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

• URL: http://arxiv.org/abs/2511.22059v1
• Date: Thu, 27 Nov 2025 03:24:06 GMT
• Title: Prediction performance of random reservoirs with different topology for nonlinear dynamical systems with different number of degrees of freedom
• Authors: Shailendra K. Rathor, Lina Jaurigue, Martin Ziegler, Jörg Schumacher,
• Abstract summary: Reservoir computing (RC) is a powerful framework for predicting nonlinear dynamical systems.<n>This work investigates how the structure of the network influences the performance of RC in four systems of increasing complexity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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