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  <doc>
    <id>7223</id>
    <completedYear/>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>012101</pageFirst>
    <pageLast>012101</pageLast>
    <pageNumber>11</pageNumber>
    <edition/>
    <issue/>
    <volume>29</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">From metastable to coherent sets - Time-discretization schemes</title>
    <abstract language="eng">In this article, we show that these well-established spectral algorithms (like PCCA+, Perron Cluster Cluster Analysis) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.</abstract>
    <parentTitle language="eng">Chaos: An Interdisciplinary Journal of Nonlinear Science</parentTitle>
    <identifier type="doi">10.1063/1.5058128</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2019-01-28</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-66074</enrichment>
    <author>Konstantin Fackeldey</author>
    <submitter>Marcus Weber</submitter>
    <author>Peter Koltai</author>
    <author>Peter Nevir</author>
    <author>Henning Rust</author>
    <author>Axel Schild</author>
    <author>Marcus Weber</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
  </doc>
  <doc>
    <id>6607</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2017-12-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">From Metastable to Coherent Sets - time-discretization schemes</title>
    <abstract language="eng">Given a time-dependent stochastic process with trajectories x(t) in a space $\Omega$, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space $M\subset\Omega$, coherent sets $M(t)\subset\Omega$ are defined in space and time. Hence, if we extend the space by the time-variable t, coherent sets are metastable sets in  $\Omega\times[0,\infty]$. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-timediscretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-66074</identifier>
    <author>Konstantin Fackeldey</author>
    <submitter>Paulina Bressel</submitter>
    <author>Péter Koltai</author>
    <author>Peter Névir</author>
    <author>Henning Rust</author>
    <author>Axel Schild</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-74</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6607/ZIB-Report_17-74.pdf</file>
  </doc>
  <doc>
    <id>8537</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Definition, detection and tracking of persistent structures in atmospheric flows</title>
    <abstract language="eng">Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing attention in recent years. Similar objectives also arise in diverse fields such as turbulence and combustion research, image analysis, and medical diagnostics under the headlines of "feature tracking", "coherent structure detection" or "image registration" - to name just a few. A host of different approaches to addressing the underlying, often very similar, tasks have been developed and successfully used. Here, several typical examples of such approaches are summarized, further developed and applied to meteorological data sets. Common abstract operational steps form the basis for a unifying framework for the specification of "persistent structures" involving the definition of the physical state of a system, the features of interest, and means of measuring their persistence.</abstract>
    <parentTitle language="eng">arXiv</parentTitle>
    <identifier type="arxiv">2111.13645</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">true</enrichment>
    <author>Johannes von Lindheim</author>
    <submitter>Natalia Mikula</submitter>
    <author>Abhishek Harikrishnan</author>
    <author>Tom Dörffel</author>
    <author>Rupert Klein</author>
    <author>Peter Koltai</author>
    <author>Natalia Mikula</author>
    <author>Annette Müller</author>
    <author>Peter Névir</author>
    <author>George Pacey</author>
    <author>Robert Polzin</author>
    <author>Nikki Vercauteren</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="ernst">Ernst, Natalia</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="projects" number="SFB1114-C06">SFB1114-C06</collection>
  </doc>
  <doc>
    <id>7014</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1455</pageFirst>
    <pageLast>1485</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>16</volume>
    <type>article</type>
    <publisherName>SIAM</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2018-10-02</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A multiscale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics</title>
    <abstract language="eng">We investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one.</abstract>
    <parentTitle language="eng">SIAM J. Multiscale Model. Simul.</parentTitle>
    <identifier type="doi">10.1137/17M1146403</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2018-08-15</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-64868</enrichment>
    <author>Péter Koltai</author>
    <submitter>Paulina Bressel</submitter>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="MOL-ANALYSIS">MOL-ANALYSIS</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
  </doc>
  <doc>
    <id>7718</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>3321</pageFirst>
    <pageLast>3366</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>30</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2020-09-10</completedDate>
    <publishedDate>2020-09-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics</title>
    <parentTitle language="deu">Journal of Nonlinear Science</parentTitle>
    <identifier type="doi">https://doi.org/10.1007/s00332-020-09652-7</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2020-08-23</enrichment>
    <author>Luzie Helfmann</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Enric Ribera Borrell</author>
    <author>Christof Schütte</author>
