Nowadays, there has been an increasing focus on integrated flight propulsion control and the inlet-exhaust design for the aero-propulsion system. Traditional component-level models are inadequate due to installed performance deviations and mismatches between the real engine and the model, failing to meet the accuracy requirements of supersonic conditions. This paper establishes a quasi-one-dimensional model for the inlet-exhaust system and conducts experimental calibration. Additionally, a mechanism-data fusion adaptive modeling scheme using an Extreme Learning Machine based on the Salp Swarm Algorithm (SSA-ELM) is proposed. The study reveals the inlet model's efficacy in reflecting installed performance, flow matching, and mitigating pressure distortion, while the nozzle model accurately predicts flow coefficients and thrust coefficients, and identifies various operational states. The model's output closely aligns with typical experimental parameters. By combining offline optimization and online adaptive correction, the mechanism-data fusion adaptive model substantially reduces output errors during regular flights and varying levels of degradation, and effectively handles gradual degradation within a single flight cycle. Notably, the mechanism-data fusion adaptive model holistically addresses total pressure errors within the inlet-exhaust system and normal shock location correction. This approach significantly curbs performance deviations in supersonic conditions. For example, at Ma = 2.0, the system error impressively drops from 34.17% to merely 6.54%, while errors for other flight conditions consistently stay below the 2.95% threshold. These findings underscore the clear superiority of the proposed method.