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

arXiv: https://arxiv.org/abs/2201.05193 · HTML: https://mlsanity.com/paper/2201.05193/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 13 Jan 2022.

## Builds on (most cited first, 5 of 5)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers](https://mlsanity.com/paper/1910.00659/) (2019)
- [Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization](https://mlsanity.com/paper/2001.06270/) (2020)
- [Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimation](https://mlsanity.com/paper/2109.12269/) (2021)
- [Model-Free Prediction of Chaotic Systems Using High Efficient Next-generation Reservoir Computing](https://mlsanity.com/paper/2110.13614/) (2021)

## Built on by (most cited first, 3 of 3)

- [Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence](https://mlsanity.com/paper/2305.00100/) (2023)
- [Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approach](https://mlsanity.com/paper/2602.18377/) (2026)
- [Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error](https://mlsanity.com/paper/2605.31438/) (2026)

## Abstract (arXiv)

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 2nd 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.