A novel framework for reservoir computing with inertial manifolds

Reservoir computing based on machine learning has garnered significant attention in the field of research regrading time series prediction. Active discussions that were recently held on the theoretical background aided the reservoir to realize some desired properties. In this study, we propose a reservoir computing framework based on the theory of inertial manifolds. Using the theoretical results for infinite-dimensional dynamical systems, we first introduce a new formulation of the echo state network as an extension of our previous work on multivariate input.