  Hybrid modeling, the combination of first principle and machine learning
models, is an emerging research field that gathers more and more attention.
Even if hybrid models produce formidable results for academic examples, there
are still different technical challenges that hinder the use of hybrid modeling
in real-world applications. By presenting NeuralFMUs, the fusion of a FMU, a
numerical ODE solver and an ANN, we are paving the way for the use of a variety
of first principle models from different modeling tools as parts of hybrid
models. This contribution handles the hybrid modeling of a complex, real-world
example: Starting with a simplified 1D-fluid model of the human cardiovascular
system (arterial side), the aim is to learn neglected physical effects like
arterial elasticity from data. We will show that the hybrid modeling process is
more comfortable, needs less system knowledge and is therefore less error-prone
compared to modeling solely based on first principle. Further, the resulting
hybrid model has improved in computation performance, compared to a pure first
principle white-box model, while still fulfilling the requirements regarding
accuracy of the considered hemodynamic quantities. The use of the presented
techniques is explained in a general manner and the considered use-case can
serve as example for other modeling and simulation applications in and beyond
the medical domain.
