Closing the gap between necessary and sufficient conditions for well-predicting reservoirs

Characterize the properties of reservoir computing systems that are both necessary and sufficient to guarantee accurate predictive performance, thereby resolving the gap between known necessary conditions (such as Echo State Property and Generalized Synchronization) and sufficient conditions for well-predicting autonomous reservoirs.

Background

The paper discusses that ESP and GS are necessary but not sufficient for successful reservoir prediction, and that universal approximation properties in continuous time are limited and often rely on connections to Neural ODEs.

Despite empirical success, a rigorous characterization of the exact conditions that guarantee reliable prediction remains incomplete, motivating the need to bridge the gap between necessary and sufficient conditions.