Human missions to Mars will require rocket-powered descent through the Martian atmosphere to safely land. Designing the propulsion system for these missions introduces the following challenges: ensuring safety, sparsity of data to validate models, and requirements for rapid simulations. ML offers opportunities for addressing these challenges. We use ML methods to develop novel data-analytic tools that support design analysis for enabling supersonic retropropulsion (SRP) technology deployment. Accordingly, we propose a hierarchical physics-embedded data-driven (HPDD) framework for predicting the key target quantity in SRP. HPDD model is trained on small-scale wind tunnel data, and the model exhibits promising accuracy and computational efficiency. Wind tunnel testing in the future will provide more data for validation and enhancement of our framework to further the understanding of SRP.