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.

对于非线性动力系统的数字孪生，其基本要求是能够生成系统的演化并预测潜在的灾难性紧急行为，以提供早期警示。数字孪生可以实时用于系统的 “健康” 监测和预测问题的解决。构建非线性动力系统的数字孪生有两种方法：稀疏优化和机器学习。本文描述了这两种方法的基本概念并讨论了它们的优势和注意事项。