  We articulate the design imperatives for machine-learning based digital twins
for nonlinear dynamical systems subject to external driving, which can be used
to monitor the ``health'' of the target system and anticipate its future
collapse. We demonstrate that, with single or parallel reservoir computing
configurations, the digital twins are capable of challenging forecasting and
monitoring tasks. Employing prototypical systems from climate, optics and
ecology, we show that the digital twins can extrapolate the dynamics of the
target system to certain parameter regimes never experienced before, make
continual forecasting/monitoring with sparse real-time updates under
non-stationary external driving, infer hidden variables and accurately predict
their dynamical evolution, adapt to different forms of external driving, and
extrapolate the global bifurcation behaviors to systems of some different
sizes. These features make our digital twins appealing in significant
applications such as monitoring the health of critical systems and forecasting
their potential collapse induced by environmental changes.
