## 6 Prediction Performance Evaluation by Reducing the Input Dimension of ML Model
It is noteworthy that the prediction performance of the model employing 17 features closely mirrors that using only 8 features. This underscores that an efficient ML model can be developed using a mere 8 of the 17 features through the RF machine learning model's feature selection process. Similarly, the variation in seismic response prediction performance of the NN model based on the number of selected features is detailed in Figure 16. The prediction accuracy (R\({}^{2}\)) enhances when three or more input features are employed, peaking at a coefficient of determination exceeding 0.9 with 11 or more features. Notably, the use of 14 features resulted in a prediction performance (R\({}^{2}\) =  
The analysis in Figures 15 and 16 was conducted to evaluate how the number and composition of input features affects the prediction performance of the models. The goal was to determine the minimum number of input variables required to maintain high accuracy, which is crucial for reducing the effort needed to build large training datasets. The results demonstrate that both RF and NN models can maintain good performance with a reduced set of features, contributing to the efficiency and practicality of the ML framework. This analysis demonstrated that reducing the number of input variables did not lead to a noticeable decline in model performance. In particular, models trained with a reduced set of eight features identified through feature importance analysis achieved prediction accuracy comparable to those using the full 17-feature set. The retained variables, including acceleration-based intensity measures and damping ratio, contributed significantly to predictive performance and offered clear physical interpretability grounded in structural dynamics. Notably, this dimensionality reduction process revealed no substantial trade-off between model accuracy and the inclusion of physically meaningful parameters. On the contrary, eliminating less informative inputs appeared to enhance efficiency and avoid potential overfitting, highlighting the benefit of feature selection guided by engineering relevance and statistical contribution. As explained previously, reducing the number of input features in a machine learning model aims to minimize the required database size for model development and to enhance training efficiency. To validate this approach, an NN model with 11 input features was developed using 200 randomly selected training datasets. Since the input features of the model were adjusted, hyperparameter optimization was reiterated. The prediction performance of the model using 11 input features was compared to that of the model employing all 17 input features and 400 training datasets in Figure 17 and Table 9. The figure and table verify that the seismic response prediction performance of the model with 11 input features closely mirrors that of the model with 17 input features. Figure 16: Results of feature selection using neural networks. In this process, the reduction in training dataset size was implemented under an optimized input configuration, where the number of features had been minimized based on prior analysis. The model simplification through input dimensionality reduction enabled a more efficient learning process, allowing for a smaller dataset to be used without degrading predictive performance. This sequential strategy supports the development of lightweight machine learning models that are both accurate and computationally efficient. Another input dimensionality reduction technique, feature extraction, typically utilizes methods such as Principal Component Analysis (PCA) and Partial Least Squares (PLS). PCA constructs new variables by forming linear combinations of inputs that maximize the covariance among them, whereas PLS constructs new variables that maximize the covariance between inputs and outputs, considering their correlation [34]. Consequently, PCA is often employed in unsupervised learning, and PLS is favored in supervised learning scenarios.