# A Model-Assisted Combined Machine Learning Method for Ionospheric TEC Prediction
## 2 Materials and Methods
### Methods
#### 2.2.3 Modeling of Neural Network Optimization Based on Genetic Algorithm  
In this section, the TEC data predicted by solar activity level index, IRI-2020, and harmonic function fitting were taken as input, and TEC data were taken as output to establish a prediction model based on BP-NN. In addition, the multi-mutation and multi-crossover adaptive genetic algorithm (MMAdapGA) was used to optimize the model, and existing data (the actual filtered TEC data, time parameter (UTC), TEC data predicted by the IRI model, and the SML-based model, etc.) were used as training dataset and testing dataset to train the model. ANN simulates the process of neuron signal transmission [35]. The neuron is a topological network established by biological research and the response mechanism of the brain, simulating the process of neural conflict. The end of multiple dendrites receives external signals and transmits them to neurons for processing and fusion. Finally, the nerve is transmitted to other neurons or effectors through axons. ANN approximates complex nonlinear functions as an algorithm model of basic nonlinear function combinations. This model has been successfully applied to TEC modeling and prediction [35]. ANN does not need to determine the mathematical equation of the mapping relationship between input and output in advance. Through its own training, ANN can obtain the result closest to the expected output value when the input value is given. As a classical algorithm, BP-NN simulates the neuronal processing process [36], which is a multi-layer feedforward network trained by error backpropagation. Its basic idea is the gradient descent method which uses the gradient search technology to minimize the mean square error of the actual output value and the expected output value of the network [37]. The input of BP-NN designed in this paper is respectively coordinated Universal Time UTC (year, month), F10.7 observation data, SSN observation data, SML-based model fitting TEC data through F10.7 (SML-F10.7), SML-based model fitting TEC data through SSN (SML-SSN), and the IRI model prediction TEC data. The output is the TEC prediction data. The input of the TEC data containing predictions of multiple models can solve the problem of a large deviation of a single model after a certain prediction time. The BP-NN constructed in this paper has a neural network with eight input neurons, one output neuron and two hidden layers. The first hidden layer comprises 15 hidden neurons, and the second hidden layer is composed of 10 hidden neurons, as shown in Figure 5.  
The BP-NN model test dataset accounts for about 10% of the total dataset, and the training set accounts for about 90% of the total dataset. The training set is represented by the formula shown below:  
\[D=\Big{(}x_{1}^{1},\dots,x_{1}^{8},y_{1}\Big{)},\Big{(}x_{2}^{1},\dots,x_{2}^{8 },y_{2}\Big{)}\dots\Big{(}x_{n}^{1},\dots,x_{n}^{8},y_{n}\Big{)}. \tag{5}\]  
The above neural network is trained. Each data set is normalized to [\(-\)1, 1] as a training set to carry out fitting training on the BP neural network model, in which the normalization formula is [38]:  
\[y_{i}=\frac{2(x_{i}-x_{min})}{x_{max}-x_{min}}-1, \tag{6}\]  
for the neuron \(i\) (\(i\) = 1, 2, \(\dots\), 15) in the first hidden layer, \(x_{i}^{1},x_{i}^{2},\cdots,x_{i}^{8}\) is the input of the neuron. The input is the independent variable that has a key influence on the system model. The input in this model is eight kinds of data, as shown in Figure 5.  
\(W_{i1}^{1},W_{i1}^{2},\cdots,W_{i1}^{8}\) is the connection weight, which is used to adjust the weight ratio of each input. According to biology, neurons are activated only when the amount of information they receive reaches a threshold. Therefore, \(\Phi_{i1}\) is used in this paper to represent the threshold value of this neuron, which is determined by the multi-mutation and multi-crossover adaptive genetic algorithm.