GDOSphere: A spherical graph neural network framework with neural operators for weather forecasting

At present, Data-Driven Weather Prediction (DDWP) can obtain accurate and efficient forecast results. However, the current weather forecasting based on two-dimensional planar grid has the problem of incompatibility between geographic information and spherical space, resulting in poor spatial convergence. Besides, the multi-order differential components of physical rules require a large parameter space for fitting, resulting in inefficient training and inference. The non-convergence and inefficiency due to the large parameter space of DDWP without physical constraints make it challenging to achieve high fidelity and training efficiency at the same time. Therefore, it is structurally and spatially sophisticated to design an efficient physically guided weather forecasting model. To this end, we propose a physics-informed architecture, GDOSphere, which leverages oriented differentiation on the multi-scale spherical spaces. GDOSphere is designed on Graph Differential Operators (GDOs) proposed by us, which contain embedded values, multi-order derivatives, and cross multiplications to establish the neural network structure in accordance with physical equations. We project the data onto a uniform spherical mesh and then apply the GDOs for iterative aggregation. Finally, we remap the data back into plane space and complement spatio-temporal details with post-processing. Through extensive experiments, we demonstrate that GDOSphere enhances prediction accuracy, achieving forecasting skills on par with the current best methods. And GDOSphere significantly reduces computation time by up to 10× compared with existing models, paving the way for its deployment in operational settings.