K–R Controlled Reservoir Computing for Enhanced Nonlinear Temporal Modeling and Long-Horizon Memory Dynamics

This study presents a K–R controlled reservoir computing framework for nonlinear temporal modeling, designed to enhance memory capacity, stability, and predictive performance without increasing reservoir size or training complexity. The proposed approach restructures internal reservoir dynamics through controlled nonlinear excitation, delay-embedded state representation, and stabilized readout learning, enabling compact reservoirs to capture long-horizon dependencies and nonlinear interactions effectively. The framework is evaluated on benchmark temporal prediction tasks, including the NARMA-30 system and the Mackey–Glass chaotic time series (τ = 30). Experimental results demonstrate substantial improvements over a baseline Echo State Network, achieving significantly lower prediction error, increased memory capacity, and improved robustness under noisy inputs and parameter variations. These findings indicate that performance gains arise from reshaping reservoir state geometry and enhancing temporal embedding rather than increasing architectural scale. The proposed method maintains computational efficiency while improving representation quality and stability, making it suitable for modeling complex dynamical systems where long-range temporal dependencies and nonlinear feedback are present. By emphasizing state-space restructuring instead of network scaling, the K–R framework offers a compact and efficient alternative to deeper reservoir architectures for temporal learning tasks. This work contributes to the advancement of reservoir computing by providing a unified strategy for improving nonlinear representation, temporal memory, and prediction reliability, with potential applications in dynamical system modeling, signal prediction, and data-driven learning environments.