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Project: Diffusion models for high-resolution probabilistic weather modelling

Description

The domain of weather forecasting is currently undergoing a significant transformation driven by advances in machine learning, where Data-Driven Models (DDMs) have demonstrated equal or superior performance compared to traditional Numerical Weather Prediction (NWP) models in predicting various variables, while operating at a fraction of the computational cost. Deterministic DDMs are characterized by blurring features and underestimation of extremes due to the mean squared error (MSE) loss function (Bouallegue et al., 2024). Probabilistic models have shown improvements with two types of models emerging: diffusion-based models and CRPS-based models. CRPS-based models minimize the pointwise CRPS score while being computationally cheaper than diffusion models (Price et al., 2024, Lang et al., 2026, Price et al., 2025). On the other hand, diffusion models are generative models that learn the data distribution by iteratively denoising samples from a sequence of progressively noised versions of the data. Diffusion models could potentially better capture high-frequency functions and have a more accurate representation of highly concentrated, multimodal distributions (Hendriks et al., 2026). However, both models still suffer from noisy artifacts at higher frequencies, which are amplified when moving to kilometer-scale resolution (Noordhagen et al. 2025). This project investigates the potential of diffusion modelling for the representation of atmospheric high-frequency spatial features, with a particular focus on analyzing the physical realism and distribution representation of probabilistic models.

Alet, F., Price, I., El-Kadi, A., Masters, D., Markou, S., Andersson, T. R., Stott, J., Lam, R., Willson, M., Sanchez-Gonzalez, A., and Battaglia, P. W. (2025). Skillful joint probabilistic weather forecasting from marginals. ArXiv, https://doi.org/10.48550/arXiv.2506.10772.

Ben Bouallègue, Z., Clare, M. C. A., Magnusson, L., Gascón, E., Maier-Gerber, M., Janoušek, M., Rodwell, M., Pinault, F., Dramsch, J. S., Lang, S. T. K., Raoult, B., Rabier, F., Chevallier, M., Sandu, I., Dueben, P., Chantry, M., & Pappenberger, F. (2024). The Rise of Data-Driven Weather Forecasting: A First Statistical Assessment of Machine Learning–Based Weather Forecasts in an Operational-Like Context. Bulletin of the American Meteorological Society, 105(6), E864-E883. https://doi.org/10.1175/BAMS-D-23-0162.1

Hendriks, F., Rokoš, O., Doškář, M., Geers, M. G. D., and Menkovski, V. (2026). Equivariant flow matching for symmetry-breaking bifurcation problems, ArXiv, https://arxiv.org/abs/2509.03340.

Lang, S., Alexe, M., Clare, M. C. A., Roberts, C., Adewoyin, R., Bouall`egue, Z. B.,Chantry, M., Dramsch, J., Dueben, P. D.,Hahner, S., Maciel, P., Prieto-Nemesio, A., O’Brien, C., Pinault, F., Polster,J., Raoult, B., Tietsche, S., and Leutbecher, M. (2026). AIFS-CRPS: Ensemble forecasting using a model trained with a loss function based on the continuous ranked probability score. npj Artificial Intelligence. 2, 18. https://doi.org/10.1038/s44387-026-00073-7.

Nordhagen, E. M., Haugen, H. H., Salihi, A. F. S., Ingstad, M. S., Nipen, T. N., Seierstad, I. A., Frogner, I.-L., Clare, M., Lang, S., Chantry, M., Dueben, P., and Kristiansen, J. (2025). High-resolution probabilistic data-driven weather modeling with a stretched-grid, ArXiv, https://arxiv.org/abs/2511.23043.

Price, I., Sanchez-Gonzalez, A., Alet, F., Andersson, T., El-Kadi, A., Masters, D., Ewalds, T., Stott, J., Mohamed, S., Battaglia, P., Lam, R., Willson, M. (2024). Probabilistic weather forecasting with machine learning. Nature. 637. 84-90. https://doi.org/10.1038/s41586-024-08252-9

Details

Supervisor

Vlado Menkovski

Secondary supervisor

SB

Sophie Buurman

External location

KNMI

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