Many dynamical processes over graphs are either exact or well-approximated by linear dynamical systems, such as random walks, heat diffusion processes, or more generally graph filtering processes, with applications in modeling traffic flow, temperature variation, and brain activities over graph networks. We will consider the inverse problem of recovering the dynamical system from (random) space-time data.

In this talk, I will present some progress on the algorithmic aspects for recovering the initial state and even the evolution operators in linear dynamical systems, levering ideas from compressed sensing, super-resolution, and matrix completion. Joint work with Jiahui Cheng, Longxiu Huang, Christian Kummererlel, Mauro Maggioni, and Deanna Needell.