## 1 Introduction
Pangu-Weather [14] further advances this line by applying a 3D Earth-specific deep learning model that achieves fast and highly accurate forecasts on a global scale. These models collectively highlight the potential of data-driven, graph-structured learning in advancing operational weather forecasting. However, a fundamental limitation of conventional GNNs lies in their reliance on pairwise edges, which restricts their ability to capture higher-order spatial dependencies involving multiple stations. Such complex interactions, common in meteorological systems like frontal zones or regional wind patterns, are difficult to express using binary connections alone, especially in the presence of noisy,incomplete, or non-locally correlated data. These challenges underscore the need for more expressive models capable of representing richer spatial structures. In light of these considerations, there is growing interest in more expressive alternatives that go beyond conventional graphs. The essence of meteorological systems involves high-order spatial interactions (e.g., frontal systems requiring coordinated modeling of multiple stations), where traditional graph neural networks' binary connections struggle to capture multi-site dependencies. Hypergraph neural networks [15] address this limitation by connecting arbitrary subsets of nodes through hyperedges, explicitly encoding regional clustering behaviors (e.g., station groups under shared synoptic influences like rain belts or wind propagation paths). This capability enables (1) modeling multi-site correlations along moisture transport corridors in short-term precipitation prediction, and (2) capturing nonlinear interactions across climatically similar regions during heatwave propagation. Such high-order expressiveness aligns fundamentally with meteorological physics, providing physically grounded spatial representations. By generalizing traditional GNNs, hypergraphs offer enhanced capacity to model complex multi-station dependencies and collective spatial behaviors. Capturing these higher-order relationships allows more accurate representation of semantic and physical intricacies in weather systems [16; 17]. Recent studies have demonstrated the efficacy of HyperGNNs in weather forecasting tasks. The Probabilistic Hypergraph Recurrent Neural Network [18] introduces probabilistic modeling into hypergraph structures, capturing dynamic node-hyperedge relationships and outperforming traditional models in time series forecasting scenarios. These advancements underscore the potential of HyperGNNs to enhance the representation of complex spatial dependencies in meteorological data, leading to more accurate and reliable weather forecasting models. Building upon these insights, we propose Hypergraph-enhanced Meteorological Pre-training (HyMePre), a two-stage framework for short-term weather forecasting, as show in Figure 1. The first stage employs a self-supervised pretraining scheme with separate spatial and temporal masking strategies to learn disentangled representations from unlabeled station-level time series data. In the second stage, a hypergraph neural network-based forecasting module is introduced, where the hypergraph is constructed using time-averaged meteorological features to capture high-order spatial dependencies among weather stations. Through this design, the model not only achieves stronger robustness and generalization in representation learning, but also naturally encodes higher-order spatial dependencies among multiple stations, thereby improving the accuracy and stability of short-term multi-station weather forecasts. In summary, our key contributions are as follows:  
* A decoupled spatial-temporal pre-training scheme tailored for meteorological time series is proposed, enabling the model to disentangle and capture long-range spatial patterns and temporal dynamics.