  Discovering non-linear dynamical models from data is at the core of science.
Recent progress hinges upon sparse regression of observables using extensive
libraries of candidate functions. However, it remains challenging to model
hidden non-observable control variables governing switching between different
dynamical regimes. Here we develop a data-efficient derivative-free method,
IHCV, for the Identification of Hidden Control Variables. First, the
performance and robustness of IHCV against noise are evaluated by benchmarking
the IHCV method using well-known bifurcation models (saddle-node,
transcritical, pitchfork, Hopf). Next, we demonstrate that IHCV discovers
hidden driver variables in the Lorenz, van der Pol, Hodgkin-Huxley, and
Fitzhugh-Nagumo models. Finally, IHCV generalizes to the case when only partial
observational is given, as demonstrated using the toggle switch model, the
genetic repressilator oscillator, and a Waddington landscape model. Our
proof-of-principle illustrates that utilizing normal forms could facilitate the
data-efficient and scalable discovery of hidden variables controlling
transitions between different dynamical regimes and non-linear models.
