Structure Matched Higher Order Reservoir Computing for Complex System Prediction

Conventional reservoir computing (RC) provides an efficient framework for chaotic time series prediction, but its random input mapping and pairwise reservoir connections do not explicitly reflect the higher order relations that often govern nonlinear dynamical systems. This paper proposes a structure matched higher order RC framework that coordinates two stages of the prediction process. In the input layer, a block structured input matrix is constructed according to the local higher order neighbor sets associated with the predicted variable, so that target related variable couplings are organized before entering the reservoir. In the reservoir layer, higher order node interactions are introduced into the state evolution equation, allowing the structured input information to be further propagated and recombined through nonlinear reservoir dynamics. Experiments on the Lorenz chaotic system show that the proposed framework achieves lower prediction errors. Parameter analysis further shows that prediction performance depends on the coordinated selection of input scaling, node block allocation, and higher order coupling strength. These results indicate that prediction performance in RC can be improved not only by increasing reservoir nonlinearity, but also by coordinating how target related structural information is injected and internally evolved. The proposed framework provides a useful route for incorporating higher order structural information into RC and may support more reliable prediction of complex systems governed by multivariable interactions.