Prediction performance of random reservoirs with different topology for nonlinear dynamical systems with different...

Reservoir computing (RC) is a powerful framework for predicting the temporal evolution of variables of 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 reservoir network influences the performance of RC on time series prediction tasks derived from four dynamical systems of increasing complexity: the Mackey-Glass system with delayed-feedback, two nonlinear models of two-dimensional thermal convection flows, 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 improve prediction accuracy for the convection-based systems 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.