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) |
| ISSN: | 1438-0064 |
| Published in: | Comm. Appl. Math. Comp. Sci. 16(1):1-32, 2021 |
| Related Identifier: | https://doi.org/10.2140/camcos.2021.16.1 |
