## 3 BP and GA-BP Neural Network Modeling  
### BP Neural Network Modeling  
The forecasting model of the BP algorithm is shown in Figure 3. The model consists of three parts: the establishment of the BP deep neural network model, training, and prediction. Firstly, modeling serves to analyze the required network topology and the precise number of nodes in each layer of this topic to build a suitable BP network model for this topic. The network is then initialized. Secondly, the relevant network parameters are set and the training function of each layer and the transfer function of each layer are selected. Then, the training of the network begins. If the training result reaches the expected value, it will enter the test part. If the training result does not reach the expected value, it will return to re\(-\)train. Then, the network is tested. Finally, the network prediction is made.  
Figure 3: BP algorithm prediction model.  
BP neural network has a multi\(-\)input and multi\(-\)output model structure. This can meet any intricate input to output with a non\(-\)linear map. By learning the samples, the reasonable solution rules can be automatically extracted, and the complex system can be adaptively modeled. After effective BP network training, the iteration time of the system is less. It can be used in real\(-\)time processing. The constructed system also has good robustness and generalization ability. However, a large number of research results show that there are still many unsatisfying aspects of the BP network in both theoretical analysis and practical operation. For example, the traditional BP algorithm uses the gradient descent method. This is a local search optimization method [29]. This method can simply fall into the local extremum during training, leading to the failure of the training. In addition, the BP algorithm is difficult to solve the contradiction between the instance scale and network scale of the application problem. This involves the relationship between the possibility and feasibility of network capacity, that is, the problem of learning complexity. Moreover, the newly added samples should affect the network that has been successfully learned.  
The BP network also has the characteristics of \"overfitting\". In general, the predictive ability of the network is proportional to the training ability. With the improvement of training ability, the prediction ability of the BP network will reach a limit. Additionally, the prediction ability will then tend to decline, which is called \"overfitting\". Even if there are more samples for network learning, it cannot reflect the internal law contained in the sample. This shows the gap ability to forecasting and the ability to train the network.  
To mitigate the limitation of the traditional BP neural network in practical forecasting applications due to the above defects, most people use an optimized algorithm based on the heuristic standard gradient descent method when training the network, including the additional momentum method and adaptive learning rate method--or improved algorithms based on standard numerical optimization, such as genetic algorithm (GA), conjugate gradient method, Bayesian regularization method and Levenberg-Marquardt method (L-M method). The speed of the improved algorithms above varies according to the model complexity, sample scale, network model, and error requirements. In general, the training efficiency of the GA numerical optimization algorithm is higher than that of the heuristic standard gradient descent method.