# Neural Multivariate Grey Model and Its Applications
## 4 Experiments
### Forecast of China's Total Amount of Renewable Energy  
This section uses the new MGM model and four other comparative models to predict China's total renewable energy production. The citation for the data can be found in the IRENA Renewable Capacity Statistics 2023 report [38] and the units for all data are Mw. This study forecasts by using data from the renewable energy statistics table from 2013 to 2022, as displayed in Table 3. As in the previous case, we compare our model with the GM, FDGM, FGM, and NOGDM models. The dataset spans from 2013 to 2019 for training and 2020 to 2022 for testing. Total renewable energy serves as the core feature, while other factors complement the analysis in both the training and testing phases. This setup allows a holistic examination of renewable energy's interrelation with various supplementary factors, enriching the model's predictive capacity. Figure 4: APE of five grey models on China’s per capita energy consumption. Figure 5: Forecast curves from five grey models for energy consumption per capita in China. The MAPE for each model in both the training and test datasets is shown in Table 4. The table also shows the predictions made by the GM, FDGM, FGM, NOGDM, and NMGM models using the data from Table 3. The optimal results are presented in bold, and the second-best results are underlined. Table 4 shows that, out of all the evaluated models, the NMGM model has the best MAPE with 0.9566% on the training data and 0.7896% on the test data. Thus, when contrasted with other grey models, the NMGM model demonstrates a superior performance. For a more intuitive comparison of the distinctions between these models, the MAPE and APE results are displayed in Figure 6 and Figure 7, respectively. In contrast to alternative grey models, the NMGM model, as defined in this paper, exhibits superior predictive accuracy when compared to MAPE and APE. Recently, the Chinese government has actively promoted the growth of the new energy sector, resulting in a consistent annual increase in China's overall renewable energy capacity. As shown in Figure 8, our experimental results can verify this very well. More accurate prediction results can provide more effective support for the government's correct decision-making. According to the above analysis, we can conclude that the NMGM model shows excellent adaptability and accuracy. In summary, depending on the generalization ability of the neural network, the proposed model can successfully recognize and understand the nonlinear features of sparse data, enabling the model to function well in most situations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Year** & **GM(I,N)** & **FDGM(I,N)** & **FGM(I,N)** & **NODGM** & **NMGM** \\ \hline
2013 & 359,516 & 359,516 & 359,516 & 359,516 & 359,516 \\
2014 & 328,586 & 416,479 & 415,830 & 415,805 & 415,042 \\
2015 & 483,737 & 473,119 & 472,310 & 477,083 & 477,580 \\
2016 & 532,637 & 537,463 & 536,461 & 543,976 & 544,277 \\
2017 & 607,781 & 610,558 & 609,326 & 617,399 & 617,482 \\
2018 & 683,109 & 693,594 & 692,087 & 698,438 & 697,311 \\
2019 & 748,340 & 787,923 & 786,090 & 788,297 & 788,556 \\ \hline MAPE & 4.7564\% & 1.351\% & 1.4129\% & 1.0188\% & **0.9566**\% \\ \hline
2020 & 926,350 & 895,080 & 882,860 & 888,266 & 892,905 \\
2021 & 1,061,307 & 1,036,811 & 1,004,132 & 999,732 & 1,011,086 \\
2022 & 1,212,928 & 1,176,097 & 1,145,877 & 1,124,203 & 1,152,380 \\ \hline MAPE & 3.8291\% & 1.1493\% & 1.5758\% & 2.1416\% & **0.7896**\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Modeling result of renewable energy data in China. The best is bold, the next best is underlined.