Sounds good, Dara. I have the dogged persistence to pursue some of this the old-fashioned way by grinding it out, but I am sure anything you can do with SVR will leave me in the dust.
The Mathieu function (which I use more frequently) is a special case of the Hill equation, where only one periodic modulation term is allowed versus any number for the more general Hill formulation.
So, to recap and avoid future confusion, there appear to be modulations in both (1) the periodic forcing function and (2) the parameters of the differential equation, the latter which describes the Mathieu or Hill equation.
The complexity of the model is increasing, but that is OK as long as we can get the machine learning performance to scale accordingly.