## 4 Description and Implementation of Neural Network Method  
The principal objective of an artificial neural method is to predict or establish relationships between input and output parameters. It is particularly useful for developing simpler forms of relations between input and output parameters for cases where the interrelations between these parameters are complex and no obvious function exists to describe them. This method is essentially based on a training phase with a database, composed of input and output parameters, with the database being randomly selected. After the training phase is completed, the neuron network can basically be used to predict new input and associated output values for the parameters. In the field of seismology, this method has been used by many researchers to derive new GMPEs [35, 36, 37, 38, 39, 77]. Two types of ANNs are used in this study: the Generalized Regression Neural Network (GRNN) and the Radial Basis Function (RBF), which are of the same family but with slightly different architecture. Both ANNs have three layers: an input layer, a hidden layer, and an output layer.  
In this study, we used a GRNN for the identification of site proxies (input parameters) for both soil types, sand and clay. To this end, we used the 324 soil profiles (soil parameters) of each type for which 11 average amplification factors (i.e., \(AF_{m}(P_{k},\theta,T_{i},PGA(lo))(P_{k},\theta,T_{i},PGA(lo))\) were computed from the different seismic signal databases with different \(PGA\) values ranging from 0.01 g to 1.05 g. That is, there was a database of 3564 (324 \(\times\) 11) cases for each soil type. The output consisted of the calculated \(AF\) values for the selected 100 periods of the structure and the amplification factors at short, intermediate, and long periods, named F\({}_{\mathrm{a}}\), F\({}_{\mathrm{v}}\), and F\({}_{\mathrm{I}}\), respectively). Half of the database was used for training, and the second half for testing. Elements of these two subgroups of the database were selected and swapped randomly from one to the other until the network parameter, which is the Gaussian width for the GRNN, was determined. The main advantage of this method is the rapidity of the training phase. Note that many possible combinations of input site parameters were considered. The performance of the GRNN model was measured with various non-independent indicators, namely, the standard deviation of residuals, the reduction in variance with respect to the initial variability, the coefficient of correlation, and the physical tendency. Based on the results obtainedwith the GRNN, the combination of input site parameters giving the best performance while being handy for engineering practice were selected. For the selected combination of parameters, the RBF neural network was used to obtain a simple prediction equation. However, the training phase needs many adjustments, such as the number and the choice of key neurons in the hidden layer, and it is time-consuming. In the training phase of the RBF, the number and the choice of key neurons can either be set randomly from the training data, or they are iteratively trained or derived using techniques such as K-means, Max-Min algorithms, or Kohonen self-organizing maps [78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93]. After this unsupervised training was carried out and the number and key neurons in the hidden layer were chosen, the weights between this layer and the output layer neurons were determined by multiple regressions in a supervised manner. We used cross-validation, with 50% of the data used for training and the remaining 50% for testing, with each half of the database randomly being swapped from one to other until the RBF network parameters were obtained. More details about the used neural networks and their implementation are given in the Supplementary File, section (d).