# High-Resolution Probabilistic Data-Driven Weather Modeling with a Stretched-Grid

arXiv: https://arxiv.org/abs/2511.23043 · HTML: https://mlsanity.com/paper/2511.23043/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 43 references that are in the map.
- First posted on arXiv 28 Nov 2025.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Skillful joint probabilistic weather forecasting from marginals](https://mlsanity.com/paper/2506.10772/) (2025)
- [FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale](https://mlsanity.com/paper/2507.12144/) (2025)
- [Probabilistic Weather Forecasting with Hierarchical Graph Neural Networks](https://mlsanity.com/paper/2406.04759/) (2024)
- [Fixing the Double Penalty in Data-Driven Weather Forecasting Through a Modified Spherical Harmonic Loss Function](https://mlsanity.com/paper/2501.19374/) (2025)
- [Regional data-driven weather modeling with a global stretched-grid](https://mlsanity.com/paper/2409.02891/) (2024)
- [ExtremeCast: Boosting Extreme Value Prediction for Global Weather Forecast](https://mlsanity.com/paper/2402.01295/) (2024)
- [Building Machine Learning Limited Area Models: Kilometer-Scale Weather Forecasting in Realistic Settings](https://mlsanity.com/paper/2504.09340/) (2025)
- [LEONARDO: A Pan-European Pre-Exascale Supercomputer for HPC and AI Applications](https://mlsanity.com/paper/2307.16885/) (2023)
- [Diffusion-LAM: Probabilistic Limited Area Weather Forecasting with Diffusion](https://mlsanity.com/paper/2502.07532/) (2025)
- [EnScale: Temporally-consistent multivariate generative downscaling via proper scoring rules](https://mlsanity.com/paper/2509.26258/) (2025)
- [A multi-scale loss formulation for learning a probabilistic model with proper score optimisation](https://mlsanity.com/paper/2506.10868/) (2025)
- [A comparison of stretched-grid and limited-area modelling for data-driven regional weather forecasting](https://mlsanity.com/paper/2507.18378/) (2025)

## Built on by (most cited first, 9 of 9)

- [Probabilistic Retrofitting of Learned Simulators](https://mlsanity.com/paper/2603.01949/) (2026)
- [(Sparse) Attention to the Details: Preserving Spectral Fidelity in ML-based Weather Forecasting Models](https://mlsanity.com/paper/2604.16429/) (2026)
- [PDE foundation models are skillful AI weather emulators for the Martian atmosphere](https://mlsanity.com/paper/2602.15004/) (2026)
- [Pointwise is Pointless? A Multimodal Ablation Study for Precipitation Nowcasting with Graph Neural Networks](https://mlsanity.com/paper/2606.18436/) (2026)
- [Bridging short- and medium-range weather forecasting with machine learning](https://mlsanity.com/paper/2608.26822/) (2026)
- [Njord: A Probabilistic Graph Neural Network for Ensemble Ocean Forecasting](https://mlsanity.com/paper/2605.15470/) (2026)
- [A Station-Based Evaluation of Machine Learning-based Weather Forecasting Models in Northern Norway](https://mlsanity.com/paper/2609.10564/) (2026)
- [Varda-single-1.0: deterministic data-driven weather forecasting at 1 km resolution over Switzerland's complex topography](https://mlsanity.com/paper/2610.01835/) (2026)
- [Efficient Analog-Initialized Latent Transport for Spatially Coherent Probabilistic Downscaling from Global to Kilometer Scales](https://mlsanity.com/paper/2610.03736/) (2026)

## Abstract (arXiv)

We present a probabilistic data-driven weather model providing ensembles of high spatial resolution realizations of 87 variables at arbitrary ensemble size and forecast length. The model uses a global stretched grid, dedicating 2.5 km resolution to our Nordic region of interest and 31 km resolution elsewhere, with 6-hour temporal resolution. Unique ensemble members are generated by a stochastic model architecture, and we train it using a loss function based on the Continuous Ranked Probability Score (CRPS) evaluated in grid-point and spectral space. The spectral loss component is shown to be necessary to create fields that are spatially coherent, which is not the case when training with mean-squared error loss, nor CRPS in grid-point space only. We evaluate the forecasts against observations from surface weather stations and compare them to high-resolution operational numerical weather prediction forecasts from the MetCoOp Ensemble Prediction System (MEPS). The model shows lower CRPS than MEPS for 2 m temperature and mean sea-level pressure, with average improvements of 13% and 10%, respectively, while differences for wind speed and precipitation are smaller. For Storm Dave, the model captures the location and structure of strong-wind systems, but underestimates the peak winds.