Infinite-dimensional next-generation reservoir computing
This work addresses hyperparameter sensitivity in NG-RC for researchers in complex systems forecasting, offering an incremental improvement with theoretical backing.
The paper tackles the challenge of selecting hyperparameters in next-generation reservoir computing (NG-RC) for spatio-temporal forecasting by encoding it as kernel ridge regression, enabling efficient training with large feature spaces and extending to infinite covariates, which outperforms traditional NG-RC in forecasting applications.
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.