  With the rapid development of computational techniques and scientific tools,
great progress of data-driven analysis has been made to extract governing laws
of dynamical systems from data. Despite the wide occurrences of non-Gaussian
fluctuations, the effective data-driven methods to identify stochastic
differential equations with non-Gaussian L\'evy noise are relatively few so
far. In this work, we propose a data-driven approach to extract stochastic
governing laws with both (Gaussian) Brownian motion and (non-Gaussian) L\'evy
motion, from short bursts of simulation data. Specifically, we use the
normalizing flows technology to estimate the transition probability density
function (solution of nonlocal Fokker-Planck equation) from data, and then
substitute it into the recently proposed nonlocal Kramers-Moyal formulas to
approximate L\'evy jump measure, drift coefficient and diffusion coefficient.
We demonstrate that this approach can learn the stochastic differential
equation with L\'evy motion. We present examples with one- and two-dimensional,
decoupled and coupled systems to illustrate our method. This approach will
become an effective tool for discovering stochastic governing laws and
understanding complex dynamical behaviors.