    <author>Peter Koltai</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="ribera.borrell">Ribera Borrell, Enric</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="tipping">Stability and Tipping in Social Systems</collection>
  </doc>
  <doc>
    <id>7732</id>
    <completedYear/>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>4232</pageFirst>
    <pageLast>4257</pageLast>
    <pageNumber/>
    <edition/>
    <issue>11</issue>
    <volume>32</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Fréchet differentiable drift dependence of Perron–Frobenius and Koopman operators for non-deterministic dynamics</title>
    <abstract language="eng">We prove the Fréchet differentiability with respect to the drift of Perron–Frobenius and Koopman operators associated to time-inhomogeneous ordinary stochastic differential equations. This result relies on a similar differentiability result for pathwise expectations of path functionals of the solution of the stochastic differential equation, which we establish using Girsanov's formula. We demonstrate the significance of our result in the context of dynamical systems and operator theory, by proving continuously differentiable drift dependence of the simple eigen- and singular values and the corresponding eigen- and singular functions of the stochastic Perron–Frobenius and Koopman operators.</abstract>
    <parentTitle language="eng">Nonlinearity</parentTitle>
    <identifier type="doi">10.1088/1361-6544/ab1f2a</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Péter Koltai</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Han Cheng Lie</author>
    <author>Martin Plonka</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="lie">Lie, Han</collection>
    <collection role="projects" number="MathPlusAA1-1">MathPlusAA1-1</collection>
  </doc>
  <doc>
    <id>7969</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>31</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-03-02</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Transition paths of marine debris and the stability of the garbage patches</title>
    <abstract language="eng">We used transition path theory (TPT) to infer "reactive" pathways of floating marine debris trajectories. The TPT analysis was applied on a pollution-aware time-homogeneous Markov chain model constructed from trajectories produced by satellite-tracked undrogued buoys from the NOAA Global Drifter Program. The latter involved coping with the openness of the system in physical space, which further required an adaptation of the standard TPT setting. Directly connecting pollution sources along coastlines with garbage patches of varied strengths, the unveiled reactive pollution routes represent alternative targets for ocean cleanup efforts. Among our specific findings we highlight: constraining a highly probable pollution source for the Great Pacific Garbage Patch; characterizing the weakness of the Indian Ocean gyre as a trap for plastic waste; and unveiling a tendency of the subtropical gyres to export garbage toward the coastlines rather than to other gyres in the event of anomalously intense winds.</abstract>
    <parentTitle language="deu">Chaos: An Interdisciplinary Journal of Nonlinear Science</parentTitle>
    <identifier type="arxiv">2009.11234</identifier>
    <identifier type="doi">https://doi.org/10.1063/5.0030535</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Philippe Miron</author>
    <author>Francisco Beron-Vera</author>
    <author>Luzie Helfmann</author>
    <author>Péter Koltai</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="tipping">Stability and Tipping in Social Systems</collection>
  </doc>
  <doc>
    <id>7886</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>31</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading</title>
    <abstract language="eng">We investigate opinion dynamics based on an agent-based model and are interested in predicting the evolution of the percentages of the entire agent population that share an opinion. Since these opinion percentages can be seen as an aggregated observation of the full system state, the individual opinions of each agent, we view this in the framework of the Mori–Zwanzig projection formalism. More specifically, we show how to estimate a nonlinear autoregressive model (NAR) with memory from data given by a time series of opinion percentages, and discuss its prediction capacities for various specific topologies of the agent interaction network. We demonstrate that the inclusion of memory terms significantly improves the prediction quality on examples with different network topologies.</abstract>
    <parentTitle language="eng">Journal of Nonlinear Science</parentTitle>
    <identifier type="doi">10.1007/s00332-020-09673-2</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Niklas Wulkow</author>
    <submitter>Kalina Tsankova</submitter>
    <author>Péter Koltai</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="INNOSPREAD">INNOSPREAD</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>6685</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>471</pageFirst>
    <pageLast>512</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>28</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2017-10-12</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics</title>
    <abstract language="eng">We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.</abstract>
    <parentTitle language="eng">Jounal of Nonlinear Science</parentTitle>
    <identifier type="doi">10.1007/s00332-017-9415-0</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-63822</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Paulina Bressel</submitter>
    <author>Péter Koltai</author>
    <author>Stefan Klus</author>
    <author>Ralf Banisch</author>
    <author>Michael Dellnitz</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB-1114-B3">SFB-1114-B3</collection>
