Evolutionary Optimization Reveals Structural Constraints on Reservoir Architecture for Spatiotemporal Chaos

2026-06-21

AI Summary

This study investigates how evolutionary selection shapes the recurrent network architecture and intrinsic constraints of reservoir computing for spatiotemporal chaotic prediction tasks. For the first time, an evolutionary algorithm is introduced to optimize reservoir design by tuning five key hyperparameters, yielding high-performing architectures evaluated on the Kuramoto–Sivashinsky equation. Integrating spectral analysis, stochastic block modeling, and Pareto front analysis, the work reveals that improved predictive performance correlates with interpretable structural patterns: optimization of low-eigenvalue modes, stabilization of modularity, and pruning of connection costs. The evolved reservoirs significantly reduce prediction error, extend the effective forecasting horizon, and achieve a joint optimization of accuracy and efficiency within the trade-off between wiring cost and modularity.

Abstract

Biological systems maintain function in fluctuating environments by transforming past stimulation into internal dynamical states that support future-oriented responses. Reservoir computing provides a computational analogue, but standard formulations often treat the recurrent substrate as a fixed random network and train only the readout. Here we ask how the substrate itself changes when reservoir architecture is placed under evolutionary selection for prediction. Using the Kuramoto--Sivashinsky equation as a testbed for spatiotemporal chaos, we evolved reservoirs over five construction hyperparameters: size, connectivity degree, spectral radius, input scaling, and readout regularization. Evolution reduced prediction error at the population level, extended the low-error forecast horizon, and organized the design space along a diminishing-return size--efficiency frontier. Structural analyses showed that evolved reservoirs remained within a conserved stochastic-block-model-like spectral envelope while refining low-eigenvalue modes, locking modularity to an intermediate band, and pruning connection cost within that band. Pareto analysis showed that elite reservoirs occupied a horizontal floor in the cost--modularity plane, indicating that accuracy and efficiency were achieved jointly rather than through a simple trade-off. These findings show that evolutionary optimization does not merely improve prediction, but exposes interpretable structural constraints on the recurrent substrate: it stabilizes a task-suitable dynamical class and refines the architectural degrees of freedom most relevant for prediction. Evolutionary reservoir computing therefore provides a bio-inspired framework for studying how predictive demands shape adaptive dynamical networks.

Problem

• reservoir computing
• evolutionary optimization
• spatiotemporal chaos
• structural constraints
• recurrent networks

Innovation

• evolutionary reservoir computing
• spatiotemporal chaos
• structural constraints
• Pareto optimization
• spectral envelope