This paper explores the dynamic hydroelastic response of a physical model of a flexible hydrofoil. Results show that system mass increases with immersion, system stiffness is larger in ventilated flows than in wetted flows, and total damping is dominated by hydrodynamic damping for the first three modes. We also presents preliminary validation of a fast unsteady fluid-structure interaction (FSI) model capable of predicting the dynamic response to external excitations on a surface piercing hydrofoil. The fast FSI model yields good predictions of the response to harmonic excitations. The inverse problem uses the FSI model to infer the unknown operating conditions and hydrodynamic load distributions, given a limited number of strain measurements. The inverse model correctly infers the mean flow conditions in fully wetted, partially cavitating, and fully ventilated flows. The data and methods establish a promising precedent for the analysis and synthesis of dynamic FSI data from experiments and fast physics-based models.