Stabilizing chaotic dynamical system reproduction in reservoir computing

TL;DR

This paper identifies the cause of instability in reservoir computing for chaotic systems and introduces a simple design principle that significantly enhances robustness and accuracy in reproducing complex dynamics.

Contribution

It proposes a deterministic input layer design to suppress spurious modes, improving stability and enabling accurate Lyapunov spectrum estimation in reservoir computing.

Findings

Dramatic improvement in robustness to initialization and noise.

Doubling the prediction horizon in chaotic system modeling.

100% success rate in Lyapunov spectrum estimation across multiple seeds.

Abstract

Reservoir Computing (RC), a type of recurrent random neural network, is a powerful framework for modeling complex and chaotic dynamics. However, its autonomous (closed-loop) operation is often plagued by inherent instability. Moreover, performance is highly sensitive to the reservoir's random initialization, leading to vulnerability to noise and/or behaviour that bears no resemblance whatsoever to the target dynamical system. Here we identify a primary cause of this unreliability: the emergence of excessive, spurious unstable or neutral modes in the closed-loop dynamics. We introduce a simple deterministic input layer design principle that directly addresses this vulnerability by structurally suppressing the emergence of these spurious modes a priori (before training). Our approach dramatically improves robustness to both initialization sensitivity and internal noise, doubling the prediction horizon. Furthermore, we demonstrate on chaotic dynamical systems that this design enables robust estimation of the full Lyapunov spectrum (100\% success rate across 50 seeds), signifying that the autonomous RC faithfully emulates the essential properties of the target dynamical system. This work provides a systematic explanation for a common RC failure mode and offers a concrete design guideline, advancing RCs from heuristic trial-and-error tuning toward a reliable tool for modeling complex systems.