## 3 The Cyclic Evolutionary Network (CENS)
### Model Framework
The dataset will gradually decrease with the progress of partitioning, and some special data will be left in the end. Therefore, the model will generate the networks with a progressive relationship. ### Evolutionary Termination Mechanism

During the phase of cyclic evolutionary network training, the evolution termination mechanism ends the training of the network. In this paper, we propose two termination mechanisms to stop training the model: dataset threshold termination and evolutionary scale termination. In dataset threshold termination, when the error of the current network on the current dataset is less than the threshold, the network will consider the requirements met and stop training. The termination condition is

\[MAE\Big{(}f^{i}(T),T\Big{)}\ <\ t \tag{8}\]

where \(t\) is the error threshold, which can be set based on expert experience. In practical experiments, the \(MAE\) value of CENS can be improved by 5-10% on the GED. Thus, in general, we set \(t\) to 90% of the \(MAE\) value of the GED. \(T\) is the dataset. In evolutionary scale termination, training will be stopped when the proportion of data in the evolution set is greater than rate \(R\), which can be set based on training experience. The termination condition is

\[\frac{\sum_{i=0}^{I}num(E_{i})}{num(T)}\ >\ R \tag{9}\]where \(I\) is the level of the current network, \(T\) is the size of the original dataset, \(num(T)\) is the amount of data in the statistical dataset, and \(E_{i}\) is the evolutionary set of \(i\). ### Application Phase of the Model

The application phase includes two parts: the network selection and prediction process. In the network selection process, the data are used to select the numerical prediction network corresponding to the value with the lowest prediction error based on the output of each level of the error prediction network, which can represent the ability of that level of the network to predict that data element accurately. In the prediction process, the data uses the selected network to obtain the final predictive result. Compared with traditional deep learning methods, this model realizes the transition from model science to data science. ## 4 Experiments

### Dataset and Hyperparameters

To test the performance of different methods, we used the data that were provided by the Physical Sciences Division, NOAA/Ocean and Atmospheric Research/Earth System Research Laboratory, Boulder, Colorado, USA. The dataset covered the global ocean from 89\({}^{\circ}\)52'30'' S to 89\({}^{\circ}\)52'30'' N, 0\({}^{\circ}\)7'30'' E to 359\({}^{\circ}\)52'30'' E. In addition, the spatial resolution was 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\). The CENS model utilizes the data of the Bohai Sea and the South China Sea. The temperature fluctuations in the Bohai Sea are significant because it is affected by the continental shelf and northern continental climate [35]. Therefore, we choose the data of the Bohai Sea to measure the accuracy of the proposed model. The data contain daily data (4749 days) from 1 January 2004 to 31 December 2016, ranging from 37.125\({}^{\circ}\) to 40.875\({}^{\circ}\) N and 119.375\({}^{\circ}\) to 121.875\({}^{\circ}\) E, basically covering the Bohai Sea, China. We selected 16 points, 100 points, and 224 points for the experiment. In addition, we also used 224 points for comparison experiments. The selected area is shown in Figure 3a-c. The experimental ranges of 16 points, 100 points, and 224 points were 37.125\({}^{\circ}\)-38.375\({}^{\circ}\) N and 119.125\({}^{\circ}\)-121.875\({}^{\circ}\) E, 37.875\({}^{\circ}\)-39.375\({}^{\circ}\) N and 119.375\({}^{\circ}\)-121.875\({}^{\circ}\) E, and 37.125\({}^{\circ}\)-40.875\({}^{\circ}\) N and 119.375\({}^{\circ}\)-121.875\({}^{\circ}\) E respectively. Moreover, the South China Sea is an open sea, and ocean currents and other factors influence it [36; 37]. We chose the data of the South China Sea. The selected sea area from 1 January 2004 to 31 December 2016. We selected 16 points, 100 points, and 674 points for the experiment.