  </doc>
  <doc>
    <id>6702</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>22</pageNumber>
    <edition/>
    <issue>1</issue>
    <volume>6</volume>
    <type>article</type>
    <publisherName>MDPI</publisherName>
    <publisherPlace>Basel, Switzerland</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal data-driven estimation of generalized Markov state models for non-equilibrium dynamics</title>
    <parentTitle language="eng">Computation</parentTitle>
    <identifier type="doi">10.3390/computation6010022</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">http://www.mdpi.com/2079-3197/6/1/22</enrichment>
    <author>Peter Koltai</author>
    <submitter>Erlinda Koernig</submitter>
    <author>Hao Wu</author>
    <author>Frank Noé</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
  </doc>
  <doc>
    <id>6250</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>51</pageFirst>
    <pageLast>77</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>3</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the numerical approximation of the Perron-Frobenius and Koopman operator</title>
    <abstract language="eng">Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the Perron-Frobenius and the Koopman operator. In this paper, we will review di� fferent methods that have been developed over the last decades to compute � infinite-dimensional approximations of these in� finite-dimensional operators - in particular Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and di� fferences between these approaches. The results will be illustrated using simple stochastic di� fferential equations and molecular dynamics examples.</abstract>
    <parentTitle language="eng">Journal of Computational Dynamics</parentTitle>
    <identifier type="doi">10.3934/jcd.2016003</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Stefan Klus</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Peter Koltai</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="ECMath-CH6">ECMath-CH6</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
  </doc>
  <doc>
    <id>6267</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>985</pageFirst>
    <pageLast>1010</pageLast>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>28</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2018-01-03</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Data-driven model reduction and transfer operator approximation</title>
    <parentTitle language="eng">Journal of Nonlinear Science</parentTitle>
    <identifier type="url">https://link.springer.com/article/10.1007/s00332-017-9437-7</identifier>
    <identifier type="doi">10.1007/s00332-017-9437-7</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Stefan Klus</author>
    <submitter>Erlinda Koernig</submitter>
    <author>Feliks Nüske</author>
    <author>Peter Koltai</author>
    <author>Hao Wu</author>
    <author>Ioannis Kevrekidis</author>
    <author>Christof Schütte</author>
    <author>Frank Noé</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
  </doc>
  <doc>
    <id>6340</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>174103</issue>
    <volume>145</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On Markov state models for non-equilibrium molecular dynamics</title>
    <parentTitle language="eng">The Journal of Chemical Physics</parentTitle>
    <identifier type="doi">10.1063/1.4966157</identifier>
    <note>2016 Editor's Choice of The Journal of Chemical Physics</note>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-57869</enrichment>
    <author>Peter Koltai</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Giovanni Ciccotti</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
  </doc>
  <doc>
    <id>6382</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2017-05-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics</title>
    <abstract language="eng">We consider complex dynamical systems showing metastable behavior but no local&#13;
separation of fast and slow time scales. The article raises the question of whether&#13;
such systems exhibit a low-dimensional manifold supporting its effective dynamics.&#13;
For answering this question, we aim at finding nonlinear coordinates, called reaction&#13;
coordinates, such that the projection of the dynamics onto these coordinates preserves&#13;
the dominant time scales of the dynamics. We show that, based on a specific&#13;
reducibility property, the existence of good low-dimensional reaction coordinates&#13;
preserving the dominant time scales is guaranteed. Based on this theoretical framework,&#13;
we develop and test a novel numerical approach for computing good reaction&#13;
coordinates. The proposed algorithmic approach is fully local and thus not prone to&#13;
the curse of dimension with respect to the state space of the dynamics. Hence, it is&#13;
a promising method for data-based model reduction of complex dynamical systems&#13;
such as molecular dynamics.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-63822</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="AcceptedDate">2017-09-23</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Paulina Bressel</submitter>
    <author>Péter Koltai</author>
    <author>Stefan Klus</author>
    <author>Ralf Banisch</author>
    <author>Michael Dellnitz</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-22</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>slow dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>effective dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition manifold</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>embedding</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transfer operator</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reaction coordinate</value>
    </subject>
