Catch-22s of reservoir computing

TL;DR

Reservoir Computing can effectively predict basins of attraction in nonlinear systems, but struggles with certain systems unless key system details are known, highlighting challenges in data-driven dynamical modeling.

Contribution

The paper reveals limitations of standard RC in basin prediction and demonstrates NGRC's ability to accurately reconstruct basins with minimal data, emphasizing the importance of system-specific nonlinearities.

Findings

Standard RC depends heavily on warm-up time for accurate basin prediction.

NGRC can reconstruct high-dimensional basins with sparse data.

Small uncertainties in system nonlinearities can drastically reduce prediction accuracy.

Abstract

Reservoir Computing (RC) is a simple and efficient model-free framework for forecasting the behavior of nonlinear dynamical systems from data. Here, we show that there exist commonly-studied systems for which leading RC frameworks struggle to learn the dynamics unless key information about the underlying system is already known. We focus on the important problem of basin prediction -- determining which attractor a system will converge to from its initial conditions. First, we show that the predictions of standard RC models (echo state networks) depend critically on warm-up time, requiring a warm-up trajectory containing almost the entire transient in order to identify the correct attractor. Accordingly, we turn to Next-Generation Reservoir Computing (NGRC), an attractive variant of RC that requires negligible warm-up time. By incorporating the exact nonlinearities in the original equations, we show that NGRC can accurately reconstruct intricate and high-dimensional basins of attraction, even with sparse training data (e.g., a single transient trajectory). Yet, a tiny uncertainty in the exact nonlinearity can render prediction accuracy no better than chance. Our results highlight the challenges faced by data-driven methods in learning the dynamics of multistable systems and suggest potential avenues to make these approaches more robust.