SDECast: Probabilistic Weather Forecasting in Continuous Time with Neural SDEs

2026-10-02

AI Summary

This study addresses the error accumulation and lack of atmospheric dynamic continuity in existing weather forecasting models caused by fixed time steps. To overcome these limitations, this work proposes a continuous-time probabilistic forecasting framework based on Neural Stochastic Differential Equations (Neural SDEs). Methodologically, by extending SDE matching techniques, the framework directly learns stochastic dynamics in physical space without requiring repeated simulations during training, thereby explicitly encoding the spatiotemporal continuity of the atmosphere. The proposed approach successfully recovers drift dynamics within simulated flows, enabling global hourly forecasting. Furthermore, it demonstrates highly skillful probabilistic prediction capabilities over a five-day lead time.

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.

Problem

• Weather Forecasting
• Error Accumulation
• Temporal Continuity
• Probabilistic Forecasting

Innovation

• Neural Stochastic Differential Equations
• Continuous-Time Forecasting
• Probabilistic Weather Forecasting
• SDE Matching
• Physical Space Learning