## 3 The Cyclic Evolutionary Network (CENS)
### Model Framework
RC-LSTM [19]: This combines the CNN model and LSTM model to study the temporal and spatial correlation of the data, which shows the state-of-the-art performance. #### 4.4.1 Results and Analysis

To validate the prediction performance of CENS, we experimented on the Bohai Sea SST dataset (224 points) with different prediction scales of 1, 3, and 7 days, respectively. The comparison methods include SVR, GBDT, RC-LSTM, and GED. The results of the experiment are shown in Table 1. The bold items in the table indicate the optimal predictive performance, i.e., the minimum _RMSE_ and _MAE_. It was clear that the performance of CENS was better than the other models in all prediction scales, and SVR always performed the worst. _MAE_ of CENS was approximately 8% lower than GED in the predicted 1-day experiment, decreasing to 3% at three days of prediction and rising to 6% in the predicted 7-day experiment. In addition, the _RMSE_ of CENS was about 7% lower than GED in the 7-day prediction experiment. The experimental results show that, compared with other models, the prediction performance of CENS is improved in different prediction scales at 1, 3, and 7 days. To verify the robustness of the model, we also experimented in the South China Sea (674 points) and the results are shown in Table 2. It can be seen that, compared with other models, the performance of CENS is the best in 1, 3, and 7-day sea surface temperature prediction. _MAE_ of CENS was 10% lower than GED in the predicted 1-day experiment, 6% at three days of prediction and 6% in the predicted 7-day experiment. In addition, the _RMSE_ of CENS remained optimal in the prediction experiments for 1, 3, and 7 days. This shows that CENS can deal with different sea areas. \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_ & 0.565 & 0.655 & 0.868 \\  & _RMSE_ & 0.512 & 0.846 & 1.345 \\ \hline \multirow{2}{*}{GBDT} & _MAE_ & 0.359 & 0.638 & 0.835 \\  & _RMSE_ & 0.471 & 0.821 & 1.125 \\ \hline \multirow{2}{*}{RC-LSTM} & _MAE_ & 0.340 & 0.598 & 0.810 \\  & _RMSE_ & 0.448 & 0.746 & 1.170 \\ \hline \multirow{2}{*}{GED} & _MAE_ & 0.322 & 0.602 & 0.812 \\  & _RMSE_ & 0.466 & 0.801 & 1.070 \\ \hline \multirow{2}{*}{CENS} & _MAE_ & **0.298** & **0.585** & **0.766** \\  & _RMSE_ & **0.415** & **0.735** & **1.002** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Time series prediction results in the Bohai Sea. #### 4.4.2 The Error Distribution of SST

This section visualizes the experimental results of the forecast 1, 3, and 7 days to obtain the error distribution of CENS and other models. The results are shown in Figures 6 and 7. Figure 6 shows the error distribution in the Bohai Sea, and Figure 7 shows the error distribution in the South China Sea. The graph circled in red is where CENS predicts better than GED. It can be seen that, compared with other models, CENS is better than other models at all prediction scales and is more accurate than GED in the offshore area in the Bohai Sea experiment. CENS is more accurate than GED in the entire sea area in the South China Sea experiment. This result shows that CENS can predict complex sea areas.