## 5 The MLPER Architecture  
In this study, we introduce a machine learning-based model designed to forecast seismic-induced responses of MDOF systems in terms of acceleration. Referred to as MLPER, which stands for machine learning-based prediction of earthquake response in building structures, this model represents a universal approach for predicting earthquake responses in building structures. A graphical representation of the MLPER is provided in Figure 7. MLPER comprises three key stages: Encoding, Latent Space, and Decoding. As previously described in Section 3, the input to our model consists of two sets of images: amplitude and phase spectrograms representing ambient responses and earthquake data, respectively. The model's output is a pair of images, consisting of amplitude and phase spectrograms, but this time capturing the earthquake-induced response. Each input and output image is a 2D representation with dimensions \(T\times F\), where \(T\) signifies the signal's time duration, and \(F\) denotes the frequency values. The third dimension, the channel, represents the monochromatic color value. For amplitude spectrograms, the channel dimension represents the amplitude of acceleration (in dB) at specific frequencies and times, while for phase spectrograms, it denotes the phase angle (in pi) of the signal at particular frequencies and times. The output images follow the same format. To offer a visual overview of the MLPER model's structure, please refer to the schematic representation in Figure 7. It is worth mentioning that all computations were conducted on an x64 PC with a 14-Core Intel(r) Xeon(r) processor with 128 GB RAM memory. The input format comprises four single-channel images, each sized at 2997 \(\times\) 201 pixels, resulting in a tensor of shape [4, 201, 2997, 1]. We begin by splitting this tensor into four individual tensors, each having a shape of [1, 201, 2997, 1]. The next step involves the Encoding stage for each signal in the frequency domain (Table 3). Initially, the two images of shape [201, 2997, 1] are concatenated to form a tensor of shape [201, 2997, 2]. Three layers of 2D convolution (Conv2D) are applied, interspersed with Batch Normalization, ReLu activation and Spatial 2D Dropout layers. Batch Normalization standardizes the inputs of each layer, promoting a faster convergence, improved generalization, and a reduced sensitivity to parameter initialization. It also acts as a regularization method. Spatial 2D Dropout is a regularization technique that randomly sets a fraction of feature maps to zero during training, preventing overfitting and encouraging the network to learn more robust features. In the encoding stage, Spatial 2D Dropout layers were set at a 15% dropout rate, meaning 15% of randomly selected neurons in these layers were set to zero during each iteration. Following the encoding, the final layer is flattened, creating a Latent Space through several Dense layers. After the Flatten layer, two Dense layers follow with ReLu activation. At this juncture, the \"paths\" for the Ambient response signal and the Earthquake signal converge. This concatenation is succeeded by a Dense layer with 20 nodes and another Dense layer with 13,399,920 nodes (Table 4). Subsequently, reshaping is necessary to transition from fully connected dense layers to image-like tensors with a shape of [height, width, channels], preparing for the Decoding phase of the network. The decoding stage (Table 5) consists of 5 Conv2D layers, with Batch Normalization and ReLu layers in between. The final two Conv2D layers use a Sigmoid activation function, which constrains output values to the [0, 1] range (representing colors). No dropout layers are utilized in the decoding portion of the network. Ultimately, the tensor produced by the Decoder, as depicted in Figure 7, is reshaped into a [2, 201, 2997, 1] tensor, resulting in two output images.