  Augmenting mechanistic ordinary differential equation (ODE) models with
machine-learnable structures is an novel approach to create highly accurate,
low-dimensional models of engineering systems incorporating both expert
knowledge and reality through measurement data. Our exploratory study focuses
on training universal differential equation (UDE) models for physical nonlinear
dynamical systems with limit cycles: an aerofoil undergoing flutter
oscillations and an electrodynamic nonlinear oscillator. We consider examples
where training data is generated by numerical simulations, whereas we also
employ the proposed modelling concept to physical experiments allowing us to
investigate problems with a wide range of complexity. To collect the training
data, the method of control-based continuation is used as it captures not just
the stable but also the unstable limit cycles of the observed system. This
feature makes it possible to extract more information about the observed system
than the open-loop approach (surveying the steady state response by parameter
sweeps without using control) would allow. We use both neural networks and
Gaussian processes as universal approximators alongside the mechanistic models
to give a critical assessment of the accuracy and robustness of the UDE
modelling approach. We also highlight the potential issues one may run into
during the training procedure indicating the limits of the current modelling
framework.
