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A probabilistic Markov Chain (MC) surrogate model for a two-dimensionalsystem of interacting particles within a square domain having inherentsymmetries is developed. Particles are assumed to be circular and identical,colliding with each other and with rigid domain walls via perfectly elasticcollisions. Simulation results over many realizations are used to develop andevaluate the surrogate MC model. The stationary quantity of interest (QoI) isthe number of particles within each of nine coarser subdomains, delineated viathree internal geometric symmetries. The surrogate model is used to quantifyQoI mean properties and uncertainty as the particle radius is varied.

A Markov Chain Surrogate Model for a Two-Dimensional Interacting Particle System with Internal Collisions