Digital twins of nonlinear dynamical systems

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.