Digital twins of nonlinear dynamical systems: A perspective
Ying-Cheng Lai
Digital twins have attracted a great deal of recent attention from a wide
range of fields. A basic requirement for digital twins of nonlinear dynamical
systems is the ability to generate the system evolution and predict potentially
catastrophic emergent behaviors so as to providing early warnings. The digital
twin can then be used for system "health" monitoring in real time and for
predictive problem solving. In particular, if the digital twin forecasts a
possible system collapse in the future due to parameter drifting as caused by
environmental changes or perturbations, an optimal control strategy can be
devised and executed as early intervention to prevent the collapse. Two
approaches exist for constructing digital twins of nonlinear dynamical systems:
sparse optimization and machine learning. The basics of these two approaches
are described and their advantages and caveats are discussed.