Lagrangian Particles for Localized Extremes in Neural Weather ODEs

Neural weather forecasts can lose skill on localized extremes even when global error remains low. We study LE-NODE, a continuous-time hybrid model that combines an Eulerian grid state with sparse, adaptively selected Lagrangian particles for localized anomalies. A synthetic advection probe characterizes high-wavenumber coefficient changes in Eulerian neural ODEs, motivating a particle state that follows localized structures. We evaluate the resulting model through forecast comparisons. On ERA5 at a five-day lead, LE-NODE obtains 221 m upper-tail Z500 RMSE versus 284 m for the strongest reported external baseline and 312 m for its Eulerian-only ablation under the same auxiliary objective. Recomputed lower-tail MSLP RMSE is 5.1 hPa versus 6.7 hPa for PanguLite. These results concern area-weighted pointwise tail metrics and the tested backbone. The results support a sparse particle branch as a useful complement to the tested Eulerian backbone.