From interacting agents to density-based modeling with stochastic PDEs

Abstract

Many real-world processes can naturally be modeled as systems of interacting\nagents. However, the long-term simulation of such agent-based models is often\nintractable when the system becomes too large. In this paper, starting from a\nstochastic spatio-temporal agent-based model (ABM), we present a reduced model\nin terms of stochastic PDEs that describes the evolution of agent number\ndensities for large populations. We discuss the algorithmic details of both\napproaches; regarding the SPDE model, we apply Finite Element discretization in\nspace which not only ensures efficient simulation but also serves as a\nregularization of the SPDE. Illustrative examples for the spreading of an\ninnovation among agents are given and used for comparing ABM and SPDE models.\n