Hydrogen is a good candidate for the next generation fuel with a high energy density and an environment friendly behavior in the energy production phase. Micro-organism based biological production of hydrogen currently suffers low hydrogen production yields because the living cells must sustain different cellular activities other than the hydrogen production to survive. To circumvent this, teams have explored the synthetic assembly of enzymes in-vitro in cell-free systems with specific functions. Such a synthetic cell-free system was recently devised by combining 13 different enzymes to synthesize hydrogen from cellulose or cellobiose with better yield than microorganism-based systems. We used methods based on differential equations calculations to investigate how the initial conditions and the kinetic parameters of the enzymes influenced the productivity of a such system and, through simulations, identified those conditions that would optimize hydrogen production starting with cellobiose as substrate. Further, if the kinetic parameters of the component enzymes of such a system are not known, we showed how, using artificial neural network, it is possible to identify alternative models that account for the rate of production of hydrogen. This work demonstrates how modeling can help in designing and characterizing cell-free systems in synthetic biology. A web-based simulator implementing our differential equations based model is provided freely as a service for noncommercial usage at http://www.bo-protscience.fr/h2.