  We develop a data-driven method to learn chemical reaction networks from
trajectory data. Modeling the reaction system as a continuous-time Markov chain
and assuming the system is fully observed, our method learns the propensity
functions of the system with predetermined basis functions by maximizing the
likelihood function of the trajectory data under $l^1$ sparse regularization.
We demonstrate our method with numerical examples using synthetic data and
carry out an asymptotic analysis of the proposed learning procedure in the
infinite-data limit.
