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From interacting
agents to density-based modeling with stochastic PDEs
Luzie Helfmann, Nataša Djurdjevac Conrad, Ana Djurdjevac, Stefanie Winkelmann and Christof Schütte |
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Vol. 16 (2021), No. 1, 1–32
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Abstract |
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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, model reduction, Dean–Kawasaki model,
SPDEs, finite element method
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Mathematical Subject Classification 2010
Primary: 60H15, 60H35, 91B69, 91B74
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Milestones
Received: 10 May 2019
Revised: 30 October 2020
Accepted: 1 November 2020
Published: 19 January 2021
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Authors |
| Luzie Helfmann | |
| Institut für Mathematik Freie Universität Berlin Berlin Germany |
Zuse-Institut Berlin Berlin Germany |
| Nataša Djurdjevac Conrad | |
| Zuse-Institut Berlin Berlin Germany |
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| Ana Djurdjevac | |
| Institut für Mathematik Freie Universität Berlin Berlin Germany |
Institut für Mathematik Technische Universität Berlin Berlin Germany |
| Stefanie Winkelmann | |
| Zuse-Institut Berlin Berlin Germany |
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| Christof Schütte | |
| Institut für Mathematik Freie Universität Berlin Berlin Germany |
Zuse-Institut Berlin Berlin Germany |
