Air-breathing hypersonic vehicles is a class of vehicles that operates at high Mach number in the atmosphere for the entire mission profile and are exposed to an extreme aerothermodynamic environment involving stochastic loads. Due to current limited capability of ground tests and the lack of available flight test data, there is a significant degree of uncertainty associated with the aerothermoelastic modeling of hypersonic vehicles and limited ability to alleviate this uncertainty through experimental testing. This work aims to provide a unified and automatic framework to discover governing equations underlying an unknown dynamical system from data measurements. In an appropriate basis, and based on the assumption that the structure of the dynamical model is governed by only a few important terms, the equations are sparse in nature and the resulting model is parsimonious. Solving a well-posed constrained onenorm optimization problem, we obtain a satisfactory zero-norm approximation solution and determine the most prevalent terms in the dynamic governing equations required to accurately represent the collected data.