## 1 Introduction  
As engineers, we are responsible for the reliable design of structures and infrastructures. This task turns out to be challenging, especially when structures are supposed to withstand natural hazards, such as earthquakes. A powerful tool to evaluate the response statistics of structures provides the statistical investigation of a set of experiments, commonly known as the Monte Carlo method. Structural failure should occur very rarely in order to save infrastructures and, consequently, human life so that the number of samples of the crude Monte Carlo method must be chosen high. Generally, experimental setups on full-scale structures are the most reliable way to collect data of the response behavior [1; 2; 3]. However, on the one hand, measured earthquake acceleration data are limited and, on the other hand, experimental setups of such a high number of samples are not realizable. One strategy to overcome this problem is the realization of hybrid simulations [4]. Although this approach significantly decreases the costs, it is still inefficient to collect enough data for reliable Monte Carlo predictions of low failure probabilities. In order to obtain a practically realizable framework, purely numerical models are used to simulate the statistical response behavior of structures. Especially when inducing structural failure, numerical simulations are much easier realizable in an engineer's every-day life environment. Nevertheless, for complex structures modeled by high-dimensional finite element models, the computational cost of the crude Monte Carlo simulation becomes excessive. There are two major options to deal with this issue:  
* Methods were developed to reduce the number of the required samples employing advanced Monte Carlo strategies to estimate the probability of failure, such as importance and asymptotic sampling [5; 6] or subset simulation techniques [7]. * Methods were developed to reduce the effort of each simulation, in this regard, model order reduction techniques have shown significant improvement of the computational burden [8; 9; 10]. Furthermore, the application of machine learning has received attention in the field of structural mechanics and showed promising results [11; 12; 13; 14]. Several studies have used neural networks for the design in earthquake engineering [15] and for the investigation of hazard events [16]. Researchers used machine learning approaches for structural response prediction, health monitoring, post-earthquake assessment, and interpretation of experimental data [17; 18; 19; 20; 21; 22; 23; 24; 25]. Special focus has been laid on the design of the structures to estimate the response or classify the damage of reinforced concrete frames and masonry shear walls [26; 27]. Furthermore, in-plane failure modes have been investigated using machine learning algorithms [28]. With particular emphasis on the estimation of the tail end probability, i.e., the occurrence of very extreme events, extended data sets were used to predict the probability of failure using various neural network architectures [29; 30]. To this end, the earthquake samples for the training sets of the neural network were generated using random factorization. This leads to sample sets with higher variance and, therefore, a larger portion of extreme events. However, these strategies need the consideration of additional extended data sets for the training procedure to obtain a suitable neural network prediction in case of very rare events--a strategy that requires a careful choice of additional intensity factors when generating earthquake training sets. In order to deal with this issue, this paper proposes a training data selection approach that enables a reliable prediction within the entire domain without extending the training data set.