Prediction performance of random reservoirs with different topology for nonlinear dynamical systems with different number of degrees of freedom

TL;DR

This study explores how the topology of reservoir networks influences their ability to predict complex nonlinear dynamical systems, revealing that symmetry enhances performance in low-dimensional systems but not in high-dimensional chaos.

Contribution

It systematically investigates the impact of reservoir topology, especially symmetry, on prediction accuracy across diverse dynamical systems, providing design insights for reservoir computing.

Findings

Symmetric reservoirs improve prediction in low-dimensional systems.

High-dimensional chaotic systems show little sensitivity to reservoir symmetry.

Structural properties of reservoirs significantly affect their learning capabilities.

Abstract

Reservoir computing (RC) is a powerful framework for predicting nonlinear dynamical systems, yet the role of reservoir topology$-$particularly symmetry in connectivity and weights$-$remains not adequately understood. This work investigates how the structure of the network influences the performance of RC in four systems of increasing complexity: the Mackey-Glass system with delayed-feedback, two low-dimensional thermal convection models, and a three-dimensional shear flow model exhibiting transition to turbulence. Using five reservoir topologies in which connectivity patterns and edge weights are controlled independently, we evaluate both direct- and cross-prediction tasks. The results show that symmetric reservoir networks substantially improve prediction accuracy for the convection-based systems, especially when the input dimension is smaller than the number of degrees of freedom. In contrast, the shear-flow model displays almost no sensitivity to topological symmetry due to its strongly chaotic high-dimensional dynamics. These findings reveal how structural properties of reservoir networks affect their ability to learn complex dynamics and provide guidance for designing more effective RC architectures.