolation
L2Proj
Average MSE
0.002153
0.000252
Table 1: Mean squared error (MSE) of atmospheric fields after mapping from the LL grid to the HP grid and then back to the LL grid. Lower is better.
Method
6-hour
1-day
4-day
7-day
10-day
Pangu-Weather [ 2 ]
0.1182
0.1859
0.4509
0.6960
0.7582
FuXi [ 7 ]
0.1258
0.2050
0.4742
0.6484
0.7831
Fengwu [ 6 ]
0.1252
0.2028
0.4860
0.6887
0.8143
GraphCast [ 18 ]
0.0784
0.1519
0.3599
0.5521
0.7006
OneForecast [ 11 ]
0.0754
0.1393
0.3275
0.5042
0.6398
S 3 N (Ours)
0.1009
0.1663
0.3171
0.4411
0.5177
Table 2: Comparison of mean normalized RMSE (lower is better) across different lead times. The best result in each column is in bold, and the second best is underlined.
Method
6-hour
1-day
4-day
7-day
6-hour
to
to
to
to
to
1-day
4-day
7-day
10-day
10-day
Pangu-Weather
0.0677
0.2650
0.2451
0.0622
0.6400
FuXi
0.0792
0.2692
0.1742
0.1347
0.6573
Fengwu
0.0776
0.2832
0.2027
0.1256
0.6891
GraphCast
0.0735
0.2080
0.1922
0.1485
0.6222
Table 3: Absolute nRMSE growth between adjacent lead times and total growth from 6 hours to 10 days. Lower is better.
Method
6-hour
1-day
4-day
7-day
10-day
S 3 N (Full)
0.1009
0.1663
0.3171
0.4411
0.5177
Fixed-Weight Path Fusion
0.2536
0.4428
0.5657
0.5936
0.6135
F. W. w/o SSM Guidance
0.2934
0.5681
1.1924
1.6932
2.1993
F. W. w/o Attention
0.4314
0.7548
1.3075
1.6489
1.9567
w/o SSM Guidance
0.1663
0.4241
1.2322
1.7837
2.3103
w/o Input Fusion
0.3585
0.6569
0.9055
1.0418
1.1598
Table 4: Component ablation study of our AQSS. Mean normalized RMSE (lower is better) across different lead times. The best result is in bold, and the second best is underlined. “w/o” means “without” , “F. W.” means “Fixed-Weight”.
Weather forecasting predicts future atmospheric conditions, from local storms to global patterns, using physical models, observations, and machine learning.
State-of-the-art AI weather models have shown impressive medium-range forecast skill and computational efficiency, but suffer two key shortcomings: their forecasts have lower spatial and temporal resolution than the best physics-based models and they are exclusively initialized with and trained on analysis data. As a result, they cannot directly make use of observations, and any biases in the analysis are inherited by the forecast. WeatherNext 3 addresses these shortcomings and establishes a new state-of-the-art for probabilistic medium-range forecasting skill. First, WeatherNext 3 generates new forecasts every hour (rather than every 6 hours like traditional global models) by ingesting low-latency geostationary satellite data. Second, WeatherNext 3's temporal and spatial resolution are on par with physics-based global models, with hourly time steps and 0.1 degree resolution for single-level variables, including solar radiation and cloud cover. Third, WeatherNext 3 moves beyond traditional analysis variables by learning to predict satellite-derived precipitation estimates, as well as tropical cyclone and station observations. Modelling sparse station data allows WeatherNext 3 to make 2m temperature and dewpoint predictions at any location and time, conditioned on local geographical features, with substantially lower error than competing global models, even when evaluated against unseen stations. Together, WeatherNext 3's capabilities move operational AI-based weather forecasting beyond emulating the traditionally distinct stages of data assimilation, forecasting and post-processing, which helps to further push the frontier of performance and granularity for global weather prediction.
We introduce Mosaic, a probabilistic weather forecasting model that addresses three failure modes of spectral degradation in ML-based weather prediction: spectral damping (statistical), high-frequency aliasing (architectural), and residual high-frequency leakage (parametric). Mosaic generates ensemble members through learned functional perturbations and operates on native-resolution grids via mesh-aligned block-sparse attention, a hardware-aligned mechanism that captures long-range dependencies at linear cost by sharing keys and values across spatially adjacent queries. At 1.5° resolution with 214M parameters, Mosaic matches or outperforms models trained on 6× finer resolution on key variables and achieves state-of-the-art results among 1.5° models, producing well-calibrated ensembles whose individual members exhibit near-perfect spectral alignment across all resolved frequencies. A 24-member, 10-day forecast takes under 12s on a single H100~GPU. Code is available at https://github.com/maxxxzdn/mosaic.
Weather forecasting offers an ideal testbed for artificial intelligence (AI) to learn complex, multi-scale physical systems. Traditional numerical weather prediction remains computationally costly for frequent regional updates, as high-resolution nests require intensive boundary coupling. We introduce Multi-Resolution Graph Neural Forecasting (MR-GNF), a lightweight, physics-aware model that performs short-term regional forecasts directly on an ellipsoidal, multi-scale graph of the Earth. The framework couples a 0.25° region of interest with a 0.5° context belt and 1.0° outer domain, enabling continuous cross-scale message passing without explicit nested boundaries. Its axial graph-attention network alternates vertical self-attention across pressure levels with horizontal graph attention across surface nodes, capturing implicit 3-D structure in just 1.6 M parameters. Trained on 40 years of ERA5 reanalysis (1980-2024), MR-GNF delivers stable +6 h to +24 h forecasts for near-surface temperature, wind, and precipitation over the UK-Ireland sector. Despite a total compute cost below 80 GPU-hours on a single RTX 6000 Ada, the model matches or exceeds heavier regional AI systems while preserving physical consistency across scales. These results demonstrate that graph-based neural operators can achieve trustworthy, high-resolution weather prediction at a fraction of NWP cost, opening a practical path toward AI-driven early-warning and renewable-energy forecasting systems. Project page and code: https://github.com/AndriiShchur/MR-GNF
Andrii Shchur, Inna Skarga-Bandurova
Kyiv School of Economics · Oxford Brookes University