###### Abstract  
In recent years, passive vehicle safety has become one of the major concerns for the automotive industry due to the considerable increase in the use of cars as a means of daily transport. Since real crash testing has a high financial cost, finite element simulations are generally used, which entail high computational cost and long simulation times. In this paper, we make use of the recent advances in the deep learning field to propose an affordable method to provide reliable approximations of the finite element simulator model that significantly reduce the computational load and time required. We compare the prediction performance in crash tests of different models, namely feed-forward neural networks and bayesian neural networks, as well as two multi-output regression methods. Our results show promising results, as deep learning models are able to drastically reduce the engineering costs while providing a feasible first approximation to the passenger's injuries in a crash event, thus being a potential game changer in the vehicle safety design process. passive vehicle safety; crashworthiness; finite elements; feed-forward neural network; bayesian neural network +
Footnote †: journal: Applied sciences  
in the event of a collision, helping to minimize the impact received by the passenger and posterior injuries. Within the passive safety field, the term \"crashworthiness\" can be found repeatedly in existing research [13]: in the automotive engineering context, this term is related to the capacity of the vehicle structure to protect its occupants in the event of collision. In order to actually assess whether a certain vehicle complies with safety standards and regulations, and before a new car model is introduced on the market, it must be subjected to vehicle safety assessment programs, e.g., in Europe, these are conducted by the European New Car Assessment Program (Euro NCAP). These assessment programs require the use of Anthropomorphic Test Devices (ATDs), also called crash test dummies, to determine the capacity of the car to protect its occupants in a crash event. To achieve that target, test dummies are equipped with a multitude of sensors capable of precisely capturing different measurements of interest exerted on each body part. However, real car crash testing demands high financial costs. To reduce the number of hardware crash tests and to better understand the underlying system, Finite Element (FE) simulations are widely used, e.g., to reconstruct the collision of a motorcycle and a car [14], to study the response of a car to a frontal crash [15], and to simulate crash scenarios [16]. Thus, FE is the state-of-the-art technique in the passive safety design process, as a recent review on crashworthiness shows [13]. FE tools lower monetary costs and speed up the process to some extent because they can simulate the real world with little error [13], but at the same time, they entail high computational costs, implying long computational times. Thus, in order to obtain the measures of interest in the test dummy during a crash event (i.e., the neck acceleration during a frontal crash), we need to run a FE model, which is usually solved by a commercial software that acts as a black box, providing only inputs and outputs of the model. This FE model takes a long time to simulate, consuming a significant amount of resources. For instance, the data used in the simulations of this paper come from a FE simulator that takes over 45 h to compute each simulation on 36 CPUs. Due to these reasons, approximation techniques, also known as meta-models, are applied to build approximate mathematical models of complex models that provide a rough but fast approximation to the crash curves [17]. In this work, we propose taking advantage of the recent advances in deep learning (DL), so we use the approximation capabilities of neural networks (NNs) in order to estimate the crash curves. In several fields where FE simulations are used, machine learning tools are being applied due to their advantages.