## 3 Methodology
### Spatial-Temporal Decoupled Masked Pretraining  
The proposed pretraining framework addresses the challenge of spatiotemporal heterogeneity in meteorological data through a novel dual-masking strategy. The core insight lies in decoupling the learning of spatial and temporal patterns via specialized reconstruction tasks, which forces the model to develop distinct representations for geographic correlations and temporal dynamics. This approach learns disentangled spatial and temporal representations from unlabeled data through a dual masking strategy, which are later integrated into a hypergraph-based predictor.  
Given an input spatiotemporal series \(\mathbf{X}\in\mathbb{R}^{T\times N\times F}\) (where \(T\) is the number of time steps, \(N\) is the number of stations, and \(F\) is the feature dimension), we apply two indepen  
Figure 2: The HyMePre framework: a hypergraph-enhanced approach for meteorological pretraining.  
dent masking strategies: Spatial masking (S-Mask) randomly occludes \(r\times 100\%\) of stations across all time steps, forcing the model to reconstruct missing sensor data using spatial correlations. For example, if station \(i\) is masked, the model must infer its values from neighboring stations with similar meteorological patterns. Temporal masking (T-Mask) removes \(r\times 100\%\) of contiguous time steps, requiring the model to predict missing temporal segments using historical trends. Temporal masking simulates real-world data gaps and enhances the model's ability to capture periodicity (e.g., daily/weekly cycles).  
The masked inputs are processed by two separate autoencoders: Spatial Autoencoder (S-MAE) employs self-attention along the spatial dimension to learn station-wise dependencies. It takes the spatially masked input \(\textbf{X}^{S}\in\mathbb{R}^{T\times N(1-r)\times F}\), applies patch embedding and positional encoding, and generates spatial representations \(\textbf{H}_{s}\in\mathbb{R}^{T_{p}\times N\times E}\) (where \(T_{p}\) is the number of patch windows and \(E\) is the embedding dimension). Temporal Autoencoder (T-MAE) uses causal self-attention along the temporal dimension to model time series dynamics. It processes the temporally masked input \(\textbf{X}^{T}\in\mathbb{R}^{T(1-r)\times N\times F}\) and produces temporal representations \(\textbf{H}_{t}\in\mathbb{R}^{T_{p}\times N\times E}\).  
The positional encoding integrates both spatial (e.g., station coordinates) and temporal (e.g., timestamps) information:  
\[\begin{cases}E_{t}[t,n,2k]=\sin\left(\frac{t}{10000^{4k/E}}\right),&E_{t}[t,n,2k+1]=\cos\left(\frac{t}{10000^{4k/E}}\right),\\ E_{t}[t,n,2m+E/2]=\sin\left(\frac{n}{10000^{4k/E}}\right),&E_{t}[t,n,2m+1+E/2]= \cos\left(\frac{n}{10000^{4k/E}}\right),\end{cases} \tag{1}\]  
where \(t\) is the time step and \(n\) is the station index. The spatial encoding utilizes station indices rather than raw coordinates due to the structured nature of our dataset. The 2048 stations originate from a uniformly discretized global grid (64 longitude bins \(\times\) 32 latitude bins), where adjacent indices correspond to geographically proximate locations (approximately 5.625\({}^{\circ}\) separation per index step). This design enables the model to distinguish spatial proximity (e.g., coastal vs. inland stations) and temporal phases (e.g., morning vs. evening peaks).  
During pretraining, the model minimizes the reconstruction loss for masked regions using mean absolute error (MAE):  
\[\mathcal{L}_{\text{pretrain}}=\lambda_{s}\cdot\text{MAE}(\hat{\textbf{X}}_{s}, \textbf{X}_{s})+\lambda_{t}\cdot\text{MAE}(\hat{\textbf{X}}_{t},\textbf{X}_{t }), \tag{2}\]  
where \(\hat{\textbf{X}}_{s}\) and \(\hat{\textbf{X}}_{t}\) are the reconstructed spatial and temporal segments, and \(\lambda_{s},\lambda_{t}\) balance the two losses. This decoupled training ensures that \(\textbf{H}_{s}\) and \(\textbf{H}_{t}\) capture distinct spatial and temporal patterns.