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

2025-11-26

AI Summary

This study investigates how reservoir topology—particularly connection and weight symmetry—affects reservoir computing (RC) performance in predicting nonlinear dynamical systems. We systematically construct five controllable topologies and evaluate them on four increasingly complex systems: the Mackey–Glass equation, two low-dimensional thermal convection models, and a three-dimensional shear-flow turbulence transition model, under both direct and cross-prediction tasks. Results show that symmetric topologies significantly improve prediction accuracy for low-dimensional convection systems, revealing an intrinsic link between structural symmetry and learning capability. In contrast, topological effects diminish for the high-dimensional turbulent system, confirming that reservoir architecture must match the target system’s degrees of freedom. Our findings provide interpretable, dynamics-aware guidelines for optimizing RC reservoir design—advancing the principled construction of task-specific RC architectures grounded in dynamical systems theory.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Cognitive Modeling & Cognitive Systems: (Computational) Cognitive Architectures
• Intelligent Robots: Multi-Robot Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Investigates how reservoir topology affects prediction accuracy in nonlinear dynamical systems.
• Evaluates symmetric networks' impact on convection models versus high-dimensional chaotic flows.
• Provides design guidance for reservoir computing architectures based on structural properties.

Innovation

• Reservoir computing uses controlled connectivity and weight topologies
• Symmetric reservoir networks enhance prediction for convection systems
• Topological symmetry less effective for high-dimensional chaotic dynamics