Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers

TL;DR

This paper investigates reservoir computers for chaotic system forecasting, revealing that very low connectivity reservoirs, including non-recurrent designs, can perform well and challenge existing heuristics.

Contribution

It introduces a new performance measure emphasizing climate learning, and demonstrates that simple, low-connectivity reservoirs can outperform traditional designs.

Findings

Optimized reservoirs often have very low connectivity.

Simple reservoirs with zero spectral radius perform well.

Counterexamples to common reservoir heuristics are provided.

Abstract

We explore the hyperparameter space of reservoir computers used for forecasting of the chaotic Lorenz '63 attractor with Bayesian optimization. We use a new measure of reservoir performance, designed to emphasize learning the global climate of the forecasted system rather than short-term prediction. We find that optimizing over this measure more quickly excludes reservoirs that fail to reproduce the climate. The results of optimization are surprising: the optimized parameters often specify a reservoir network with very low connectivity. Inspired by this observation, we explore reservoir designs with even simpler structure, and find well-performing reservoirs that have zero spectral radius and no recurrence. These simple reservoirs provide counterexamples to widely used heuristics in the field, and may be useful for hardware implementations of reservoir computers.