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.
| 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 |
| Volume: | 16 |
| Issue: | 1 |
| First Page: | 1 |
| Last Page: | 32 |
| Year of first publication: | 2021 |
| ArXiv Id: | http://arxiv.org/abs/1905.13525 |
| Preprint: | urn:nbn:de:0297-zib-73456 |
| DOI: | https://doi.org/10.2140/camcos.2021.16.1 |
