mlsanityData to 14 Oct 2026

A multi-scale loss formulation for learning a probabilistic model with proper score optimisation

arXiv 2506.10868 ↗First posted 12 Jun 2025physics.ao-ph cs.AIcited by 6

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Abstract (arXiv)

We assess the impact of a multi-scale loss formulation for training probabilistic machine-learned weather forecasting models. The multi-scale loss is tested in AIFS-CRPS, a machine-learned weather forecasting model developed at the European Centre for Medium-Range Weather Forecasts (ECMWF). AIFS-CRPS is trained by directly optimising the almost fair continuous ranked probability score (afCRPS). The multi-scale loss better constrains small scale variability without negatively impacting forecast skill. This opens up promising directions for future work in scale-aware model training.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 9 of its 25 references that are in the map. First posted on arXiv 12 Jun 2025.

Builds on

9 of 25 references.

References · 9

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  4. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  5. 2023Neural General Circulation Models for Weather and Climatecited by 239
  6. 2023GenCast: Diffusion-based ensemble forecasting for medium-range weathercited by 177
  7. 2021Probabilistic Forecasting with Generative Networks via Scoring Rule Minimizationcited by 37
  8. 2025Diffusion-LAM: Probabilistic Limited Area Weather Forecasting with Diffusioncited by 11
  9. 2023Stochastic Latent Transformer: Efficient Modelling of Stochastically Forced Zonal Jetscited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 3.

6 papers.

  1. 2025High-Resolution Probabilistic Data-Driven Weather Modeling with a Stretched-Gridcited by 9
  2. 2026WeatherNext 3: Increasing resolution and performance of global weather models with raw observationscited by 2
  3. 2025CSU-PCAST: A Dual-Branch Transformer Framework for medium-range ensemble Precipitation Forecastingcited by 1
  4. 2026On the sensitivity of machine-learned probabilistic weather forecast models to scale-aware scoring rulescited by 1
  5. 2025Revealing the Potential of Learnable Perturbation Ensemble Forecast Model for Tropical Cyclone Predictioncited by 0
  6. 2026Rescene: band-limited stochastic forcing turns a frozen neural weather operator into a climate emulatorcited by 0