## 5 Conclusions  
In this work, we have investigated the feasibility of applying different DL models to approximate the curves of interest to predict passenger injuries in a crash event so that the design process of passive safety elements in vehicles can be significantly accelerated compared to standard FE simulations. To this end, we proposed to implement two DL models: FFNNs and BNNs, in addition to two other multi-output regression methods, which served as baseline.  
The results obtained are very positive: both FFNNs and BNNs provide a very high prediction accuracy; BNNs can also provide an uncertainty estimate; and there are significant savings in computational load and time when compared to SST, ERC, and especially FE. Thus, note that the combination of high accuracy and low training time makes our DL proposal a potential game changer in the design process of passive security elements. That is why this tool is ready to use within the company's context, as it already gets good results to provide reliable first approximations on car crash responses.  
This promising work also allows for several other future lines of research. The first one has to do with the number of samples: in this work, we have used only 140 samples. It is possible to gather more sequences, but it is also possible to use Deep Generative Models [41] to generate synthetic data in order to increase the number of data available. In addition to that, instead of considering only data coming from the FE simulator, data coming from real car crash tests could also be added and weighted so that the networks would give more relevance to them than to the simulated values. Furthermore, it is also proposed to optimize FFNNs using fewer training samples, investigating what is the limit number of samples with which good results continue to be obtained due to the high cost of generating these samples. Another possible research direction, related to this idea, is the use of few-shot learning techniques [42; 43] in order to test whether we can further reduce the minimal number of samples needed for learning. It could also be possible to test other machine learning models different from the ones proposed in this paper, such as Support Vector Machines or Random Forests, to mention two. And finally, it is also important to test the generalization abilities of the models proposed, even out of the training distribution, as shown in [44].  
Conceptualization: M.L.N., J.S.J., P.A.A., J.P., S.Z. and M.G.; Methodology: M.L.N., J.S.J., P.A.A., J.P., S.Z. and M.G.; Formal analysis and investigation: M.L.N., J.S.J., P.A.A., J.P., S.Z. and M.G.; Writing--original draft preparation: M.L.N.; Writing--review and editing: M.L.N., J.S.J., P.A.A., J.P., S.Z. and M.G.; Resources: [PERSON] and M.G.; Supervision: [PERSON], [PERSON] and M.G. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Data Availability Statement: The data used in this paper is published along with the code in the following link: [[https://github.com/marlhaozn/DL_for_vehicle_safety](https://github.com/marlhaozn/DL_for_vehicle_safety)]([https://github.com/marlhaozn/DL_for_vehicle_safety](https://github.com/marlhaozn/DL_for_vehicle_safety)) (accessed on 2 September 2024). The data published has been anonymized to fulfill BMW Group disclosure policies.  
We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan V GPU used for this research.  
Author [PERSON] was employed by the company BMW Group. The remaining authors declare that the re-search was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.