Deterministic Reservoir Computing for Chaotic Time Series Prediction
This work addresses the need for deterministic alternatives in reservoir computing for time series forecasting, offering a novel approach that could benefit researchers in machine learning and dynamical systems, though it appears incremental as it builds upon prior methods.
The authors tackled the problem of deterministic reservoir computing for chaotic time series prediction by proposing a new method using Logistic and Chebyshev maps with the Lobachevsky function as activation, achieving up to 99.99% improvement for non-chaotic series and 87.13% for chaotic ones compared to existing methods.
Reservoir Computing was shown in recent years to be useful as efficient to learn networks in the field of time series tasks. Their randomized initialization, a computational benefit, results in drawbacks in theoretical analysis of large random graphs, because of which deterministic variations are an still open field of research. Building upon Next-Gen Reservoir Computing and the Temporal Convolution Derived Reservoir Computing, we propose a deterministic alternative to the higher-dimensional mapping therein, TCRC-LM and TCRC-CM, utilizing the parametrized but deterministic Logistic mapping and Chebyshev maps. To further enhance the predictive capabilities in the task of time series forecasting, we propose the novel utilization of the Lobachevsky function as non-linear activation function. As a result, we observe a new, fully deterministic network being able to outperform TCRCs and classical Reservoir Computing in the form of the prominent Echo State Networks by up to $99.99\%$ for the non-chaotic time series and $87.13\%$ for the chaotic ones.