Reservoir Computing via Multi-Scale Random Fourier Features for Forecasting Fast-Slow Dynamical Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908663129571328 |
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| author | Laha, S. K. |
| author_facet | Laha, S. K. |
| contents | Forecasting nonlinear time series with multi-scale temporal structures remains a central challenge in complex systems modeling. We present a novel reservoir computing framework that combines delay embedding with random Fourier feature (RFF) mappings to capture such dynamics. Two formulations are investigated: a single-scale RFF reservoir, which employs a fixed kernel bandwidth, and a multi-scale RFF reservoir, which integrates multiple bandwidths to represent both fast and slow temporal dependencies. The framework is applied to a diverse set of canonical systems: neuronal models such as the Rulkov map, Izhikevich model, Hindmarsh-Rose model, and Morris-Lecar model, which exhibit spiking, bursting, and chaotic behaviors arising from fast-slow interactions; and ecological models including the predator-prey dynamics and Ricker map with seasonal forcing, which display multi-scale oscillations and intermittency. Across all cases, the multi-scale RFF reservoir consistently outperforms its single-scale counterpart, achieving lower normalized root mean square error (NRMSE) and more robust long-horizon predictions. These results highlight the effectiveness of explicitly incorporating multi-scale feature mappings into reservoir computing architectures for modeling complex dynamical systems with intrinsic fast-slow interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reservoir Computing via Multi-Scale Random Fourier Features for Forecasting Fast-Slow Dynamical Systems Laha, S. K. Neural and Evolutionary Computing Machine Learning Forecasting nonlinear time series with multi-scale temporal structures remains a central challenge in complex systems modeling. We present a novel reservoir computing framework that combines delay embedding with random Fourier feature (RFF) mappings to capture such dynamics. Two formulations are investigated: a single-scale RFF reservoir, which employs a fixed kernel bandwidth, and a multi-scale RFF reservoir, which integrates multiple bandwidths to represent both fast and slow temporal dependencies. The framework is applied to a diverse set of canonical systems: neuronal models such as the Rulkov map, Izhikevich model, Hindmarsh-Rose model, and Morris-Lecar model, which exhibit spiking, bursting, and chaotic behaviors arising from fast-slow interactions; and ecological models including the predator-prey dynamics and Ricker map with seasonal forcing, which display multi-scale oscillations and intermittency. Across all cases, the multi-scale RFF reservoir consistently outperforms its single-scale counterpart, achieving lower normalized root mean square error (NRMSE) and more robust long-horizon predictions. These results highlight the effectiveness of explicitly incorporating multi-scale feature mappings into reservoir computing architectures for modeling complex dynamical systems with intrinsic fast-slow interactions. |
| title | Reservoir Computing via Multi-Scale Random Fourier Features for Forecasting Fast-Slow Dynamical Systems |
| topic | Neural and Evolutionary Computing Machine Learning |
| url | https://arxiv.org/abs/2511.14775 |