Molecular dynamics simulations were performed to evaluate the penetration of two different fluids (i.e., a Lennard-Jones fluid and a polymer) through a designed nanochannel. For both fluids, the length of permeation as a function of time was recorded for various wall-fluid interactions. A novel methodology, namely, the artificial neural network (ANN) approach was then employed for modeling and prediction of the length of imbibition as a function of influencing parameters (i.e., time, the surface tension and the viscosity of fluids, and the wall-fluid interaction). It was demonstrated that the designed ANN is capable of modeling and predicting the length of penetration with superior accuracy. Moreover, the importance of variables in the designed ANN, i.e., time, the surface tension and the viscosity of fluids, and the wall-fluid interaction, was demonstrated with the aid of the so-called connection weight approach, by which all parameters are simultaneously considered. It was revealed that the wall-fluid interaction plays a significant role in such transport phenomena, namely, fluid flow in nanochannels.