The application of hydrogen for energy storage and as a vehicle fuel necessitates efficient and effective storage technologies. In addition to traditional cryogenic and high-pressure tanks, an alternative approach involves utilizing porous materials such as activated carbons within the storage tank. The adsorption behaviour of hydrogen in porous structures is described using the Dubinin-Astakhov isotherm. To model the flow of hydrogen within the tank, we rely on the equations of mass conservation, the Navier-Stokes equations, and the equation of energy conservation, which are implemented in a computational fluid dynamics code and additional terms account for the amount of hydrogen involved in sorption and the corresponding heat release. While physical models are valuable, data-driven models often offer computational advantages. Based on the data from the physical adsorption model, a data-driven model is derived using various machine learning techniques. This model is then incorporated as source terms in the governing conservation equations, resulting in a novel hybrid formulation which is computationally more efficient. Consequently, a new method is presented to compute the temperature and concentration distribution during the charging and discharging of hydrogen tanks and identifying any limiting phenomena more easily.