Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers
This work addresses forecasting challenges in chaotic systems like the Lorenz '63 attractor, offering insights for hardware implementations, though it is incremental in refining reservoir computer designs.
The researchers tackled the problem of forecasting chaotic systems by optimizing reservoir computers for global climate learning rather than short-term prediction, finding that low-connectivity reservoirs, including those with zero spectral radius and no recurrence, performed well and challenged existing heuristics.
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.