  Next generation reservoir computing based on nonlinear vector autoregression
(NVAR) is applied to emulate simple dynamical system models and compared to
numerical integration schemes such as Euler and the $2^\text{nd}$ order
Runge-Kutta. It is shown that the NVAR emulator can be interpreted as a
data-driven method used to recover the numerical integration scheme that
produced the data. It is also shown that the approach can be extended to
produce high-order numerical schemes directly from data. The impacts of the
presence of noise and temporal sparsity in the training set is further examined
to gauge the potential use of this method for more realistic applications.
