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  <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>9152</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>L022301</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>109</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-02-07</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Learning interpretable collective variables for spreading processes on networks</title>
    <abstract language="eng">Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this Letter, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barabási model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically.</abstract>
    <parentTitle language="eng">Physical Review E</parentTitle>
    <identifier type="arxiv">2307.03491</identifier>
    <identifier type="doi">10.1103/PhysRevE.109.L022301</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2023-12-29</enrichment>
    <author>Marvin Lücke</author>
    <submitter>Marvin Lücke</submitter>
    <author>Stefanie Winkelmann</author>
    <author>Jobst Heitzig</author>
    <author>Nora Molkenthin</author>
    <author>Péter Koltai</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>
    <collection role="projects" number="DFG-CollectiveVariables">DFG-CollectiveVariables</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>
  <doc>
    <id>10257</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>034311</pageNumber>
    <edition/>
    <issue/>
    <volume>113</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2026-03-18</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Accurate mean-field equation for voter model dynamics on scale-free networks</title>
    <abstract language="eng">Understanding the emergent macroscopic behavior of dynamical systems on networks is a crucial but challenging task. One of the simplest and most effective methods to construct a reduced macroscopic model is given by mean-field theory. The resulting approximations perform well on dense and homogeneous networks but poorly on scale-free networks, which, however, are more realistic in many applications. In this paper, we introduce a modified version of the mean-field approximation for voter model dynamics on scale-free networks. The two main deviations from classical theory are that we use degree-weighted shares as coarse variables and that we introduce a correlation factor that can be interpreted as slowing down dynamics induced by interactions. We observe that the correlation factor is only a property of the network and not of the state or of parameters of the process. This approach achieves a significantly smaller approximation error than standard methods without increasing dimensionality.</abstract>
    <parentTitle language="eng">Physical Review E</parentTitle>
    <identifier type="arxiv">2509.13485</identifier>
    <identifier type="doi">10.1103/vkpx-5cvt</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2026-02-24</enrichment>
    <author>Marvin Lücke</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Stefanie Winkelmann</author>
    <author>Peter Koltai</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="DFG-CollectiveVariables">DFG-CollectiveVariables</collection>
  </doc>
</export-example>
