mlsanityData to 14 Oct 2026

Fixing the Double Penalty in Data-Driven Weather Forecasting Through a Modified Spherical Harmonic Loss Function

arXiv 2501.19374 ↗First posted 31 Jan 2025cs.LG physics.ao-phcited by 28

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Abstract (arXiv)

Recent advancements in data-driven weather forecasting models have delivered deterministic models that outperform the leading operational forecast systems based on traditional, physics-based models. However, these data-driven models are typically trained with a mean squared error loss function, which causes smoothing of fine scales through a "double penalty" effect. We develop a simple, parameter-free modification to this loss function that avoids this problem by separating the loss attributable to decorrelation from the loss attributable to spectral amplitude errors. Fine-tuning the GraphCast model with this new loss function results in sharp deterministic weather forecasts, an increase of the model's effective resolution from 1,250km to 160km, improvements to ensemble spread, and improvements to predictions of tropical cyclone strength and surface wind extremes.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). Builds on 11 of its 38 references that are in the map. First posted on arXiv 31 Jan 2025.

Builds on

11 of 38 references.

References · 11

  1. 2023WeatherBench 2: A benchmark for the next generation of data-driven global weather modelscited by 236
  2. 2023Spherical Fourier Neural Operators: Learning Stable Dynamics on the Spherecited by 233
  3. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 216
  4. 2022FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operatorscited by 188
  5. 2022Forecasting Global Weather with Graph Neural Networkscited by 168
  6. 2020Improving data-driven global weather prediction using deep convolutional neural networks on a cubed spherecited by 96
  7. 2024ArchesWeather & ArchesWeatherGen: a deterministic and generative model for efficient ML weather forecastingcited by 32
  8. 2024A Practical Probabilistic Benchmark for AI Weather Modelscited by 25
  9. 2024Leveraging data-driven weather models for improving numerical weather prediction skill through large-scale spectral nudgingcited by 8
  10. 2024Efficient fine-tuning of 37-level GraphCast with the Canadian global deterministic analysiscited by 4
  11. 2022Can we integrate spatial verification methods into neural-network loss functions for atmospheric science?cited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 8; 2026: 20.

28 papers.

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  1. 2025FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scalecited by 62
  2. 2025High-Resolution Probabilistic Data-Driven Weather Modeling with a Stretched-Gridcited by 9
  3. 2025HRRRCast: a data-driven emulator for regional weather forecasting at convection allowing scalescited by 7
  4. 2025STCast: Adaptive Boundary Alignment for Global and Regional Weather Forecastingcited by 7
  5. 2025FastNet: Improving the physical consistency of machine-learning weather prediction models through loss function designcited by 5
  6. 2026(Sparse) Attention to the Details: Preserving Spectral Fidelity in ML-based Weather Forecasting Modelscited by 5
  7. 2026PhysMetrics.Weather: An Evaluation Framework for Physical Consistency in ML Weather Modelscited by 5
  8. 2025A comparison of stretched-grid and limited-area modelling for data-driven regional weather forecastingcited by 4
  9. 2026Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecastingcited by 4
  10. 2026WIND: Weather Inverse Diffusion for Zero-Shot Atmospheric Modelingcited by 3
  11. 2026On Neural Scaling Laws for Weather Emulation through Continual Trainingcited by 2
  12. 2026Multi-Scale Wavelet Transformers for Operator Learning of Dynamical Systemscited by 1
16 more
  1. 2026Toward generative machine learning for boosting ensembles of climate simulationscited by 1
  2. 2025Revealing the Potential of Learnable Perturbation Ensemble Forecast Model for Tropical Cyclone Predictioncited by 0
  3. 2025MeltwaterBench: Deep learning for spatiotemporal downscaling of surface meltwatercited by 0
  4. 2026WADEPre: A Wavelet-based Decomposition Model for Extreme Precipitation Nowcasting with Multi-Scale Learningcited by 0
  5. 2026The Rise of AI in Weather and Climate Information and its Impact on Global Inequalitycited by 0
  6. 20263DTCR: Vortex-following generative reconstruction improves tropical cyclone intensity prediction from global AI weather forecastscited by 0
  7. 2026FuXiWeather2: Learning accurate atmospheric state estimation for operational global weather forecastingcited by 0
  8. 2026Improving Ensemble Forecasts of Abnormally Deflecting Tropical Cyclones with Fused Atmosphere-Ocean-Terrain Datacited by 0
  9. 2026ThousandWorlds: A benchmark for climate emulation of potentially habitable exoplanetscited by 0
  10. 2026Do AI weather models miss extremes?cited by 0
  11. 2026Diffusion-Based Refinement for Kilometer-Scale Probabilistic Precipitation Nowcastingcited by 0
  12. 2026Neptune: An AI model for Global Ocean Subseasonal Predictioncited by 0
  13. 2026Aries: A Proprietary Medium-Range Weather Prediction Model for the Energy Industrycited by 0
  14. 2026Lightweight Probabilistic Downscaling from a Deterministic Base Modelcited by 0
  15. 2026Varda-single-1.0: deterministic data-driven weather forecasting at 1 km resolution over Switzerland's complex topographycited by 0
  16. 2026Xaurora: Generative Weather Forecasting with Denoising Stochastic Interpolants from a Foundation Model Priorcited by 0