## 5 Performance Evaluation of the RNN Simulation Model
One LSTM cell was used for the RNN model, because it was sufficient to predict the seismic responses of the examples considered in this study. The aim of RNN is to detect dependencies in sequential data. This means RNN intends to find correlations between different points within the seismic response time histories. Finding such dependencies makes it possible for RNN to recognize patterns in sequential data and use this information to predict a trend. An appropriate sequence length of the input data needs to be selected to make RNN effectively predict seismic responses. However, there is no rule to determine a feasible sequence length. This value totally depends on the nature of the training and verification data, and the inner correlations. In this paper, in order to find a proper sequence length of input, the RNN model for Example 1 was evaluated by changing the sequence length. The default hyperparameter values in Table 3 except sequence length were used for training and verification of the RNN model. After all the simulations were completed, Table 4 lists the loss and RMSE values to investigate the effect of sequence length on the accuracy of the RNN model. Because there was a deviation in the errors of the RNN model in each epoch, the average of loss and RMSE values of the last 10 epochs are presented. [PERSON]'s correlation coefficients (CC) are also presented in Table 4 to investigate the relationship between the FEM and RNN models. [PERSON]'s correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. A correlation coefficient of 1 means that two variables are perfectly positively related. Table 4 shows that as the sequence length increased, both errors of training and verification data decreased until 6, but they increased after that. This means that too long a sequence length actually worsens the prediction performance of the RNN model. This is probably because it is difficult for the RNN model to find the correlations between different points in sequential data that are too lengthy. This phenomenon can be found in the correlation coefficients. The correlation coefficients between the FEM and RNN models increased until the sequence length of 6, but they decreased after that. \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Value** \\ \hline Sequence length & 5 \\ RNN cell number & 1 \\ Dropout rate & 0.8 \\ Hidden layer dimension & 5 \\ Learning rate & 0.01 \\ RNN type & LSTM \\ Activation function & tanh \\ Optimizer & Adam \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Default hyperparameter values and function. The hidden layer size is a very important hyperparameter that affects the prediction performance of the RNN model. However, optimization of the number of hidden layers remains one of the difficult tasks in the design of the RNN model. Setting too few or too many hidden layers causes high training errors or high generalization errors, respectively. Table 5 lists the average loss and RMSE values of the last 10 epochs, by changing the number of hidden layers. The value of average loss of the training process was consistently reduced as the hidden layer size increased. The value of the average RMSE of the verification process decreased until the hidden layer size of 20, but after that it increased as the hidden layer size increased. If the RNN model size is too large, the model may become overtrained on the training data, and begin to memorize it. This is also termed 'overfitting', which is defined as the ability to produce correct results for the training data, while being unable to generalize data that has not been seen before. Table 5 shows that overfitting occurred when the hidden layer size of the RNN model for Example 1 was greater than 20. Therefore, the hidden layer size of 20 was selected for the RNN model of Example 1. Despite the value of the average RMSE having increased after the hidden layer size of 20, the correlation coefficients between the FEM and RNN models continuously increased.