# Trajectory learning for ensemble forecasts via the continuous ranked probability score: a Lorenz '96 case study

arXiv: https://arxiv.org/abs/2508.21664 · HTML: https://mlsanity.com/paper/2508.21664/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 47 references that are in the map.
- First posted on arXiv 29 Aug 2025.

## Builds on (most cited first, 4 of 4)

- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Model](https://mlsanity.com/paper/1909.04711/) (2019)
- [Decompositions of the mean continuous ranked probability score](https://mlsanity.com/paper/2311.14122/) (2023)
- [Comparison of neural closure models for discretised PDEs](https://mlsanity.com/paper/2210.14675/) (2022)

## Abstract (arXiv)

This paper demonstrates the feasibility of trajectory learning for ensemble forecasts by employing the continuous ranked probability score (CRPS) as a loss function. Using the two-scale Lorenz '96 system as a case study, we develop and train both additive and multiplicative stochastic parametrizations to generate ensemble predictions. Results indicate that CRPS-based trajectory learning produces parametrizations that are both accurate and sharp. The resulting parametrizations are straightforward to calibrate and outperform derivative-fitting-based parametrizations in short-term forecasts. This approach is particularly promising for data assimilation applications due to its accuracy over short lead times.