7345
eng
reportzib
0
--
2019-06-11
--
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.
1438-0064
urn:nbn:de:0297-zib-73456
false
true
Luzie Helfmann
Luzie Helfmann
Natasa Djurdjevac Conrad
Ana Djurdjevac
Stefanie Winkelmann
Christof Schütte
ZIB-Report
19-21
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Schütte, Christof
Conrad, Natasa
Winkelmann, Stefanie
Helfmann, Luzie
INNOSPREAD
https://opus4.kobv.de/opus4-zib/files/7345/main.pdf
7339
2019
eng
article
0
--
--
--
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.
under review
urn:nbn:de:0297-zib-73456
yes
Luzie Helfmann
Luzie Helfmann
Natasa Djurdjevac Conrad
Ana Djurdjevac
Stefanie Winkelmann
Christof Schütte
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Schütte, Christof
Conrad, Natasa
Winkelmann, Stefanie
Helfmann, Luzie
INNOSPREAD
7188
2019
2018
2019
eng
68
masterthesis
0
--
--
2019-01-29
Stochastic Modeling of Interacting Agent Systems
urn:nbn:de:0297-zib-71887
Christof Schütte
Luzie Helfmann
Luzie Helfmann
Natasa Djurdjevac Conrad
Numerical Mathematics
Computational Molecular Design
Helfmann, Luzie
INNOSPREAD
Freie Universität Berlin
https://opus4.kobv.de/opus4-zib/files/7188/Masterarbeit_Helfmann.pdf