Mohammadamin Moradi

Data-driven model discovery of complex dynamical systems can be done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of elementary mathematical functions. Examples where sparse optimization fails abound, including the classic Ikeda or optical-cavity map in nonlinear dynamics, as well as a wide variety of ecosystems.

The ever-increasing complexity of modern power grids makes them vulnerable to cyber and/or physical attacks. To protect them, accurate attack detection is essential. A challenging scenario is that a localized attack has occurred on a specific transmission line but only a small number of transmission lines elsewhere can be monitored.

Anticipating a tipping point, a transition from one stable steady state to another, is a problem of broad relevance due to the ubiquity of the phenomenon in diverse fields. The steady-state nature of the dynamics about a tipping point makes its prediction significantly more challenging than predicting other types of critical transitions from oscillatory or chaotic dynamics.