`Next Generation' Reservoir Computing: an Empirical Data-Driven Expression of Dynamical Equations in Time-Stepping Form. (arXiv:2201.05193v1 [cs.LG])

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 …

arxiv computing data data-driven time