Clustered Ensemble Averaging: A Technique for Visualizing Qualitative Features of Stochastic Simulations

Abstract

Stochastic simulations of fluid flow deal with the evolution of uncertainties in initial and boundary conditions, parameters, and physical models. These uncertainties may lead to qualitatively different behaviors of the flow, raising the question of how to visualize random flow variables in a meaningful way. Our approach is to cluster the simulation data by qualitative phenomenon and then to compute average flow quantities within each cluster, a technique we call "clustered ensemble averaging." This tactic extends the basic visualization strategy of extracting features from within a computational domain defined within time and space. The abstract features we seek are defined across the space of all possible simulations: each feature (cluster) is the subspace of simulations that share a basic behavior. We illustrate this technique on data from molecular dynamics simulations of laser-assisted particle removal, where the explosive evaporation of a laser-heated fluid acts on minute particle contaminants on a substrate, sometimes removing them and sometimes failing to do so. We ran the simulation a hundred times, comprising a hundred samples of the simulation space, and clustered each according to the behavior it exhibits. The images that result from clustered ensemble averaging reveal characteristics common to each cluster that are hidden when the average is calculated over all outcomes.