Explore the inverse problem of determining system equations and structures from time series data in this 48-minute lecture by Ying Cheng Lai from PCS Institute for Basic Science. Delve into the history and recent progress of sparse optimization techniques used to discover equations of complex dynamical systems. Learn about applications in predicting critical transitions, inferring network topologies, and identifying partial differential equations for spatiotemporal systems. Examine the effectiveness of sparse optimization in various scenarios and its relationship with delay-coordinate embedding and machine learning-based prediction frameworks. Gain insights into nonlinear dynamics, complex networks, and data-driven approaches for understanding and predicting complex system behavior.