Modeling and inference of collective behavior in complex system
“Collective behavior” is a term that evokes many of most enigmatic and fascinating phenomena in the world: animal flocking, information spreading and social dynamics, coherent structures in fluid flows, traffic jams, cascading failures in electric power or other infrastructure systems; and so on. There is a rich tradition of building models that help us characterize, predict, or otherwise understand such systems. My goal is to build mathematical tools to take data from complex systems and deliver a mathematical description of the collective behavior it undergoes. To do this I use toy models, specifically coupled oscillators (the Kuramoto model). I will give two examples of such work and discuss ongoing work to incorporate a further level of model complexity, namely memory.