  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.
