## 3 Methodology
### Problem Definition and Network Architecture  
The weather forecast predicts future atmospheric conditions by analyzing the historical observation records from monitoring stations. In this paper, the inputs to the HyMePre model include the geographical locations of the weather stations and their historical weather data, the data from all weather stations \(N\) at the \(t\)-th time step denoted as \(\{X_{t}=\{x_{1}^{t},x_{2}^{t},\ldots,x_{S}^{t}\}\in R^{N\times F}\}_{t=1}^{T_ {in}}\), where \(T_{in}\) represents the time dimension and \(F\) is the number of meteorological features. The task of the model is based on the historical time series for \(m\) time steps as input \(\{X_{t-m},\ldots,X_{t-1},X_{t}\}\) to predict the future time series \(\{X_{t+1},\ldots,X_{t+l-1},X_{t+l}\}\) for \(l\) time steps. As shown in Figure 2, the framework operates through three sequential stages: input representation, preprocessing with masked pretraining, and hypergraph-based forecasting.  
**Input Representation**  
The input consists of historical multivariate time series data and station metadata. Each station provides a sequence of observations (e.g., hourly temperature, wind speed) organized as a tensor, where the dimensions correspond to stations, time steps, and meteorological variables. Station metadata includes geographic coordinates (latitude and longitude), which are used to derive spatial relationships. To model complex dependencies between stations, a hypergraph is constructed by connecting groups of stations based on feature similarity. This similarity is computed from historical data, capturing stations with correlated meteorological behavior (e.g., stations experiencing simultaneous rainfall patterns or temperature fluctuations). The hypergraph structure enables the representation of multi-station interactions beyond pairwise connections, such as regional weather systems or clustered microclimates.  
**Preprocessing with Masked Pretraining**  
The raw input data undergoes a preprocessing phase where it is mapped into a latent embedding space. A self-supervised pretraining task is applied using a dual-masking strategy: spatial masking randomly occludes observations from a subset of stations, while temporal masking removes contiguous blocks of time steps. The model is trained to reconstruct the masked regions, forcing it to infer missing spatial information from neighboring stations and recover temporal patterns through historical trends. Spatial reconstruction emphasizes learning regional correlations, whereas temporal reconstruction focuses on capturing periodic phenomena. This stage produces disentangled embeddings that separately encode spatial context and temporal dynamics.  
**Hypergraph-Based Forecasting**  
The pretrained embeddings are integrated into a hypergraph neural network for final prediction. The hypergraph structure dynamically aggregates features from meteorologically related stations, propagating information through hyperedges that group stations with similar behavioral patterns. For example, a hyperedge might link stations affected by the same frontal system, allowing the model to collectively update their predictions based on shared atmospheric conditions. The forecasting module combines the spatial-temporal embeddings with hypergraph-derived features, refining predictions through iterative message passing. This process ensures that localized weather patterns and large-scale atmospheric dynamics are jointly considered, enhancing the accuracy of multi-step forecasts.