# Response Prediction for Linear and Nonlinear Structures Based on Data-Driven Deep Learning
### Structural Response Analysis  
Structural dynamic response analysis is key to ensuring the safe service of building structures during earthquakes, and it is also a key and difficult point of structural seismic design. In order to explore the dynamic characteristics, influencing factors, and control strategies for buildings during earthquakes, many academics at home and abroad have carried out a series of studies [8; 9; 10]. These investigations comprise seismic testing, theoretical analysis, and numerical analysis (as shown in Table 1).  
Seismic testing usually uses a seismic simulator or shaking table to imitate the actual seismic dynamic environment, and is one of the most effective methods for studying the dynamic responses of structures [11; 12; 13]. Its benefits include reliable data, intuitive phenomena, and the ability to consider the complexity and uncertainty of actual structures. Nevertheless, there are some challenges with seismic testing, including high costs, high equipment requirements, limited test conditions, and model errors.  
In order to overcome the deficiency of seismic test research, a series of theoretical analysis methods have been proposed. At present, the methods commonly used in the theoretical seismic response analysis of building structures are the static force method, response spectrum method, energy method, and push-over method [14; 15; 16]. These methods have the advantages of simple calculation and stable analysis results, so they are widely used in practical seismic design. However, these methods only investigate structural performance as a whole and cannot reflect the dynamic characteristics of a structure during the seismic process. They are not suitable for structures with complex forms.  
The advancement of numerical technology has given structural dynamic response analysis strong technological backing during the 20 th century. Numerical analysis typically discretizes a structure into small finite elements or discrete elements to predict the response by solving dynamic equations [17; 18; 19; 20]. This method can simulate a variety of seismic conditions and consider the influence of various structural parameters (such as material properties, structural forms, etc.) while providing a wider range of structural data, such as displacement, stress, etc. However, the responses of various buildings differ substantially because of the strong nonlinear, aperiodic, and non-stationary properties of ground motion. Therefore, several numerical calculations are frequently required for different buildings, which results in significant computational cost. In addition, as the application scenarios become more and more complex, the accuracy and efficiency of numerical techniques face great challenges in engineering applications due to the limitations of grid division and complex structural forms [21].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Typical Method** & **Advantages/Disadvantages** & **References** \\ \hline Seismic testing & \begin{tabular}{c} Shaking table loading \\ Seismic simulator \\ \end{tabular} & \begin{tabular}{c} Reliable results, intuitive phenomena/High costs, high \\ equipment requirements, limited test conditions \\ \end{tabular} & [11; 12; 13] \\ \hline Theoretical analysis & \begin{tabular}{c} Response spectrum method \\ Push-over method \\ Energy method \\ \end{tabular} & \begin{tabular}{c} Simple calculation, low computing costs, stable analysis \\ results/Cannot reflect the dynamic characteristics, limited \\ range of application, poor accuracy \\ \end{tabular} & [14; 15; 16] \\ \hline Numerical analysis & \
\begin{tabular}{c} Finite element method \\ Finite difference method \\ Finite volume method \\ \end{tabular} &
\begin{tabular}{c} Providing a wider range of structural data, wide range of \\ application/Complex analysis process, high computational \\ cost, high requirements for computing equipment \\ \end{tabular} & [17; 18; 19; 20] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Structural response analysis methods.