## 3 The Cyclic Evolutionary Network (CENS)
### Model Framework
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{**Metrics**} & \multicolumn{3}{c}{**Prediction Length (Day(s))**} \\ \cline{3-5}  & & **1** & **3** & **7** \\ \hline \multirow{2}{*}{SVR} & _MAE_ & 0.400 & 0.507 & 0.712 \\  & _RMSE_ & 0.526 & 0.687 & 0.895 \\ \hline \multirow{2}{*}{GBDT} & _MAE_ & 0.214 & 0.427 & 0.632 \\  & _RMSE_ & 0.286 & 0.566 & 0.834 \\ \hline \multirow{2}{*}{RC-LSTM} & _MAE_ & 0.206 & 0.390 & 0.563 \\  & _RMSE_ & 0.296 & 0.546 & 0.735 \\ \hline \multirow{2}{*}{GED} & _MAE_ & 0.195 & 0.396 & 0.581 \\  & _RMSE_ & 0.284 & 0.536 & 0.762 \\ \hline \multirow{2}{*}{CENS} & _MAE_ & **0.176** & **0.368** & **0.531** \\  & _RMSE_ & **0.241** & **0.478** & **0.687** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Time series prediction results in the South China Sea. Figure 6: Error distribution in the Bohai Sea for different models in 1, 3, and 7-day sea surface temperature prediction. The error plots of SVR, GBDT, RC-LSTM, GED, and CENS are shown from left to right, and the error results of prediction one day, prediction three days, and prediction seven days are shown from top to bottom. The color bar on the right is the _MAE_ value. #### 4.4.3 Computation Efficiency

This section will calculate the elapsed time of each method to test the efficiency of CENS. In the Bohai experiment, we selected 224 points as an input, and the data contained daily data (4749 days) from 1 January 2004 to 31 December 2016. In the South China Sea experiment, we selected 674 points as an input, and the data contained daily data from 1 January 2004 to 31 December 2016. The results are shown in Table 3. SVR is the fastest during the training phase, and CENS is the slowest because CENS is made up of N GED models, and CENS needs to train N GED models. CENS is also the slowest during the test phase because CENS is required to calculate the error network first to obtain the relative data prediction network. Although the speed of CENS is slow, CENS can identify the characteristics of data in complex sea areas, clustering the data automatically, and CENS has a high prediction accuracy. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{**Times (s)**} & \multicolumn{2}{c}{**Region**} \\ \cline{3-4}  & & **Bohai Sea** & **South China Sea** \\ \hline \multirow{2}{*}{SVR} & train & 21.23 & 56.87 \\  & test & 4.72 & 13.13 \\ \hline \multirow{2}{*}{GBDT} & train & 224.77 & 730.74 \\  & test & 0.04 & 0.08 \\ \hline \multirow{2}{*}{RC-LSTM} & train & 767.53 & 843.22 \\  & test & 0.76 & 0.82 \\ \hline \multirow{2}{*}{GED} & train & 905.56 & 964.56 \\  & test & 0.96 & 1.45 \\ \hline \multirow{2}{*}{CENS} & train & 3867.54 & 5732.81 \\  & test & 12.41 & 20.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The elapsed time of each method. Figure 7: Error distribution in the South China Sea for different models in 1, 3, and 7-day sea surface temperature prediction. The error plots of SVR, GBDT, RC-LSTM, GED, and CENS are shown from left to right, and the error results of prediction one day, prediction three days, and prediction seven days are shown from top to bottom. The color bar on the right is the _MAE_ value. ### Discussion

The experimental results show the effectiveness of our proposed model. In this section, we discuss the advantages of the model and the limitations that exist. #### 4.5.1 The Advantage of CENS

The model shows high accuracy. In practice, the accuracy of the CENS model is higher compared to other baselines, which suggests the capability of the model to extract implicit features from the data. The model can be relied on to divide and cluster datasets with different characteristics automatically. When used to predict large-scale areas, traditional models routinely rely on DTW and other means to divide the dataset at first, such as RC-LSTM. Differently, our model is an end-to-end model without the need for additional operations, and the classification of the dataset is performed independently.