FROM INTERACTING AGENTS TO DENSITY-BASED MODELING WITH STOCHASTIC PDES

Abstract

Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatiotemporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations while retaining the inherent model stochasticity. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply finite element discretization in space, which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models.