Attractor reconstruction in attracting subspaces: Slow-spectrum preshaping for reservoir computing under partial observation

Abstract

Data-driven reproduction of chaotic dynamics under partial observation remains a challenge despite its practical importance. Reservoir computing (RC) and other data-driven approaches often succeed in short-term prediction, yet they are sensitive to hyperparameters and fail to reproduce the long-term statistical properties of the system. We identify one cause of this failure: the reconstructed attractor set is placed in a transversally unstable region of the representation space. We therefore propose a design principle for RC that introduces a few slow modes into its evolution rule in advance, so that a designated attracting low-dimensional subspace retains the history of the input series. We show that this achieves attractor reconstruction in attracting subspaces (ARAS) and, without relying on a posteriori performance-based tuning, enables robust prediction and reproduction of chaos under partial observation.