Optimizing the complex geometries that characterize turbo-machinery systems, pursued through performance evaluation using high-resolution numerical models, remains computationally expensive. This makes it difficult to explore large design spaces, whether for conventional or unconventional configurations. At the same time, the mathematical model must be streamlined to be computationally efficient, typically limited to steady-state simulations and, when possible, to exploiting axial symmetry. In other words, it restricts performance analysis to design points where flow conditions are considered nominal, often performing simulation with low fidelity solvers (i.e. by employing coarse grid resolution). To make the complexity of the configuration manageable, it is often necessary to narrow the design space. The Design Space Reduction (DSR) process, however, should not focus on abandoning exploration of regions within it, but rather on using transformations that lower its dimensionality with respect to control variables. The goal of this work is to propose and validate in this new application a DSR-based technique enriched with physical information from numerical analysis results, such as integral parameters, field variables, and the geometry of the compressor sections. In parallel, the number of numerical analyses is reduced through adaptive sampling of the (reduced) design space using smart sampling, which draws information from the same (parallel) engine through which the design space was reduced . In this work, a simple compressor configuration is optimized with a DSR engine that explores a parallel space, with a flowchart illustrated in Figure 1. Several DSR engine configurations are explored, like the NASA rotor37, in view of a subsequent optimization of a larger compressor configuration. Future work could employ a multi-fidelity approach, coupling high-fidelity 3D CFD simulations with fine mesh resolution for validation and verification of baseline and optimized configurations. The evaluations of the objective function are performed with Multall: an open-source 3D Navier-Stokes solver that adopts a H-shape grid approach. This solver could be consider a 'low fidelity' respect to 3D-CFD RANS parallel code, due to internal limitation to the grid refinement level. The activities described in this work have been carried out under the project MYTHOS, which has received funding from CINEA under the Horizon Europe programme.