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From interacting agents to density-based modeling with stochastic PDEs

  • 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:Article
Parent Title (English):Communications in Applied Mathematics and Computational Science
First Page:1
Last Page:32
Year of first publication:2021
ArXiv Id:http://arxiv.org/abs/1905.13525
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