# Sequence Deep Learning for Seismic Ground Response Modeling: 1D-CNN, LSTM, and Transformer Approach
## 1 Introduction  
Accurate estimation of seismic ground response is crucial for the design and safety of civil infrastructure, as it is the foundation to determine the impact of earthquake-generated ground motion on structures. Accurately modeling this response is vital for establishing effective mitigation measures against seismic risks and hazards for structures built on the ground [1, 2]. The mechanics of seismic wave propagation during an earthquake involve intricate physical processes. When a fault occurs, it releases energy in the form of seismic waves. These waves propagate from the source through the soil media to the site. During this propagation, some wave components are filtered, while others are amplified depending on the site conditions, a phenomenon known as the site effect [3]. Seismic ground response analysis evaluates ground surface motions based on bedrock motion, accounting for the site effect. This process is inherently complex and includes uncertainties due to the heterogeneous nature of soil layers, varying soil properties, and underground geometries [4]. As a simplified approach, the one-dimensional wave propagation model [5; 6; 7; 8] is widely adopted for site response analysis. This model assumes that seismic waves travel vertically through a horizontally layered medium and has proven reasonable for many practical applications as a physics-based model. [PERSON] et al. [9] apply a one-dimensional wave propagation model to analyze the seismic response in the Mississippi embayment. [PERSON] et al. [10] use this model for site response analysis in the New Madrid seismic zone. [PERSON] et al. [8] evaluate this model using borehole arrays. It is also widely used as the benchmark model to calibrate the nonlinear soil models for response analysis [9; 11; 12]. To capture the full complexity of wave propagation, full 3D numerical models can be employed, but describing the 3D underground geometry is challenging work, and entails significant computational costs [13; 14; 15]. Recent studies have demonstrated the potential of data-driven models using machine learning (ML) as successful surrogates for physics-based models. These models learn complex physical phenomena from data, achieving outstanding performance in various applications, such as global weather forecasting [16; 17], the dynamics of granular flow and rigid body interaction, and fluid flow simulation [18; 19; 20]. By leveraging machine learning architectures tailored to focus on learning specific physical phenomena, these models often surpass conventional physics-based models in terms of accuracy or computational efficiency. In terms of the application of data-driven approaches for ground motion prediction, [PERSON] et al. [21] introduce an autoencoder-based system for the real-time estimation of ground motion acceleration. The framework efficiently processes initial p-wave data to predict spectral acceleration with high accuracy, implying its validity for on-site earthquake early warning systems. [PERSON] et al. [22] propose a hybrid computational intelligence approach that integrates genetic algorithms, neural networks, and regression analysis to predict spectral acceleration. Their model outperforms the accuracy of traditional ground motion models such as [PERSON] et al. and [PERSON] et al. [23; 24]. [PERSON] et al. [25] utilize PCA and genetic algorithms to simulate ground motion, effectively matching the amplitude, spectrum, and duration characteristics for realistic seismic input generation. For seismic response analysis, where data consist of motion sequences or time series, sequence deep learning architectures can be promising options for learning the underlying sequential behavior of the motions. Popular architectures for sequence deep learning include 1D convolutional neural networks (1D-CNNs) [26], which capture local patterns in the sequence, and long short-term memory (LSTM) [27] networks, which can model long-term dependencies.