Locality Blended Next Generation Reservoir Computing For Attention Accuracy

Abstract: We extend an advanced variation of a machine learning algorithm, next-generation reservoir Computing (NGRC), to forecast the dynamics of the Ikeda map of a chaotic laser. The machine learning model is created by observing time-series data generated by the Ikeda map, and the trained model is used to forecast the behavior without any input from the map. The Ikeda map is a particularly challenging problem to learn because of the complicated map functions. We overcome the challenge by a novel improvement of the NGRC concept by emphasizing simpler polynomial models localized to well-designed regions of phase space and then blending these models between regions, a method that we call locality blended next-generation reservoir computing (LB-NGRC). This approach allows for better performance with relatively smaller data sets, and gives a new level of interpretability. We achieve forecasting horizons exceeding five Lyapunov times, and we demonstrate that the `climate' of the model is learned over long times.