Reservoir Computing via Multi-Scale Random Fourier Features for Forecasting Fast-Slow Dynamical Systems

• URL: http://arxiv.org/abs/2511.14775v1
• Date: Tue, 04 Nov 2025 08:01:08 GMT
• Title: Reservoir Computing via Multi-Scale Random Fourier Features for Forecasting Fast-Slow Dynamical Systems
• Authors: S. K. Laha,
• Abstract summary: We present a novel reservoir computing framework that combines delay embedding with random Fourier feature (RFF) mappings to capture such dynamics.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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