## 3 The Cyclic Evolutionary Network (CENS)  
### Model Framework  
CENS uses multiple networks to split the data in terms of the error of the prediction results, where the results with different errors represent different data features. This model trains several networks to form a network group for prediction, thereby improving the accuracy and precision of prediction. As shown in Figure 1, the model consists of two phases: the training phase and the application phase. The training phase is comprised of the single network unit, dataset partition mechanism, and evolutionary termination mechanism. The single network unit trains the data and obtains the test error. The error of each data element is different due to the various characteristics of the data. The dataset partition mechanism splits the original data into an evolution set and an elimination set automatically based on the prediction error, thus enabling clustering of the data. The evolutionary termination mechanism is used to determine whether the model stops training. CENS can obtain a single network unit after each round of training. We define a CENS with N single network units as N levels of CENS. Finally, the model will generate networks with several levels adaptively using this mechanism. The application phase and the training phase are relatively independent of each other. In the test phase, the data are first put into the prediction network of each level. Then, the prediction network with the minimum prediction error is selected. Finally, the data are used with the selected network to obtain the final prediction result. The details are shown in Algorithm 1. ``` Assume that the region consists of k data grid points
1. Data preprocessing: slice the data through sliding window to obtain data sample. 2. Put the data samples into single network unit for training. 3. Use the dataset partition mechanism to divide data samples into evolution sets and elimination sets. 4. The elimination set is treated as a new data sample to repeat steps 2 and 3 until the evolutionary termination mechanism terminates the training of the network. 5. Finally, the CENS consists of N single network units, the size of which is determined by how many times the steps are repeated. Note: Considering that the first network captures the features of the overall dataset, the first network is used as a pre-trained model in the later networks, which not only allows the model to fit faster, but also improves the overall accuracy of prediction. The hyperparameters of each single network unit are the same. The difference is that the input samples of each single network unit are different. The first single network unit has the most input samples, and the second single network unit has the second most input samples, and so on. The following parts will introduce the single network unit, dataset partition mechanism, evolutionary termination mechanism, and application phase of the model. Figure 1: Structure of the CENS model. ### Single Network Unit

Each unit consists of a numerical prediction network and an error prediction network. The numerical prediction network is used to obtain the absolute error of the data. The error prediction network is used to obtain the difference between the characteristics of the individual data and those of the dataset. The error prediction network is used to predict the error of the sample data in the data prediction network. Combining the data prediction network and the error prediction network, the model can extract the overall characteristics of the data. If the data error is small, the characteristics of the data match the characteristics of the overall data. Conversely, if the data error is large, the characteristics of the data do not match the characteristics of the overall dataset. Therefore, the error can be used as a criterion for data partition in the cyclic evolutionary network.