Reservoir computing on manifolds

Reservoir computing has attracted considerable attention as an effective method for learning chaotic time series generated by dynamical systems. In this paper, we propose a new reservoir computing approach that is adapted to dynamical systems on general manifolds, representing a natural extension of the usual method for dynamical systems on the Euclidean spaces. We also present numerical results for learning the hyperbolic toral automorphism and the tripling map on the circle to demonstrate that the proposed method performs effectively.