SDECast: Probabilistic Weather Forecasting in Continuous Time with Neural SDEs
Abstract
Existing machine learning weather forecasting models typically generate forecasts through autoregressive rollouts at a fixed temporal resolution. While highly efficient for long-range prediction, this formulation can suffer from severe error accumulation when used with shorter time steps and does not explicitly encode the locality and temporal continuity of atmospheric dynamics. To address these limitations, we introduce **SDECast**, a Neural Stochastic Differential Equation (SDE) framework for continuous-time probabilistic weather forecasting. SDECast extends SDE Matching to learn stochastic dynamics directly in physical space, without requiring repeated SDE simulation during training. On a simulated geophysical flow, we show that SDECast recovers meaningful drift dynamics and faithfully reproduces the underlying continuous-time behavior. We then demonstrate its scalability to global weather forecasting at hourly resolution, where SDECast produces skillful probabilistic forecasts for lead times of up to five days.
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BibTeX
@misc{marchenko2026sdecast,
title = {{SDECast: Probabilistic Weather Forecasting in Continuous Time with Neural SDEs}},
author = {Maria Marchenko and Martin Andrae and Fredrik Lindsten and Christian A. Naesseth},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03313},
eprint = {2610.03313},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03313},
}
RIS
TY - UNPB
TI - SDECast: Probabilistic Weather Forecasting in Continuous Time with Neural SDEs
AU - Maria Marchenko
AU - Martin Andrae
AU - Fredrik Lindsten
AU - Christian A. Naesseth
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03313
UR - https://arxiv.org/abs/2610.03313
AB - Existing machine learning weather forecasting models typically generate forecasts through autoregressive rollouts at a fixed temporal resolution. While highly efficient for long-range prediction, this formulation can suffer from severe error accumulation when used with shorter time steps and does not explicitly encode the locality and temporal continuity of atmospheric dynamics. To address these limitations, we introduce **SDECast**, a Neural Stochastic Differential Equation (SDE) framework for continuous-time probabilistic weather forecasting. SDECast extends SDE Matching to learn stochastic dynamics directly in physical space, without requiring repeated SDE simulation during training. On a simulated geophysical flow, we show that SDECast recovers meaningful drift dynamics and faithfully reproduces the underlying continuous-time behavior. We then demonstrate its scalability to global weather forecasting at hourly resolution, where SDECast produces skillful probabilistic forecasts for lead times of up to five days.
ER -