HelmGeoNet: Physics-Embedded Forecasting of Global Geostrophic Currents via Helmholtz Decomposition

Accurate and stable long-horizon forecasting of global ocean currents remains difficult. Data-driven models typically learn the velocity field as a whole and forecast it autoregressively. Without explicit guidance on the evolution of its physically distinct components, they capture the overall trend but learn each component inaccurately, so forecasts of currents and kinetic energy lose accuracy and stability at long horizons. To address this, we propose HelmGeoNet for more energy-faithful forecasting of geostrophic currents. Specifically, we embed the Helmholtz decomposition into the network architecture, so that the model explicitly learns the evolution of each physically distinct component. We also introduce a physics-guided relaxation mechanism that filters out redundant information from the input field, mitigating the error accumulation. Experiments on daily geostrophic currents confirm that HelmGeoNet outperforms eight spatiotemporal backbones in currents forecasting. At the 20-day lead, its eddy kinetic energy RMSE is 0.0029 m${}^2$/s${}^2$ lower than that of the best baseline, and its EKE remains stable across the forecast horizon.