Deep neural networks have seen tremendous success over the last years. Since the training is performed on digital hardware, in this paper, we analyze what actually can be computed on current hardware platforms modeled as Turing machines, which would lead to inherent restrictions of deep learning. For this, we focus on the class of inverse problems, which, in particular, encompasses any task to reconstruct data from measurements. We prove that finite-dimensional inverse problems are not Banach-Mazur computable for small relaxation parameters. In fact, our result even holds for Borel-Turing computability., i.e., there does not exist an algorithm which performs the training of a neural network on digital hardware for any given accuracy. This establishes a conceptual barrier on the capabilities of neural networks for finite-dimensional inverse problems given that the computations are performed on digital hardware.

Machine learning (ML) offers a lot of potential for applications in Industry 4.0. By applying ML many processes can be improved. Possible benefits in production are a higher accuracy, an early detection of failures, a better resource efficiency or improvements in quantity control. The use of ML in industrial production systems is currently not widespread. There are several reasons for this, among others the different expertise of data scientists and automation engineers. There are no specific tools to apply ML to industrial facilities neither guidelines for setting up, tuning and validating ML implementations. In this paper we present a taxonomy structure and according method which assist the design of ML architectures and the tuning of involved parameters. As this is a very huge and complex field, we concentrate on a ML algorithm for time series forecast, as this can be used in many industrial applications. There are multiple possibilities to approach this problem ranging from basic feed-forward neural networks to recurrent networks and (temporal) convolutional networks. These different approaches will be discussed and basic guidelines regarding the model selection will be presented. The introduced assistance method will be validated on a industrial dataset.

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