Reservoir computing with generalized readout based on generalized synchronization

Reservoir computing is a machine learning framework that exploits nonlinear dynamics, exhibiting significant computational capabilities. One of the defining characteristics of reservoir computing is that only linear output, given by a linear combination of reservoir variables, is trained. Inspired by recent mathematical studies of generalized synchronization, we propose a novel reservoir computing framework with a generalized readout, including a nonlinear combination of reservoir variables. Learning prediction tasks can be formulated as an approximation problem of a target map that provides true prediction values. Analysis of the map suggests an interpretation that the linear readout corresponds to a linearization of the map, and further that the generalized readout corresponds to a higher-order approximation of the map. Numerical study shows that introducing a generalized readout, corresponding to the quadratic and cubic approximation of the map, leads to a significant improvement in accuracy and an unexpected enhancement in robustness in the short- and long-term prediction of Lorenz and Rössler chaos. Towards applications of physical reservoir computing, we particularly focus on how the generalized readout effectively exploits low-dimensional reservoir dynamics.