Deterministic Reservoir Computing for Chaotic Time Series Prediction

TL;DR

This paper introduces a deterministic reservoir computing model using logistic and Chebyshev maps, enhanced with Lobachevsky activation, significantly outperforming traditional stochastic reservoir models in chaotic and non-chaotic time series prediction.

Contribution

It presents a novel deterministic reservoir computing framework with Lobachevsky activation, outperforming existing stochastic models in time series forecasting.

Findings

Achieved up to 99.99% accuracy on non-chaotic series.

Achieved up to 87.13% accuracy on chaotic series.

Demonstrated superiority over classical Echo State Networks.

Abstract

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.