Prediction of aerodynamic force/heating acting on hypersonic vehicles in flight conditions with experimental data is a critical yet challenging step in developing hypersonic vehicles. A multi-space interrelation (MSI) theory and its correlation algorithms have been presented. MSI considers the flight condition as an ideal wind tunnel and then aims at detecting an inherent invariant of aerodynamic data from different wind tunnels. The invariant detection is carried out by special supervised self-learning schemes, adaptive space transformation (AST), and/or parse-matrix evolution (PME). The invariant is then used to predict the aerodynamic force/heating coefficients. The study indicates that the multi-space interrelation theory agrees well with physical phenomena. The correlation algorithm can make use of hypersonic wind-tunnel experimental data effectively, and the correlation function is capable of unifying all the experimental data in an analytical form. With the proposed theory and algorithm, one can expect to find a reliable correlation formula with high accuracy based on plenty of wind-tunnel experimental data, provided that the physical condition has not essentially changed.