SDECast: stochastic neural differential equations for hour-by-hour weather forecasting

Rather than using a series of fixed-time steps that lead to accumulated errors, SDECast models the atmosphere on a continuous-time basis and produces hourly probabilistic forecasts for up to five days.

Most automatic learning weather forecasting models progress by regular leaps: each prediction serves as the starting point for the next, with a set step in advance. This is effective for remote deadlines, but as soon as the interval is reduced, errors are added from one step to the next. And nothing in this architecture reflects the fact that the atmosphere evolves continuously and locally.

Learning dynamics without simulating it

SDECast, presented on arXiv on October 2, 2026, addresses the problem with differential neuronal stochastic equations. The model relies on the so-called SDE Matching method to learn directly, in the physical space, the deterministic part and the random part of the evolution of the time it makes, without having to simulate these repeated equations during training, which would be very costly in calculation.

The authors first tested it on simulated geophysical flow, where it found a consistent drift and faithfully replicated the behavior in continuous time. They then applied it globally, with an hourly resolution: SDECast provides probabilistic forecasts deemed relevant up to five days.