Authors: Helfmann, Luize
Conrad Đurđevac, Nataša
Đurđevac, Ana 
Winkelmann, Stefanie
Schütte, Christof
Title: FROM INTERACTING AGENTS TO DENSITY-BASED MODELING WITH STOCHASTIC PDES
Journal: Communications in Applied Mathematics and Computational Science
Volume: 16
Issue: 1
First page: 1
Last page: 32
Issue Date: 1-Jan-2021
Rank: ~M21a
ISSN: 1559-3940
DOI: 10.2140/CAMCOS.2021.16.1
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.
Keywords: agent-based modeling | Dean-Kawasaki model | finite element method | model reduction | SPDEs
Publisher: Mathematical Science Publishers

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