Numerical computations comprising of Grand Canonical-Monte Carlo (GCMC) and Canonical Statistical Ensemble (NVT) Molecular Dynamics (MD) simulations were used to study the diffusion and sorption characteristics primarily for methane, ethane, and ethene molecules and for their ternary mixtures at different temperatures in ZIF-8 porous material. Methane as pure component or in mixture proved to be the sorbed hydrocarbon with the higher molecular mobility at the temperature range of 273-373 K among alkanes and alkenes. In addtion, alkenes were the hydrocarbons with the higher self-diffusion coefficients compared to the respective alkanes. In the ternary mixtures ethane was preferentially sorbed in ZIF-8 at all temperatures studied. Direct comparisons of the self-diffusivity data obtained from the NVT-MD simulations with recently reported Magic Angle Spinning Pulsed Field Gradient Nuclear Magnetic Resonance (MAS PFG NMR) measurements showed reasonable agreement. Furthermore, the NVT-MD self-diffusivity coefficients in conjunction with the aforementioned MAS PFG NMR experimental measurements, and sorption thermodynamic data obtained from the present GCMC simulations were utilized for the development of individual Artificial Neural Networks (ANNs) predictive modeling procedures in order to provide additional quantitative and qualitative information regarding the diffusion and sorption of small alkanes, alkenes in ZIF-8. The ANNs predictions were in good agreement with the experimental measurements and with the molecular simulation data. The modeling and analysis capabilities of ANNs along with their fast computations using moderate computer resources can significantly assist the irreplaceable molecular simulation and experimental approaches to cope with complicated problems at the molecular level.