Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen
OPUS4-7345 misc Helfmann, Luzie; Djurdjevac Conrad, Natasa; Djurdjevac, Ana; Winkelmann, Stefanie; Schütte, Christof 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. urn:nbn:de:0297-zib-73456 Numerical Mathematics
OPUS4-7339 Wissenschaftlicher Artikel Helfmann, Luzie; Djurdjevac Conrad, Natasa; Djurdjevac, Ana; Winkelmann, Stefanie; Schütte, Christof 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. Numerical Mathematics
OPUS4-7188 Masterarbeit / Diplomarbeit Helfmann, Luzie Stochastic Modeling of Interacting Agent Systems 2019 68 urn:nbn:de:0297-zib-71887 Numerical Mathematics