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.

翻译：下一代储备池计算（NG-RC）因其在复杂系统时空预测中的优异性能及易于实现的特点而备受关注。本文证明，NG-RC可编码为核岭回归，即使所选多项式特征空间非常大，也能实现高效可行的训练。此外，该方法可扩展至无限个协变量，从而使其对作为解释因素的过去时滞数量以及多项式协变量数量（传统NG-RC中的重要超参数）具有无关性。我们证明该方法具有坚实的理论基础，且基于文献中已建立的核普适性性质表现出良好性能。多项数值示例表明，这些NG-RC的推广形式在多种预测应用中优于传统方法。