## 3 A Fast Prediction Model for the Coupling Coefficient  
### Structure and Parameters of the PSO-BP Neural Network  
In the process of BP network training, it is possible to fall into the local minimum, where the amount of backpropagation training is excessive and the convergence speed of the network training is slow, which may lead to the problem of poor network model results. The PSO algorithm can be used to optimize the weights and thresholds of the BP neural network. When the BP network is trained by the PSO algorithm, the weights and thresholds between each layer of neuron nodes in the neural network structure are encoded into a particle swarm. The fitness value is the mean squared error of the network output. First, the weight and threshold vector is initialized and then the PSO algorithm is used to search for the optimal result, that is, the weights of the neuron nodes of each layer are searched within a defined number of iterations to minimize the output mean squared error of the network structure. The specific steps are:  
1. Initialize each particle and randomly generate velocity and position vectors. 2. Evaluate the fitness of each particle. 3. Update the individual extreme value and global extreme value of each particle. Figure 4: The magnitude of the electric field at the window of the carriage. Figure 5: The electric field measured by the antenna on the roof. (4) Update the velocity and position of the particle. (5) Determine the convergence. If the given error is reached, the next iteration is carried out. If the given error is not satisfied, the previous step is returned until the maximum number of iterations is reached. (6) Output the optimal solution. In [17], the specific description of the PSO algorithm is as follows: in the continuous space, assuming that M is the population size of the particle swarm, the position of particle \(i\) at time \(t\) in coordinates can be expressed as \(X_{i}^{t}=(x_{i1},^{t},x_{i2},\ldots,x_{im})\), \(i=1,\,2,\,\ldots,\) M. The velocity of particle \(i\) is the displacement of each iteration, expressed as \(V_{i}^{t}=(v_{i1},^{t},v_{i2},\ldots,\)\(v_{im}^{t})\), \(i=1,\,2,\,\ldots,\) M. The velocity and position of particle \(i\) at time \(t\) are updated according to the following formulas:  
\[v_{id}^{t}=wv_{id}^{t-1}+c_{1}\tau_{1}(p_{i}d-x_{id}^{t-1})+c_{2}\tau_{2}(g_{d }-x_{id}^{t-1}), \tag{1}\]  
\[x_{id}^{t}=x_{id}^{t-1}+v_{id}^{t}, \tag{2}\]  
where \(w\) is the weighted inertia value, which is used to indicate the degree of retention with the original velocity. The higher the value, the more the velocity of the particle is affected by the velocity of the previous generation. \(c_{1}\) is the acceleration factor, which is the coefficient that tracks its own historical optimum. \(c_{2}\) is the acceleration factor, which indicates the learning degree of the current particle for the global optimal particle. \(\tau_{1}\) and \(\tau_{2}\) are randomly generated positive numbers less than 1. \(p_{i}\) is the historical optimal value of the current particle and \(g_{d}\) is the historical optimal value of the global particle. \(v_{id}^{t-1}\) is the velocity of the \((t-1)\) iteration of the particle. \((p_{i}d-x_{id}^{t-1})\) is the particle's knowledge of itself, which is used to guide the particle to move to the best position in its own history, constantly pushing the particle to reduce the error. \((g_{d}-x_{id}^{t-1})\) is the embodiment of individual cooperation in the particle swarm, where each particle guides all particles in the swarm to seek the global optimal solution by sharing information. In summary, the specific flow block diagram of the PSO-BP neural network model algorithm is shown in Figure 6.  
Figure 6: The specific flow block diagram of the PSO-BP neural network. In this paper, the PSO-BP neural network is trained. The parameters of the PSO-BP algorithm are given in Table 2. The PSO-BP neural network topology is shown in Figure 7. The input dimension of network I is 3 and the output dimension is 1.