Equivariant and Invariant Message Passing for Global Subseasonal-to-seasonal Forecasting

Accurate weather forecasting on Subseasonal-to-Seasonal (S2S) timescale is critical to human society such as agriculture planning and extreme weather preparation. Although data-driven models have become alternatives to computationally intensive Numerical Weather Prediction (NWP) systems, existing Transformer-based approaches suffer from biases due to planar projections distorting the spherical geometry and inadequate handling of vector-scalar variable interactions (e.g., wind velocity vs. temperature). To address these limitations, we propose a graph-based Equivariant and Invariant Message Passing (EIMP) framework that directly processes spherical grid data. It maintains SO(3) equivariant embeddings for vector data and SO(3) invariant embeddings for scalar data, which are interacted by a shared invariant message embedding. Guaranteed equivariant and invariant message aggregation functions are proposed to update embeddings under strict symmetry constraints. Extensive experiments on the Earth Reanalysis 5 (ERA5) reanalysis dataset of 41 years demonstrate the proposed model achieves significant improvement over advanced data-driven models and skillful numerical ECMWF systems. Additionally, we empirically show that EIMP demonstrates geometrically superior predictions and conduct ablation studies to validate the efficacy of its design.