NAR Broad Learning System for dynamical systems prediction

Dynamical systems evolve over time, and predicting their behavior is difficult because of their complex spatiotemporal relationship. Although data-driven models have achieved great success in dynamical system analysis, extracting temporal dynamic and spatial features simultaneously and maintaining fast training and updating speeds are always the bottleneck of data-driven methods. In this paper, we propose the Nonlinear Autoregression Broad Learning System (NAR-BLS), a novel shallow network for dynamical system prediction. NAR-BLS is a shallow randomized flatten network. It embeds a temporal feature capture branch into the original structure of BLS to extract temporal dynamic features of the input data, and simultaneously extracts the spatial features of the system by mapping feature nodes and enhancement nodes in a separated-aggregated way. The dynamic features and the spatial features are concatenated to the output layer for prediction. Only the weights of the output layer of NAR-BLS are computed using ridge regression. Thus, it has the excellent advantage of rapid training speed and updating ability. Experimental results on two typical chaotic systems and four real-world datasets demonstrate the superior performance of NAR-BLS.