  Model-free and data-driven prediction of tipping point transitions in
nonlinear dynamical systems is a challenging and outstanding task in complex
systems science. We propose a novel, fully data-driven machine learning
algorithm based on next-generation reservoir computing to extrapolate the
bifurcation behavior of nonlinear dynamical systems using stationary training
data samples. We show that this method can extrapolate tipping point
transitions. Furthermore, it is demonstrated that the trained next-generation
reservoir computing architecture can be used to predict non-stationary dynamics
with time-varying bifurcation parameters. In doing so, post-tipping point
dynamics of unseen parameter regions can be simulated.
