## 3 BPNN-Based PGA Prediction  
The application of neural networks to compute multi-parameter fitting problems has been widely used in structural engineering [33], where a non-linear computational power can effectively reduce the time to analyze the mechanism while ensuring computational accuracy. [PERSON] [34] used the BPNN to predict the probability of earthquakes in Taiwan, a method that can be commercialized at a relatively low cost and with minimal resources and equipment using only the earthquake catalogues. Combined with the statistical data, it is easy to find that the PGA, as an important part of the strong motion data, is affected by the propagation speed and the location of the strong motion station and has not yet achieved the purpose of obtaining effective real motion data for each earthquake; the amount of recorded seismic data is much larger than the strong motion data, and the supplemental PGA, through seismic data, has also become an important part of the PSHA. Previously, the GMPE was used to supplement the PGA, and this method generally fitted the seismic magnitude separately according to the polar difference of one (e.g., Richter scales four, five, and six). The fitted equations also differed due to the distinct geological considerations, and the goodness-of-fit was low. The GMPE is an empirical prediction relationship, as shown in Equation (1) [35] and Equation (2) [36], that represents the ground motion parameters (including the PGA, spectral acceleration at a given frequency, peak velocity, or peak displacement) as a function of other parameters (such as the earthquake magnitude and epicentral distance):  
\[\ln PGA=C_{1}+C_{2}m+C_{3}\ln R+C_{4}R \tag{1}\]  
\[\ln PGA=C_{1}+C_{2}m-C_{3}\ln(R+C_{4}\exp(C_{5}m)) \tag{2}\]  
where \(m\) is the earthquake magnitude; \(R\) is the epicentral distance or hypocentral distance; and \(C_{1}\), \(C_{2}\), \(C_{3}\), \(C_{4}\), and \(C_{5}\) are constants that are independent of \(m\) and \(R\). As a traditional PGA prediction method, the GMPE varies greatly under different regions and is influenced by the geological soil and other conditions; however, there is still no uniform model. This paper makes use of the better non-linear computational ability of the BPNN to compensate for the computational errors caused by the lack of understanding of geology in the engineering field and to improve the problem that multiple GPMEs need to be considered for supplementing PGAs across different regions. Due to the complex  
Figure 5: Histogram of magnitude frequency distribution. non-linear correlation between the input and the output quantities, the accuracy of the previous primary function fitting was deemed to be poor, while the neural network, as a tool to describe the correlation between the multiple quantities, has a strong non-linear fitting ability, and the above mapping relationship has been considered by the neural network. The process of predicting the PGA using the BPNN is as follows:  
1. The known PGA data are randomly split into a training set, a validation set, and a test set in the ratio of 7:1.5:1.5 to avoid errors in the prediction results caused by large differences in the order of magnitude using data normalization. 2. The BPNN (Figure 6) is constructed with three elements (a magnitude of Richter scale, focal depth, and the epicentral distance) in the input layer and one element (PGA) in the output layer. To avoid underfitting and overfitting, the number of hidden layers is set to two, each layer has four neurons, and the number of neurons is obtained by considering the number of elements in the input and output layers in combination with several attempts, where the transfer function (transig) and the training function (trainlm) are non-linear functions [37]. 3. The data set is trained with the determinants of the coefficients that are greater than 0.95 as the index to obtain the fitted network, where the regression fitting results are shown in Figure 7.
4. After saving the network, the normalized unknown PGA data are inputted into the network.