Train Interpretable Neural Networks That Accurately Extrapolate from Small Data

Thanks, I've always wondered how one can incorporate some structural knowledge into machine learning instead of full-on black box.

Is it possible to learn the system without a direct measurement of the states of the ODE but using its outputs (y) which are a function of the states (xdot = f(x,u), y = g(x,u)) ?

Is there some criteria like observability that indicates what are the minimum measurements (ex: number of states) needed to learn a given ODE system ?