Coarse-Graining Agent-Based Computations: Equation-Free and Variable-Free Computations

We explore several computational issues involving the coarse-graining of agent based models and illustrate them through an example involving belief propagation initially studied by Omurtag and Sirovich. Depending on the parameter regime chosen, we find that the agent-based model can effectively close as an nonlinear, nonlocal evolution equation (reminiscent of Fokker-Planck equations), or as an effective stochastic differential equation in terms of a single coarse variable (observable). We use data-mining techniques (and, in particular, diffusion maps) to detect good coarse variables for this latter closure: this is the “variable-free” component of the work. We estimate escape times through direct simulations as well as through Kramers' approximations based on the effective equation. We also demonstrate the performance of alternative coarse-grained computational tasks (such as coarse-control of unstable, macroscopically stationary agent distributions). We conclude by exploring the modifications arising when the interaction between the agents does not occur in an “all-to-all” communication manner, but on a communication network with prescribed characteristics (e.g. with prescribed degree distribution).