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

`Next Generation' Reservoir Computing: an Empirical Data-Driven Expression of Dynamical Equations in Time-Stepping Form