Coarse-Graining of an Agent-Based Swarming Model Using the Wavelet Earth Mover's Distance

Abstract

This thesis studies an agent-based swarming model that exhibits an interesting breakup phenomenon in a parameter regime at the boundary between two qualitative states. We discuss the Earth Mover’s Distance and the Wavelet Earth Mover’s Distance and provide proofs of two fundamental theorems regarding these topics, and we also discuss diffusion maps and Equation-Free modeling. We then use the above techniques to uncover a natural coarse reaction coordinate for the system and to develop a stochastic model of this coarse variable. This model allows us to understand the breakup phenomenon at the macroscopic level of the entire population