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As microscopic (e.g. atomistic, stochastic, agent-based, particle-based) simulations become increasingly prevalent in the modeling of complex systems, so does the need to systematically coarse-grain the information they provide. Before even starting to formulate relevant coarse-grained equations, we need to determine the right macroscopic observables—the right variables in terms of which emergent behavior will be described. This paper illustrates the use of data mining (and, in particular, diffusion maps, a nonlinear manifold learning technique) in coarse-graining the dynamics of a particle-based model of animal swarming. Our computational data-driven coarse-graining approach extracts two coarse (collective) variables from the detailed particle-based simulations, and helps formulate a low-dimensional stochastic differential equation in terms of these two collective variables; this allows the efficient …