Prior to the detailed design of turbines, turbomachinery engineers must rely on mean-line and throughflow models to come to a preliminary design. These models are based on empirical loss correlations and are often derived from cascade experiments and numerical analyses that are confined to the subsonic and transonic regime. Axial turbines for rocket propulsion applications are characterised by a near zero degree of reaction and supersonic stator vanes that yield a complex flow field, making the prediction of losses challenging with existing correlations. The goal of this study is to investigate the variation of loss generation in supersonic axial turbine stator vanes with the isentropic exit Mach number. The profile losses will be split into components that can be attributed to different loss generation mechanisms whose relative magnitude may point to where performance improvement can be made. The investigation is performed on stator vanes that are used in the first turbine stage of a 1MN-class gas generator cycle type rocket engine. The stator vanes will be optimised for the profile losses by exploiting a novel adjoint optimisation framework for turbomachinery and the effect on the exit flow field will be investigated. The computational risk will be mitigated to ensure that the feasibility of the research is not jeopardised. The successful outcome of this research will lead to supersonic loss characteristics of axial turbine stator vanes, reduced development costs, increased efficiency levels and pave the way for future work on optimisation methods for turbomachinery applications.