  Identifying accurate dynamic models is required for the simulation and
control of various technical systems. In many important real-world
applications, however, the two main modeling approaches often fail to meet
requirements: first principles methods suffer from high bias, whereas
data-driven modeling tends to have high variance. Additionally, purely
data-based models often require large amounts of data and are often difficult
to interpret. In this paper, we present physics-informed neural ordinary
differential equations (PINODE), a hybrid model that combines the two modeling
techniques to overcome the aforementioned problems. This new approach directly
incorporates the equations of motion originating from the Lagrange Mechanics
into a deep neural network structure. Thus, we can integrate prior physics
knowledge where it is available and use function approximation--e. g., neural
networks--where it is not. The method is tested with a forward model of a
real-world physical system with large uncertainties. The resulting model is
accurate and data-efficient while ensuring physical plausibility. With this, we
demonstrate a method that beneficially merges physical insight with real data.
Our findings are of interest for model-based control and system identification
of mechanical systems.
