Résumé : Today's rising demand on hypersonic aircraft and cruise vehicles has strongly boosted interest in the research and development of combined-cycle air-breathing engines. They offer not only an efficient operation in terms of specific impulse as compared to their rocket opponents, but also an impeccable propulsion with an extended flight speed range under stratospheric altitude conditions. However, the operation at high speeds has many challenges and requires further complex design and optimization studies of the propulsion systems. The difficulties in the design of the engines used for this purpose vary from figuring out the interaction between multiple cycles to providing optimal fuel-air mixing and flame distributions at the high altitude conditions where the atmospheric conditions are unfavorable enough to impede the supersonic combustion. The numerical simulations in preliminary early design stages are essential to discuss roughly the feasibility of these systems and estimate engine performance for making first guess about the trajectory reliability. In this sense, the accuracy of these critical studies of the hypersonic engines strongly depends on the trustworthiness of the existing low fidelity numerical tools. This doctoral thesis concerns firstly the design and analysis of a combined-cycle air-breathing engine propelling a civil hypersonic transporter mainly at Mach 8 and stratospheric conditions by means of numerical modeling and performing transient simulations with extended version of state-of-the-art tools and analysis methods which are combination of First and Second Laws, secondly develops new generic reduced-order modeling methodologies to improve accuracy of the existing tools in a manner of performing some high-fidelity numerical simulations both for reactive and non-reactive flows and coupling them with advanced machine learning techniques such as Kernel regression, Gaussian Process Regression, and Artificial Neural Network. It also investigates deeply supersonic flow physics via multi-dimensional CFD simulations because the validity of reduced-order modeling relies on proper understanding of the physical phenomena observed in high-fidelity analysis. It is found that the combined-cycle engine performance to highly depend on flow area allocations in nozzle component where the cycles' discharged flows meet. Most of the exergy is generally lost in the nozzle (20-30%). The system efficiency reached its maximum value around mid-supersonic flight speeds corresponding to Mach 2-3. In the reduced-order design and analysis of ramjet engine, optimal range of intake exit Mach number varies between 0.53-0.57 to yield an efficient burning in combustor and favorable system performance. In the reduced-order modeling studies devoted to improve accuracy of the current low-fidelity models by formulating supersonic fuel-air mixing, the regression is found more difficult in the vicinity of fuel struts (due to turbulence/shock effects) and easier further downstream from the struts, but ANN performs generally better than other regression models by computing the thrust of a hypersonic engine with less than 10% error. On the other hand, the regression becomes more challenging in further zones from the struts when the reactions are switched on. This strongly depends on the strength of shock pattern in post strut region and where the ignition takes place which are function of fuel strut configurations (struts location, V-settlement angle, and wedge angle). The sensitivity analysis and detailed discussion show that the strut wedge angle to be the most influencing parameter on the mixing and combustion phenomena and aerodynamic losses.