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

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.

@article{lang2025_2506.10868,
  title={ A multi-scale loss formulation for learning a probabilistic model with proper score optimisation },
  author={ Simon Lang and Martin Leutbecher and Pedro Maciel },
  journal={arXiv preprint arXiv:2506.10868},
  year={ 2025 }
}