Dynamics-informed reservoir computing with visibility graphs.

Accurate prediction of complex and nonlinear time series remains a challenging problem across engineering and scientific disciplines. Reservoir computing (RC) offers a computationally efficient alternative to traditional deep learning by training only the readout layer while employing a randomly structured and fixed reservoir network. Despite its advantages, the largely random reservoir graph architecture often results in suboptimal and oversized networks with poorly understood dynamics. Addressing this issue, we propose a novel Dynamics-Informed Reservoir Computing (DyRC) framework that systematically infers the reservoir network structure directly from the input training sequence. This work proposes to employ the visibility graph (VG) technique, which converts time series data into networks by representing measurement points as nodes linked by mutual visibility. The reservoir network is constructed by directly adopting the VG network from a training data sequence, leveraging the parameter-free visibility graph approach to avoid expensive hyperparameter tuning. This process results in a reservoir that is directly informed by the specific dynamics of the prediction task under study. We assess the DyRC-VG method through prediction tasks involving the canonical nonlinear Duffing oscillator, evaluating prediction accuracy and consistency. Compared to an Erdős-Rényi (ER) graph of the same size, spectral radius, and fixed density, we observe higher prediction quality and more consistent performance over repeated implementations in the DyRC-VG. An ER graph with density matched to the DyRC-VG can in some conditions outperform both approaches.