Constraints on parameter choices for successful reservoir computing
This work addresses a specific limitation in reservoir computing for time-series prediction, offering incremental insights into parameter selection.
The study investigated the conditions beyond synchronization necessary for successful time-series prediction using echo-state networks, identifying two key parameters and conducting a parameter sweep to find successful prediction regions, which vary based on the amount of phase space information provided during training.
Echo-state networks are simple models of discrete dynamical systems driven by a time series. By selecting network parameters such that the dynamics of the network is contractive, characterized by a negative maximal Lyapunov exponent, the network may synchronize with the driving signal. Exploiting this synchronization, the echo-state network may be trained to autonomously reproduce the input dynamics, enabling time-series prediction. However, while synchronization is a necessary condition for prediction, it is not sufficient. Here, we study what other conditions are necessary for successful time-series prediction. We identify two key parameters for prediction performance, and conduct a parameter sweep to find regions where prediction is successful. These regions differ significantly depending on whether full or partial phase space information about the input is provided to the network during training. We explain how these regions emerge.