Collective dynamics and model verification: Connecting kinetic modeling to data

Equation-free and Variable-free computations for agent based/complex system models

Yannis Kevrekidis

Princeton University

I will start by briefly outlining our equation-free approach to the computer-assisted study of agent based / complex system models by effectively solving closed kinetic equations without deriving them in closed form. I will then discuss the "variable-free" part of the program - the use of data mining/manifold learning techniques in order to detect the "right variables" for the collective modeling - the right observables of the microscopic model in terms of which macroscopic evolution rules would be written. The translation between different levels of description (going from particle models to diffusion map models and back) is less trivial than, say, going between PDE discretizations and their PCA/POD compression - I will discuss and illustrate ways of working with/around this difficulty.