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  <doc>
    <id>7345</id>
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    <publishedDate>2019-06-11</publishedDate>
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    <title language="eng">From interacting agents to density-based modeling with stochastic PDEs</title>
    <abstract language="eng">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.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-73456</identifier>
    <enrichment key="SourceTitle">Comm. Appl. Math. Comp. Sci. 16(1):1-32, 2021</enrichment>
    <enrichment key="zib_relatedIdentifier">https://doi.org/10.2140/camcos.2021.16.1</enrichment>
    <author>Luzie Helfmann</author>
    <submitter>Luzie Helfmann</submitter>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Ana Djurdjevac</author>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-21</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
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    <collection role="persons" number="schuette">Schütte, Christof</collection>
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    <file>https://opus4.kobv.de/opus4-zib/files/7345/main.pdf</file>
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  <doc>
    <id>7339</id>
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    <publishedYear>2021</publishedYear>
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    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>32</pageLast>
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    <title language="eng">From interacting agents to density-based modeling with stochastic PDEs</title>
    <abstract language="eng">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.</abstract>
    <parentTitle language="eng">Communications in Applied Mathematics and Computational Science</parentTitle>
    <identifier type="arxiv">1905.13525</identifier>
    <identifier type="doi">10.2140/camcos.2021.16.1</identifier>
    <enrichment key="AcceptedDate">2020-11-01</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-73456</enrichment>
    <author>Luzie Helfmann</author>
    <submitter>Luzie Helfmann</submitter>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Ana Djurdjevac</author>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="INNOSPREAD">INNOSPREAD</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>10268</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
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    <title language="eng">Mean-field optimal control with stochastic leaders</title>
    <abstract language="eng">We consider interacting agent systems with a large number of stochastic agents (or particles) influenced by a fixed number of external stochastic lead agents. Such examples arise, for example in models of opinion dynamics, where a small number of leaders (influencers) can steer the behaviour of a large population of followers. In this context, we study a partial mean-field limit where the number of followers tends to infinity, while the number of leaders stays constant. The partial mean-field limit dynamics is then given by a McKean-Vlasov stochastic differential equation (SDE) for the followers, coupled to a controlled Itô-SDE governing the dynamics of the lead agents. For a given cost functional that the lead agents seek to minimise, we show that the unique optimal control of the finite agent system convergences to the optimal control of the limiting system. This establishes that the low-dimensional control of the partial (mean-field) system provides an effective approximation for controlling the high-dimensional finite agent system. In addition, we propose a stochastic gradient descent algorithm that can efficiently approximate the mean-field control. Our theoretical results are illustrated on opinion dynamics model with lead agents, where the control objective is to drive the followers to reach consensus in finite time.</abstract>
    <identifier type="arxiv">2512.19201</identifier>
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    <enrichment key="SubmissionStatus">under review</enrichment>
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    <author>Sebastian Zimper</author>
    <submitter>Natasa Conrad</submitter>
    <author>Ana Djurdjevac</author>
    <author>Carsten Hartmann</author>
    <author>Christof Schütte</author>
    <author>Natasa Djurdjevac Conrad</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
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  <doc>
    <id>2655</id>
    <completedYear>2014</completedYear>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>191</pageFirst>
    <pageLast>212</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>1</volume>
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    <title language="eng">Modularity revisited: A novel dynamics-based concept for decomposing complex networks</title>
    <parentTitle language="eng">Journal of Computational Dynamics</parentTitle>
    <identifier type="url">http://publications.mi.fu-berlin.de/1127/</identifier>
    <identifier type="doi">10.3934/jcd.2014.1.191</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">http://publications.mi.fu-berlin.de/1127/1/AMScompstruct.pdf</enrichment>
    <author>Marco Sarich</author>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Sharon Bruckner</author>
    <author>Tim Conrad</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="conrad">Conrad, Tim</collection>
    <collection role="institutes" number="bioinf">Bioinformatics in Medicine</collection>
    <collection role="projects" number="MIP_FORMATION">MIP_FORMATION</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="NonequiMSM">NonequiMSM</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="projects" number="SFB765-C2">SFB765-C2</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="projects" number="DynOOCompNet">DynOOCompNet</collection>
  </doc>
  <doc>
    <id>2663</id>
    <completedYear>2012</completedYear>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>29</pageFirst>
    <pageLast>50</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1-2</issue>
