Cross-predicting nonlinear dynamical systems from delayed coordinate mappings with reservoir computing

Abstract Providing accurate predictions from known information to future states of nonlinear dynamical systems is challenging, and data-driven techniques have emerged as powerful tools for addressing this problem. In this work, we proposed a data-driven and model-free framework delayed coordinate mapping-reservoir computing (DCM-RC) for long-term accurate prediction of nonlinear dynamical systems through the synergy between DCM and a novel RC method. For dynamic systems, DCM-RC constructs delayed attractors conjugated to the original attractor topology by converting the spatial information of the dynamic system into the temporal dynamics of the target variables through the delayed embedding theorem. The basic architecture of multistep prediction is constructed by finding DCM, and RC with fused polynomial libraries is applied to cross-predict all states of the dynamical system, thus obtaining information about the future of the dynamical system. The effectiveness and accuracy of DCM-RC are demonstrated on the Lorenz-63 system and the Rőssler system.