<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>9659</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Discovering collective variable dynamics of agent-based models</title>
    <abstract language="eng">Analytical approximations of the macroscopic behavior of agent-based models (e.g.&#13;
via mean-field theory) often introduce a significant error, especially in the transient phase. For an example model called continuous-time noisy voter model, we use two data-driven approaches to learn the evolution of collective variables instead. The first approach utilizes the SINDy method to approximate the macroscopic dynamics without prior knowledge, but has proven itself to be not particularly robust. The second approach employs an informed learning strategy which includes knowledge about the agent-based model. Both approaches exhibit a considerably smaller error than the conventional analytical approximation.</abstract>
    <parentTitle language="eng">25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022</parentTitle>
    <identifier type="doi">https://doi.org/10.15495/EPub_UBT_00006809</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Marvin Lücke</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Peter Koltai</author>
    <author>Stefanie Winkelmann</author>
    <author>Nora Molkethin</author>
    <author>Jobst Heitzig</author>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="luecke">Lücke, Marvin</collection>
    <collection role="projects" number="MathPlusEF4-8">MathPlusEF4-8</collection>
  </doc>
  <doc>
    <id>8790</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>166</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2023-09-20</completedDate>
    <publishedDate>2023-09-30</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Large population limits of Markov processes on random networks</title>
    <abstract language="eng">We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a mean-field ordinary differential equation are proved. We discuss the convergence to this mean-field limit for a continuous-time noisy version of the so-called "voter model" on Erdős-Rényi random graphs, on the stochastic block model, as well as on random regular graphs. Moreover, a heterogeneous population of agents is studied. For each of these types of interaction networks, we specify the convergence conditions in dependency on the corresponding model parameters.</abstract>
    <parentTitle language="eng">Stochastic Processes and their Applications</parentTitle>
    <identifier type="doi">10.1016/j.spa.2023.09.007</identifier>
    <identifier type="arxiv">2210.02934</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2023-09-13</enrichment>
    <author>Marvin Lücke</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Jobst Heitzig</author>
    <author>Péter Koltai</author>
    <author>Nora Molkethin</author>
    <author>Stefanie Winkelmann</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="luecke">Lücke, Marvin</collection>
    <collection role="projects" number="MathPlusEF4-8">MathPlusEF4-8</collection>
  </doc>
</export-example>
