Prediction of spatiotemporal dynamic systems by data-driven reconstruction

Prediction in nonlinear systems is critical and challenging in various fields. Data-driven methods provide the theoretical basis for predicting nonlinear systems. On this basis, a data-driven prediction framework for improved reservoir computing (RC) combined with higher order dynamic mode decomposition (HODMD) is proposed. First, HODMD extracts the eigenmodes of the nonlinear system through higher order Koopman assumptions and retains the principal modes to reconstruct the system. The subsequent process uses the reconstructed system to train a unique weight matrix through the quadratic readout of the reservoir feature vectors; the reusable feature of RC training is employed to accomplish autonomous prediction of the nonlinear system. The practical consideration of the data-driven prediction framework is to enhance the ability of the RC to learn the internal evolutionary laws of the nonlinear system. Numerical results by Kuramoto-Sivashinsky equation demonstrate that the HODMD-RC framework improves the short-term and long-term prediction of nonlinear systems.