Repository: Freie Universität Berlin, Math Department

From interacting agents to density-based modeling with stochastic PDEs

Helfmann, L. and Djurdjevac Conrad, N. and Djurdjevac, A. and Winkelmann, S. and Schütte, Ch. (2021) From interacting agents to density-based modeling with stochastic PDEs. Commun. Appl. Math. Comput. Sci., 16 . pp. 1-32. ISSN Online: 2157-5452; Print: 1559-3940

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Official URL: https://msp.org/camcos/2021/16-1/index.xhtml

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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2489
Deposited By: Ulrike Eickers
Deposited On:17 Feb 2021 15:18
Last Modified:17 Feb 2021 15:18

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