  Reservoir computing is a machine learning approach that can generate a
surrogate model of a dynamical system. It can learn the underlying dynamical
system using fewer trainable parameters and hence smaller training data sets
than competing approaches. Recently, a simpler formulation, known as
next-generation reservoir computing, removes many algorithm metaparameters and
identifies a well-performing traditional reservoir computer, thus simplifying
training even further. Here, we study a particularly challenging problem of
learning a dynamical system that has both disparate time scales and multiple
co-existing dynamical states (attractors). We compare the next-generation and
traditional reservoir computer using metrics quantifying the geometry of the
ground-truth and forecasted attractors. For the studied four-dimensional
system, the next-generation reservoir computing approach uses $\sim 1.7 \times$
less training data, requires $10^3 \times$ shorter `warm up' time, has fewer
metaparameters, and has an $\sim 100\times$ higher accuracy in predicting the
co-existing attractor characteristics in comparison to a traditional reservoir
computer. Furthermore, we demonstrate that it predicts the basin of attraction
with high accuracy. This work lends further support to the superior learning
ability of this new machine learning algorithm for dynamical systems.