    <volume>6</volume>
    <type>article</type>
    <publisherName>European Society of Computational Methods in Sciences and Engineering</publisherName>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
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    <title language="eng">Random Walks on Complex Modular Networks</title>
    <parentTitle language="eng">Journal of Numerical Analysis, Industrial and Applied Mathematics</parentTitle>
    <identifier type="url">http://publications.imp.fu-berlin.de/1090/</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Stefanie Bruckner</author>
    <author>Tim Conrad</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="conrad">Conrad, Tim</collection>
    <collection role="projects" number="NonequiMSM">NonequiMSM</collection>
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    <id>8101</id>
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    <publishedYear>2021</publishedYear>
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    <language>eng</language>
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    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>16</volume>
    <type>article</type>
    <publisherName>Public Library of Science</publisherName>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-04-22</completedDate>
    <publishedDate>--</publishedDate>
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    <title language="eng">Prediction of Covid-19 spreading and optimal coordination of counter-measures: From microscopic to macroscopic models to Pareto fronts</title>
    <parentTitle language="eng">PLOS One</parentTitle>
    <identifier type="doi">10.1371/journal.pone.0249676</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Hanna Wulkow</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Tim Conrad</author>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Sebastian A. Müller</author>
    <author>Kai Nagel</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="conrad">Conrad, Tim</collection>
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    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
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    <collection role="projects" number="MODUS-COVID">MODUS-COVID</collection>
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  <doc>
    <id>2666</id>
    <completedYear>2012</completedYear>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>61</pageFirst>
    <pageLast>81</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>10</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Estimating the eigenvalue error of Markov State Models</title>
    <parentTitle language="eng">Multiscale Modeling &amp; Simulation</parentTitle>
    <identifier type="url">http://publications.imp.fu-berlin.de/914/</identifier>
    <identifier type="doi">10.1137/100798910</identifier>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Marco Sarich</author>
    <author>Christof Schütte</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
  </doc>
  <doc>
    <id>2689</id>
    <completedYear>2010</completedYear>
    <publishedYear>2010</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On Markov State Models for Metastable Processes</title>
    <parentTitle language="eng">Proceedings of the International Congress of Mathematics, Hyderabad, India, Section Invited Talks. (ICM) 2010</parentTitle>
    <identifier type="url">http://publications.imp.fu-berlin.de/991/</identifier>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Marco Sarich</author>
    <author>Christof Schütte</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
  </doc>
  <doc>
    <id>6949</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
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    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>24</pageNumber>
    <edition>EPJ Data Science</edition>
    <issue>1</issue>
    <volume>7</volume>
    <type>article</type>
    <publisherName>EPJ Data Science</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-07-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach</title>
    <abstract language="eng">Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution.</abstract>
    <parentTitle language="eng">EPJ Data Science</parentTitle>
    <identifier type="doi">10.1140/epjds/s13688-018-0153-9</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2018-07-02</enrichment>
    <enrichment key="SourceTitle">EPJ Data Science</enrichment>
    <author>Natasa Djurdjevac Conrad</author>
    <submitter>Natasa Djurdjevac Conrad</submitter>
    <author>Luzie Helfmann</author>
    <author>Johannes Zonker</author>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="INNOSPREAD">INNOSPREAD</collection>
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  <doc>
    <id>7596</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>37</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>15</volume>
    <type>article</type>
    <publisherName>Public Library of Science</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2020-11-12</completedDate>
    <publishedDate>2020-11-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Furnace and the Goat—A spatio-temporal model of the fuelwood requirement for iron metallurgy on Elba Island, 4th century BCE to 2nd century CE</title>
    <parentTitle language="eng">PLOS ONE</parentTitle>
    <identifier type="doi">10.1371/journal.pone.0241133</identifier>
    <identifier type="url">https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0241133</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SourceTitle">PLOS ONE</enrichment>
    <author>Fabian Becker</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Raphael A. Eser</author>
    <author>Luzie Helfmann</author>
    <author>Brigitta Schütt</author>
    <author>Christof Schütte</author>
    <author>Johannes Zonker</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="projects" number="INNOSPREAD">INNOSPREAD</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusEF5-1">MathPlusEF5-1</collection>
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