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From interacting agents to density-based modeling with stochastic PDEs

Please always quote using this URN: urn:nbn:de:0297-zib-73456
  • 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.

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Author:Luzie HelfmannORCiD, Natasa Djurdjevac ConradORCiD, Ana Djurdjevac, Stefanie WinkelmannORCiD, Christof Schütte
Document Type:ZIB-Report
Date of first Publication:2019/06/11
Series (Serial Number):ZIB-Report (19-21)
Published in:Comm. Appl. Math. Comp. Sci. 16(1):1-32, 2021
Related Identifier:https://doi.org/10.2140/camcos.2021.16.1
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