This work presents a hybrid modeling framework developed using the Gaussian process regression (GPR) algorithm, aimed at addressing high-dimensional design challenges more effectively than traditional standalone methods. The framework combines forward and inverse modeling techniques and is applied to model a compact, circularly polarized octagonal microstrip antenna tailored for X-band applications. To provide a comparative analysis, separate forward and inverse models are also developed using GPR, multilayer perceptron (MLP) and support vector regression (SVR). The performance of these models is evaluated using key metrics, namely the average percentage relative error (APRE) and the correlation coefficient (CC). The results demonstrate that the hybrid model, particularly with GPR, significantly outperforms the forward and inverse models, showcasing superior accuracy and reliability. This comprehensive analysis highlights the potential of the proposed hybrid framework as a valuable tool for advanced antenna design and optimization, offering promising prospects for future research and practical applications in wireless communication systems.