## 4 Experiments
### Experiment Setup  
The experiment used the WeatherBench high-resolution dataset with 2048 global nodes, specifically on a \(5.625^{\circ}\times 5.625^{\circ}\) grid (64 longitude \(\times\) 32 latitude bins) covering global areas, recording real weather data. The focus of this study is to conduct hourly weather forecasts using a subset extracted from the WeatherBench dataset. This subset covers variables such as temperature, cloud cover, humidity, and ground wind speed. It includes nodes with continuous hourly records from 1 January 2010 to 31 December 2018, to ensure data integrity for model training and testing. For detailed analysis, the prediction results of these four meteorological variables were compared separately. The input and prediction time steps of the HyMePre model were both set to 12 h. The dataset was divided into 1994 training samples, 664 validation samples, and 644 test samples. HyMePre is a deep learning network used for weather forecasting. To verify the accuracy of our experimental comparisons, we compared it with traditional forecasting models and other deep learning networks. The specific comparison method is as follows:  
* HA predicts future values by calculating the average of historical observations at corresponding time steps across previous days or cycles. * ARIMA models time series data by combining autoregressive terms, differencing operations, and moving average components to capture temporal structures. * RNN models sequential data by maintaining a hidden state that is updated at each time step, enabling the network to learn temporal dependencies across the input sequence
* STGCN [39] applies one-dimensional convolution along the time axis to learn temporal dependencies from time series inputs. This approach effectively captures both short- and long-term temporal patterns within a predefined window. * ASTGCN [40] incorporates spatial attention to model spatial dependencies and temporal attention to learn correlations across different time steps, enabling comprehensive spatiotemporal feature extraction. * AGCRN [41] adaptively captures spatiotemporal dependencies by combining node-level representation learning with dynamic graph construction. It extracts individualized features for each node and generates time-sensitive adjacency structures that reflect evolving relationships among nodes. * SimpleSTG [42] captures spatiotemporal dependencies through a unified framework that merges spatial and temporal modules. It leverages a simplified Neural Architecture Search method based on stochastic search to optimize model design. * FCSTGNN [43] provides comprehensive modeling of spatiotemporal dependencies in multi-sensor time series data by constructing fully connected graphs to link all sensors and timestamps. It employs sliding-window-based convolution and pooling GNN layers for efficient feature extraction. The model was optimized using the AdamW optimizer with an initial learning rate of \(\eta_{0}=5\times 10^{-4}\), adopting a cosine annealing schedule over training epochs. Training employed a dynamic batch size strategy starting from 32 samples and progressively increasing to 128 based on gradient stability. The spatial-temporal attention layers utilized GeLU activation functions, while hypergraph convolution employed Tanh activations for bounded feature propagation. The training protocol ran for 300 maximum epochs with early stopping triggered after 25 epochs of validation plateau (\(\Delta<10^{-4}\)), maintaining dropout rates of \(p=0.3\) across all transformer layers for regularization.