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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.23457 |
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| _version_ | 1866909558178316288 |
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| author | Gauthier, Daniel J. Pomerance, Andrew Bollt, Erik |
| author_facet | Gauthier, Daniel J. Pomerance, Andrew Bollt, Erik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23457 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Locality Blended Next Generation Reservoir Computing For Attention Accuracy Gauthier, Daniel J. Pomerance, Andrew Bollt, Erik Chaotic Dynamics 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. |
| title | Locality Blended Next Generation Reservoir Computing For Attention Accuracy |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2503.23457 |