`Next Generation' Reservoir Computing: an Empirical Data-Driven Expression of Dynamical Equations in Time-Stepping Form
This work addresses the challenge of data-driven dynamical system modeling for computational science applications, representing an incremental advancement in reservoir computing methods.
The researchers tackled the problem of emulating dynamical systems by applying next-generation reservoir computing based on nonlinear vector autoregression (NVAR) to recover numerical integration schemes from data, showing it can produce high-order schemes and examining noise and temporal sparsity effects.
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.