  This paper introduces a machine learning approach to take a nonlinear
differential-equation model that exhibits qualitative agreement with a physical
experiment over a range of parameter values and produce a hybrid model that
also exhibits quantitative agreement. The underpinning idea is that the
bifurcation experiment structure of an experiment can be revealed using
techniques such as control-based continuation and then used to generate a
simplified normal-form-like model. A machine learning approach is then used to
learn a coordinate transform from the normal-form-like model to the physical
coordinates of the experiment. This approach is demonstrated on a mathematical
model of aero-elastic flutter, where good agreement at the level of the
bifurcation diagrams is shown between the hybrid model and the underlying
ground truth. Moreover, individual phase portraits and time series are also
reproduced accurately, even in regions away from training data. As such, the
approach holds significant promise for producing quantitatively accurate models
that exhibit the correct nonlinear behaviour over a range of parameter values.
