We develop novel methods to estimate the gas permeation within the mixed matrix membranes (MMMs) fabricated by polycarbonate (PC), p-nitroaniline (pNA), and zeolite 4A. To this end, molecular simulation including molecular dynamics and grand ganonical Monte Carlo methods were utilized to determine the diffusivity and solubility coefficients of H-2, CH4, CO2, O-2, and N-2 gas molecules within the PC/pNA/zeolite 4A membranes. Coupled with other analysis such as X-ray diffraction, fractional free volume, and radial distribution function, structural and separation features like glass-transition temperature, mean square displacement, density, and adsorption isotherms define the solution-diffusion separation mechanism. Two state-of-the-art and accurate artificial intelligence (AI) models, viz ant colony optimization-adaptive neuro-fuzzy inference system (ACO-ANFIS) and genetic programming (GP) are developed to estimate the permeability of mentioned gas molecules within the MMMs. The R-2 value for ACO-ANFIS and GP was obtained as 0.97 and 0.96, respectively. The mean squared error value for ACO-ANFIS and GP was obtained as 0.41 and 0.51, respectively. Although the accuracy of ACO-ANFIS is higher, both models can be regarded as efficient models. The findings of the study demonstrate that the AI models are accurate. In addition, the effects of various key parameters like zeolite and pNA loading and kinetic diameter of gases are investigated. Also, it was concluded that the simple PC membrane indicated the best performance compared to other prepared MMMs.