Locality blended next-generation reservoir computing for attention accuracy

We extend an advanced variation of a machine learning algorithm, next-generation reservoir computing (NGRC), to forecast synthetic data generated by the Ikeda map, which is a model of a nonlinear optical cavity with an injected laser beam. The machine learning model is created by observing time-series data generated by the Ikeda map during a training phase, and the trained model is used to forecast the behavior in a closed-loop mode where it is no longer supplied with data 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. This approach allows for better performance with relatively smaller data sets in comparison to deep learning methods and gives a new level of interpretability. We achieve forecasting horizons exceeding five Lyapunov times, and we demonstrate that the model reproduces the invariant measure of the attractor beyond the short-term forecasting horizon.