# Infinite-dimensional next-generation reservoir computing

arXiv: https://arxiv.org/abs/2412.09800 · HTML: https://mlsanity.com/paper/2412.09800/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 51 references that are in the map.
- First posted on arXiv 13 Dec 2024.

## Builds on (most cited first, 11 of 11)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Reservoir Computing Universality With Stochastic Inputs](https://mlsanity.com/paper/1807.02621/) (2018)
- [Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems](https://mlsanity.com/paper/1712.00754/) (2017)
- [Fading memory echo state networks are universal](https://mlsanity.com/paper/2010.12047/) (2020)
- [Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2203.13294/) (2022)
- [Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components](https://mlsanity.com/paper/2102.07819/) (2021)
- [Learning strange attractors with reservoir systems](https://mlsanity.com/paper/2108.05024/) (2021)
- [Controlling Chaos Using Edge Computing Hardware](https://mlsanity.com/paper/2406.12876/) (2024)
- [Controlling Chaotic Maps using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2307.03813/) (2023)
- [Universalities of Reproducing Kernels Revisited](https://mlsanity.com/paper/1310.5543/) (2013)

## Built on by (most cited first, 9 of 9)

- [Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning](https://mlsanity.com/paper/2505.11349/) (2025)
- [On the emergence of numerical instabilities in Next Generation Reservoir Computing](https://mlsanity.com/paper/2505.00846/) (2025)
- [Adaptive Nonlinear Vector Autoregression: Robust Forecasting for Noisy Chaotic Time Series](https://mlsanity.com/paper/2507.08738/) (2025)
- [Kernel-based optimization of measurement operators for quantum reservoir computers](https://mlsanity.com/paper/2602.14677/) (2026)
- [Next-Generation Reservoir Computing for Dynamical Inference](https://mlsanity.com/paper/2509.11338/) (2025)
- [A tensor network approach for chaotic time series prediction](https://mlsanity.com/paper/2505.17740/) (2025)
- [Reservoir Computing via Multi-Scale Random Fourier Features for Forecasting Fast-Slow Dynamical Systems](https://mlsanity.com/paper/2511.14775/) (2025)
- [Next-generation reservoir computing validated by classification task](https://mlsanity.com/paper/2512.12903/) (2025)
- [Kolmogorov-Arnold Reservoir Computing](https://mlsanity.com/paper/2606.19984/) (2026)

## Abstract (arXiv)

Next-generation reservoir computing (NG-RC) has attracted much attention due to its excellent performance in spatio-temporal forecasting of complex systems and its ease of implementation. This paper shows that NG-RC can be encoded as a kernel ridge regression that makes training efficient and feasible even when the space of chosen polynomial features is very large. Additionally, an extension to an infinite number of covariates is possible, which makes the methodology agnostic with respect to the lags into the past that are considered as explanatory factors, as well as with respect to the number of polynomial covariates, an important hyperparameter in traditional NG-RC. We show that this approach has solid theoretical backing and good behavior based on kernel universality properties previously established in the literature. Various numerical illustrations show that these generalizations of NG-RC outperform the traditional approach in several forecasting applications.