## 1 Introduction
### Artificial Neural Network Strategy for Structural Response Prediction  
The main goal of this study is to use artificial neural networks to decrease the computational effort and, therefore, to make the Monte Carlo method attractive for real-life applications. We focus on predicting the peak story drift ratio (PSDR) for the output instead  
Figure 5: Graph of a feedforward neural network with one hidden layer. of predicting the complete response time history. The latter would require more complex neural network architectures, such as recurrent neural networks. Using feedforward architectures, there are several options, i.e., convolutions, to extract the features from the accelerogram [30]. However, the failure prediction is more accurate using a relatively small artificial neural network with fewer training samples. Therefore, this strategy is supposed to have the highest speed up compared to the full simulation procedure [43]. Carefully preprocessing the input data allows us to use a simple artificial neural network architecture. The challenge of so-called feature engineering is the generation of physically meaningful input parameters. In this context, in earthquake engineering, extensive research has been carried out to characterize seismic motion in terms of single magnitudes, such as earthquake intensities [44]. These intensity measures are used as input parameters for neural networks in this paper. Hereby, the Arias intensity \(I_{A}\), the characteristic intensity \(I_{c}\), and the cumulative absolute velocity (CAV) were already used for response predictions [45; 46]. Besides using features directly from the accelerogram, one may extract additional spectral features. Therefore, the displacement, velocity, and acceleration response spectra as well as the spectral values at the first eigenfrequency of the structure are used to evaluate additional relevant input features. As a result of this, a meaningful combination of several intensity measures as input parameters was extensively studied [47]. For a steel frame structure, the combination of the effective peak ground acceleration (EPA), the spectral acceleration at the natural period \(S_{a}(T_{1})\), the velocity spectrum intensity \(\int_{0.1}^{2.5}S_{o}\), the spectral displacement at the natural period \(S_{d}(T_{1})\), the cumulative absolute velocity (CAV), and the peak ground acceleration (PGA) revealed promising prediction results [29]. A set of relevant input parameters that can be calculated from an accelerogram are summarized in Table 1.  
We first calculate the set of artificial earthquake records \(\mathcal{S}\), based on which we extract the corresponding intensity set \(\mathcal{I}\) that contains the intensity vectors  
\[\mathbf{X}=[I_{a},S_{a}(T_{1}),\int_{0.1}^{2.5}S_{o},S_{d}(T_{1}),\text{CAV}, \text{PGA}]\text{:}\]  
\[\mathcal{S}=<\ddot{x}_{g}^{(1)}(t),\cdots,\ddot{x}_{g}^{(l)}(t)>\Rightarrow\ \mathcal{I}=<\mathbf{X}^{(1)},\cdots,\mathbf{X}^{(l)}>. \tag{11}\]  
Applying supervised learning, the neural network learns from training data. Therefore, at first, a subset of \(\mathcal{S}\) must be evaluated:  
\[\mathcal{S}_{t}=<\ddot{x}_{g}^{(1)}(t),\cdots,\ddot{x}_{g}^{(n)}(t)>\Rightarrow \ \mathcal{R}_{t}=<\mathbf{x}^{(1)},\cdots,\mathbf{x}^{(n)}>. \tag{12}\]