Basic constituents of the methodology for the numerical solution of compressor blade row gasdynamics inverse problems Choice of the starting values of the blade row design parameters Intelligent search for the starting values of the blade row design parameters using artificial neural networks Numerical simulation of the blade row gas flow Mathematical model: - potential gas flow equations; - Euler set of equations Method of solution: effective conservative finite-difference scheme The computed and target aerodynamic characteristics do not coincide Comparison of the computed and target aerodynamic characteristics The computed and target aerodynamic characteristics coincide Blade row geometry refinement Choice of design parameters: aerodynamic form parametric description technique Search for new values of the design parameters : - gradient methods; - direct search method; - evolutionary methods Final geometry of blade row The research will be of key importance in the solution of the topical problem of aerodynamic design of modern gas turbine aeroengine compressor blade rows