DeepPrim: a Physics-Driven 3D Short-term Weather Forecaster via Primitive Equation Learning

Solving primitive equations is essential for accurate weather forecasting. However, traditional numerical weather prediction (NWP) methods often incorporate various simplifications that limit their effectiveness in parameterizing unresolved physical processes. Meanwhile, existing deep learning-based models mostly focus on pure data-driven paradigms, overlooking the fundamental physical principles that govern atmospheric dynamics. To address these challenges, we present DeepPrim, a novel 3D \underline{deep} weather forecaster designed to learn \underline{prim}itive equations of the Earth’s atmosphere. Specifically, DeepPrim aims at accurately modeling 3D atmospheric motion through Navier-Stokes equation in pressure coordinates, and effectively capturing the interactions between the solved advection and key weather variables (e.g., temperature and water vapor) through corresponding equations. By seamlessly integrating fundamental atmospheric physics with advanced data-driven techniques, our model effectively approximates complicated physical processes without relying on empirical simplifications. Experimentally, DeepPrim achieves impressive performance in both short-term global and regional weather forecasting tasks, and exhibits the superior capacity to capture 3D atmospheric dynamics. The code is available at https://anonymous.4open.science/r/DeepPrim.