Topology Optimization of a Linear Reservoir Computer for Estimation Tasks

• Collaborators: Nicholas Mecholsky, Francesco Sorrentino,
• May 2024 - September 2025

• Project Codes

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. In this research, we focused on optimizing the connectivity of a linear RC to improve its performance and interpretability.

We improved the performance and interpretability of a linear RC by optimizing its topology, which we achieved 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 showed 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. We also showed that our method can be extended to nonlinear RC, but with a new formulation.