Optimizing the Network Topology of a Linear Reservoir Computer

arXiv:2509.23391v3 Announce Type: replace-cross Abstract: Machine learning has become a fundamental approach for modeling, prediction, and control, enabling systems to learn from data and perform complex tasks. Reservoir computing is a machine learning tool that leverages high-dimensional dynamical systems to efficiently process temporal data for prediction and observation tasks. Traditionally, the connectivity of the network that underlies a reservoir computer (RC) is generated randomly, lacking a principled design. Here, we focus on optimizing the connectivity of a linear RC to improve its performance and interpretability, which we achieve by decoupling the RC dynamics into a number of independent modes. We then proceed to optimize each one of these modes to perform a given task, which corresponds to selecting an optimal RC connectivity in terms of a given set of eigenvalues of the RC adjacency matrix. Simulations on networks of varying sizes show that the optimized RC significantly outperforms randomly constructed reservoirs in both training and testing phases and often surpasses nonlinear reservoirs of comparable size. This approach provides both practical performance advantages and theoretical guidelines for designing efficient, task-specific, and analytically transparent RC architectures.