2025/03/30 by Daniel J. Gauthier, Gauthier, Daniel J., Andrew Pomerance +4 · 1 voice · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Ferroelectric and Negative Capacitance Devices #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #nlin.CD
paper · pdf · doi:10.48550/arxiv.2503.23457
openalex publication_date 2025/03/30 · arxiv published 2025/03/30 · arxiv updated 2025/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.