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极大时仍能实现高效可行的训练。此外，该方法可扩展至无限维协变量，使其无需预先确定作为解释因子的历史滞后阶数，也无需设定传统NG-RC中重要的超参数——多项式协变量数量。我们证明该方法具有坚实的理论基础，其良好性能源于文献中已建立的核普适性理论。多项数值实验表明，这种NG-RC的推广形式在多种预测应用中均优于传统方法。