## 5 Case Study
### Baseline Model  
M2 GSNet is our proposed model and it has three features. First, it utilizes the feature of cubic NWP wind speed by using the multi-modal learning. Second, it adopts the spatiotemporal model for the geographical information extraction. Third, it uses the multi-task learning to predict the power of each wind farm. To illustrate the accuracy improvement by each feature, we design the baseline model and other GCN model for ablation study.  
(1) MLP [6]: This is the multilayer perception model for regression and the hidden state number is 800. The historical wind power of each wind farm, including 40 time steps as the input and output, is the wind power of the same wind farm including 16 time steps. The sum of the wind power for each wind farm is the regional wind power.  
(2) LSTM [9]: This includes two LSTM layers and the dropout rate is 0.25. The historical wind power of each wind farm, including 40 time steps as the input and output, is the wind power of the same wind farm including 16 time steps.  
(3) ELM [35]: This uses the classic ELM model parameter. The historical wind power of each wind farm, including 40 time steps as the input and output, is the wind power of the same wind farm including 16 time steps. The sum of the wind power for each wind farm is the regional wind power.  
(4) LSTNet [10]: This uses the standard LSTNet structure and parameter and it can take consideration of the spatiotemporal relationship of wind farms. However, it cannot make use of the geographical information of the wind farms when extracting the spatial feature of the wind farms. The input only includes the historical wind power of each wind farm. The output is the wind power of each wind farm including 16 time steps.  
(5) LSTNet_NWP: This uses the same structure and parameter with LSTNet. However, it also uses the cubic NWP windspeed as input and it concatenates the spatial-temporal feature of historical wind power and NWP. The output is the wind power of each wind farm including 16 time steps.  
We also compare different M2 GSNet models for the ablation study and the characteristic of each model is as shown in Table 1.  
Where M2 GSNet means the model that uses the information of the cubic NWP wind speed, the w/o CW means the GCN model that only uses the raw data of NWP but without using the cubic NWP wind speed. The w/o AD means the GCN model that uses the information of cubic NWP wind speed but uses the wind speed time series correlation to define the graph. The w/o W means the GCN model that does not use the NWP. The w/o MT1 means the GCN model that does not use the multi-task learning and predicts the wind power of the region directly. The w/o MT2 means the GCN model that does not use the multi-task learning and predict the wind power of each wind farm separately. We use same model structure but train the model individually. The training hyper-parameter is the same as the description above and only the model structure is different.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Model Type**} \\ \hline
**Method** & **Multi-Modal** & **Multi-Task** & **Adjacent Matrix** & **Prediction Granularity** \\ \hline M2 GSNet & Cubic wind speed & Yes & Distance based & Power of each wind farm \\ \hline w/o CW & Raw wind speed & Yes & Distance based & Power of each wind farm \\ \hline w/o AD & Cubic wind speed & Yes & Correlation based & Power of each wind farm \\ \hline w/o W & No wind speed & Yes & Distance based & Power of each wind farm \\ \hline w/o MT1 & Cubic wind speed & No & Distance based & Regional power \\ \hline w/o MT2 & Cubic wind speed & No & Distance based & Power of each wind farm \\ \hline \hline \end{tabular}
\end{table}
Table 1: The structure of different M2 GSNet models.