  We propose a new hybrid modelling approach that combines a mechanistic model
with a machine-learnt model to predict the limit cycle oscillations of physical
systems with a Hopf bifurcation. The mechanistic model is an ordinary
differential equation normal-form model capturing the bifurcation structure of
the system. A data-driven mapping from this model to the experimental
observations is then identified based on experimental data using machine
learning techniques. The proposed method is first demonstrated numerically on a
Van der Pol oscillator and a three-degree-of-freedom aeroelastic model. It is
then applied to model the behaviour of a physical aeroelastic structure
exhibiting limit cycle oscillations during wind tunnel tests. The method is
shown to be general, data-efficient and to offer good accuracy without any
prior knowledge about the system other than its bifurcation structure.
