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

TL;DR

This paper develops a Markov Chain surrogate model to efficiently simulate and analyze the behavior of a two-dimensional interacting particle system with internal symmetries, focusing on particle counts within subdomains.

Contribution

It introduces a novel Markov Chain surrogate for a complex particle system with internal symmetries, enabling efficient uncertainty quantification of key quantities.

Findings

The surrogate accurately predicts particle counts within subdomains.

The model quantifies uncertainty as particle radius varies.

Simulation results validate the surrogate's effectiveness.

Abstract

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