## 3 The Cyclic Evolutionary Network (CENS)
### Model Framework
In addition, we also used 674 points for comparison experiments. The selected area is shown in Figure 3d-e. The experimental ranges of 16 points, 100 points, and 674 points were 6.325\({}^{\circ}\)-7.375\({}^{\circ}\) N and 106.325\({}^{\circ}\)-114.875\({}^{\circ}\) E, 6.375\({}^{\circ}\)-15.375\({}^{\circ}\) N and 106.325\({}^{\circ}\)-130.375\({}^{\circ}\) E, and 6.375\({}^{\circ}\)-30.625\({}^{\circ}\) N and 106.325\({}^{\find the part with better experimental results. Then, use grid search to obtain the optimal hyperparameters. In the single network unit training phase, the window length was set to 30 for a one-day forecast, 45 for a three-day forecast, and 75 for a seven-day forecast, the learning rate was set to 0.002, batch size was set to 128, the cell size of the GRU in the GED model was set to 32, and we chose Adam optimizer for training. In the dataset partition phase, the threshold was set to the average of the error. In the evolutionary termination phase, considering the limited performance improvement of CENS in small area, we set the rate R to 0.9. ### Evaluation Metrics

Root mean square error (\(RMSE\)) and mean absolute error (\(MAE\)) are mainly used as the criteria for evaluating the quality of the model. \(RMSE\) is the square root of the square of the difference between the measured value and the true value and \(MAE\) is the average value of the absolute error. The Equations are as follows

\[RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(X_{i}^{p}-X_{i}^{r}\right)^{2}} \tag{12}\] \[MAE = \frac{1}{n}\sum_{i=1}^{n}\left|X_{i}^{p}-X_{i}^{r}\right| \tag{13}\]

where \(n\) is the number of data, \(X^{p}\) is the prediction of the model. \(X^{r}\) is the true value of the data. ### Ablation Experiment

To verify the effectiveness of the framework of the model and the effect of the different levels on the prediction, we conducted experiments on the temperature of the Bohai Sea and the South China Sea. Different levels of the CENS were compared to the experiment. Using the evolutionary termination mechanism, CENS generates 3-levels, 4-levels, and

Figure 3: Location maps of the experiment. The red dots indicate the predicted points. (**a–c**) represent the predicted areas at 16, 100 and 224 points in the Bohai Sea. (**d–f**) represent the predicted areas at 16, 100 and 674 points in the South China Sea. Comparing the experimental results of 16 prediction points in the Bohai Sea and the South China Sea, we can see that when the prediction area is small, the _MAE_ and _RMSE_ of CENS will generally decrease with the increase in the number of levels, but the improvement is not large. Figure 5: Results of CENS in the South China Sea for different levels. It means that CENS can capture the spatial dimension information, but the improvement in the prediction of small areas is limited. Comparing the experimental results of 224 points in the Bohai Sea region and 674 points in the South China Sea region, we can see that the _MAE_ and _RMSE_ of CENS decrease significantly with the increasing number of levels in a larger prediction area, which means that CENS is able to capture the spatial information of a complex sea area well. On the whole, CENS predictions of 1-7 days becomes more accurate as the number of levels increases, which shows that CENS can cope with different sea areas and forecast times and indirectly indicates the effectiveness and robustness of the CENS framework. ### BaseLines and Time Series Prediction

In this section, we compare our model with the baselines on the two datasets. The four baselines are as follow:

SVR: Support Vector Regression, which is widely used in time series prediction. GBDT: Gradient Boosting Decision Tree. This algorithm consists of multiple decision trees, and the results of all trees are accumulated to make predictions. It is the classical algorithm for ensemble learning. GED [20]: This is a model of GRU encoder-decoder with SST code and dynamic influence link (DIL).