  In this paper, we are interested in the acceleration of numerical
simulations. We focus on a hypersonic planetary reentry problem whose
simulation involves coupling fluid dynamics and chemical reactions. Simulating
chemical reactions takes most of the computational time but, on the other hand,
cannot be avoided to obtain accurate predictions. We face a trade-off between
cost-efficiency and accuracy: the simulation code has to be sufficiently
efficient to be used in an operational context but accurate enough to predict
the phenomenon faithfully. To tackle this trade-off, we design a hybrid
simulation code coupling a traditional fluid dynamic solver with a neural
network approximating the chemical reactions. We rely on their power in terms
of accuracy and dimension reduction when applied in a big data context and on
their efficiency stemming from their matrix-vector structure to achieve
important acceleration factors ($\times 10$ to $\times 18.6$). This paper aims
to explain how we design such cost-effective hybrid simulation codes in
practice. Above all, we describe methodologies to ensure accuracy guarantees,
allowing us to go beyond traditional surrogate modeling and to use these codes
as references.
