Most “learning” in big data is driven by the data alone. Some people may believe this is sufficient because of the sheer data size. If the physical world is involved, this approach is often insufficient. In this talk I will give a recent study to illustrate how physics and data are used jointly to learn about the “truth” of the physical world. In the quest for advanced propulsion systems, a new design methodology is needed which combines engineering physics, computer simulations and statistical modeling. There are two key challenges: the simulation of high-fidelity spatial-temporal flows (using the Navier-Stokes equations) is computationally expensive, and the analysis and modeling of this data requires physical insights and statistical tools. First, a surrogate model is presented for efficient flow prediction in swirl injectors with varying geometries, devices commonly used in many engineering applications. The novelty lies in incorporating properties of the fluid flow as simplifying model assumptions, which allows for quick emulation in practical turnaround times, and also reveals interesting flow physics which can guide further investigations. Next, a flame transfer function framework is proposed for modeling unsteady heat release in a rocket injector. Such a model is useful not only for analyzing the stability of an injector design, but also identifies key physics which contribute to combustion instability.