Slow-spectrum preshaping for reservoir computing: Attractor reconstruction in attracting submanifolds 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 but are sensitive to hyperparameters and frequently fail to reproduce the long-term statistical properties of the system. As recently shown, a major cause of this failure is spurious slow modes induced by training, which render the reconstructed invariant set transversally unstable in the representation space. To address this, a design principle called Attractor Reconstruction in Attracting Submanifolds (ARAS) was proposed, which requires the reconstruction to lie in a low-dimensional, transversally attracting submanifold. Under full observation, ARAS was realized by an input-layer design that limits the number of slow modes perturbed during training and anchors the remaining modes to stay fast, thereby suppressing spurious slow modes. However, under partial observation, this design alone fails because the submanifold designed to be attracting cannot retain the observation history needed to unfold the observed data into a faithful reconstruction. In this study, we propose slow-spectrum preshaping, which introduces a slow spectrum into the reservoir prior to feeding input data. The induced slow modes then retain a memory of past observations within the submanifold, while the input-layer design makes the submanifold transversally attracting, so that ARAS is realized under partial observation. Through numerical experiments on various chaotic systems, we show that our approach enables reliable short-term prediction and long-term reproduction of chaos over a wide range of hyperparameters without a posteriori tuning.
Related
- Reservoir computing generalized: Exploiting complex dynamics via time-invariant transformation
- Nonlinear pluggable optics: Digital signal processing-free Intensity Modulated Direct Detection links using analog photonic Next Generation Reservoir Computing
- Dynamics tuning with reservoir computer control
- Microscopic Theory of Drag in a Bose Condensate Interacting with a Moving Reservoir
- Reservoir as a Dynamical System: A Tutorial Review
BibTeX
@misc{oishi2026slowspectrum,
title = {{Slow-spectrum preshaping for reservoir computing: Attractor reconstruction in attracting submanifolds under partial observation}},
author = {Satoshi Oishi and Hiroshi Yamashita and Hideyuki Suzuki and Sho Shirasaka},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.24303},
eprint = {2606.24303},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.24303},
}
RIS
TY - UNPB
TI - Slow-spectrum preshaping for reservoir computing: Attractor reconstruction in attracting submanifolds under partial observation
AU - Satoshi Oishi
AU - Hiroshi Yamashita
AU - Hideyuki Suzuki
AU - Sho Shirasaka
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2606.24303
UR - https://arxiv.org/abs/2606.24303
AB - 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 but are sensitive to hyperparameters and frequently fail to reproduce the long-term statistical properties of the system. As recently shown, a major cause of this failure is spurious slow modes induced by training, which render the reconstructed invariant set transversally unstable in the representation space. To address this, a design principle called Attractor Reconstruction in Attracting Submanifolds (ARAS) was proposed, which requires the reconstruction to lie in a low-dimensional, transversally attracting submanifold. Under full observation, ARAS was realized by an input-layer design that limits the number of slow modes perturbed during training and anchors the remaining modes to stay fast, thereby suppressing spurious slow modes. However, under partial observation, this design alone fails because the submanifold designed to be attracting cannot retain the observation history needed to unfold the observed data into a faithful reconstruction. In this study, we propose slow-spectrum preshaping, which introduces a slow spectrum into the reservoir prior to feeding input data. The induced slow modes then retain a memory of past observations within the submanifold, while the input-layer design makes the submanifold transversally attracting, so that ARAS is realized under partial observation. Through numerical experiments on various chaotic systems, we show that our approach enables reliable short-term prediction and long-term reproduction of chaos over a wide range of hyperparameters without a posteriori tuning.
ER -