For the simulation of fluid-structure interaction, mostly computational intensive methods are used until today, which achieve a very high accuracy, but are usually very expensive. The data-based approach presented here uses training data from the first few time steps of a classical simulation to train neural networks that provide a good prediction for subsequent time steps. The multiphysics domain of fluid flow and structural deformation is split into two single-physics domains. Each solver uses the solutions of the last time steps to predict the solution in the next time step in its own domain. The coupled solvers exchange data via a coupling library, which also provides the control of the simulation. This work aims to show, on the one hand, that the extension of machine learning for solving coupled partial differential equations of fluid-structure interaction is an endeavor that can scientifically tie in with the success of artificial intelligence in many other fields and, on the other hand, to show challenges that this extension presents. These challenges are important for future work on this topic. Mainly, deep neural networks are implemented, which consist of a combination of convolutional neural network, recurrent neural network and fully connected layers. This can be used to learn both spatial and temporal dependencies in the data. Based on the simulation of a fluid flow through a one-dimensional elastic tube, it is shown that the predicted solutions agree to a large extent with the classical numerical solution. Special attention was paid to the fact that the presented solvers can be easily transferred to other problems and are suitable to be combined with classical numerical methods, in order to accelerate the coupling convergence of these methods by predicting an accurate initial guess.