  Despite rapid progress in live-imaging techniques, many complex biophysical
and biochemical systems remain only partially observable, thus posing the
challenge to identify valid theoretical models and estimate their parameters
from an incomplete set of experimentally accessible time series. Here, we
combine sensitivity methods and ranked-choice model selection to construct an
automated hidden dynamics inference framework that can discover predictive
nonlinear dynamical models for both observable and latent variables from
noise-corrupted incomplete data in oscillatory and chaotic systems. After
validating the framework for prototypical FitzHugh-Nagumo oscillations, we
demonstrate its applicability to experimental data from squid neuron activity
measurements and Belousov-Zhabotinsky (BZ) reactions, as well as to the Lorenz
system in the chaotic regime.
