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 spatio-temporal 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. 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.
Cite
@article{arxiv.1905.13525,
title = {From interacting agents to density-based modeling with stochastic PDEs},
author = {Luzie Helfmann and Natasa Djurdjevac Conrad and Ana Djurdjevac and Stefanie Winkelmann and Christof Schütte},
journal= {arXiv preprint arXiv:1905.13525},
year = {2021}
}