Infinite-dimensional next-generation reservoir computing

TL;DR

This paper introduces an efficient, theoretically grounded extension of next-generation reservoir computing that uses kernel ridge regression to handle infinite covariates, improving forecasting performance.

Contribution

It presents a novel kernel-based formulation of NG-RC allowing for infinite covariates and hyperparameter flexibility, with strong theoretical support.

Findings

Outperforms traditional NG-RC in multiple forecasting tasks.

Efficient training via kernel ridge regression.

Theoretically justified by kernel universality.

Abstract

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.