  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.