    <collection role="msc" number="47B38">Operators on function spaces (general)</collection>
    <collection role="msc" number="60H35">Computational methods for stochastic equations [See also 65C30]</collection>
    <collection role="msc" number="82C31">Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6382/ZIB-Report_17-22.pdf</file>
  </doc>
  <doc>
    <id>6486</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2017-09-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A multi scale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics</title>
    <abstract language="eng">We investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-64868</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2018-08-15</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <author>Péter Koltai</author>
    <submitter>Paulina Bressel</submitter>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-49</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov state model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-equilibrium molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>two timescale master equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-stationary forcing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <collection role="msc" number="34E13">Multiple scale methods</collection>
    <collection role="msc" number="60J20">Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]</collection>
    <collection role="msc" number="60J60">Diffusion processes [See also 58J65]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6486/ZIB-Report_17-49.pdf</file>
  </doc>
  <doc>
    <id>5786</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition>145</edition>
    <issue/>
    <volume>174103</volume>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-03-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On metastability and Markov state models for non-stationary molecular dynamics</title>
    <abstract language="eng">We utilize the theory of coherent sets to build Markov state models for non- equilibrium molecular dynamical systems. Unlike for systems in equilibrium, “meta- stable” sets in the non-equilibrium case may move as time evolves. We formalize this concept by relying on the theory of coherent sets, based on this we derive finite-time non-stationary Markov state models, and illustrate the concept and its main differences to equilibrium Markov state modeling on simple, one-dimensional examples.</abstract>
    <parentTitle language="eng">The Journal of Chemical Physics</parentTitle>
    <subTitle language="deu">2016 Editor's Choice of The Journal of Chemical Physics</subTitle>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-57869</identifier>
    <identifier type="doi">10.1063/1.4966157</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SourceTitle">Appeared in: The Journal of Chemical Physics 145 (2016)</enrichment>
    <author>Peter Koltai</author>
    <submitter>Erlinda Koernig</submitter>
    <author>Giovanni Ciccotti</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-11</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>coherent set,</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov state model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-equilibrium molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <collection role="msc" number="60J20">Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]</collection>
    <collection role="msc" number="60J35">Transition functions, generators and resolvents [See also 47D03, 47D07]</collection>
    <collection role="msc" number="60J60">Diffusion processes [See also 58J65]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5786/ZIB_16-11_new.pdf</file>
  </doc>
  <doc>
    <id>8524</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2021-12-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Data-driven modelling of nonlinear dynamics by barycentric coordinates and memory</title>
    <abstract language="eng">We present a numerical method to model dynamical systems from data. We use the recently introduced method Scalable Probabilistic Approximation (SPA) to project points from a Euclidean space to convex polytopes and represent these projected states of a system in new, lower-dimensional coordinates denoting their position in the polytope. We then introduce a specific nonlinear transformation to construct a model of the dynamics in the polytope and to transform back into the original state space. To overcome the potential loss of information from the projection to a lower-dimensional polytope, we use memory in the sense of the delay-embedding theorem of Takens. By construction, our method produces stable models. We illustrate the capacity of the method to reproduce even chaotic dynamics and attractors with multiple connected components on various examples.</abstract>
    <parentTitle language="eng">J. Stat. Phys.</parentTitle>
    <identifier type="arxiv">2112.06742</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <submitter>Ekaterina Engel</submitter>
    <author>Niklas Wulkow</author>
    <author>Péter Koltai</author>
    <author>Vikram Sunkara</author>
    <author>Christof Schütte</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="sunkara">Sunkara, Vikram</collection>
    <collection role="projects" number="SFB-1114-B3">SFB-1114-B3</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="projects" number="MathPlus-AA1-2">MathPlus-AA1-2</collection>
  </doc>
  <doc>
    <id>8436</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>449</pageFirst>
    <pageLast>488</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>21</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal Reaction Coordinates: Variational Characterization and Sparse Computation</title>
    <abstract language="eng">Reaction coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and provide conditions for their existence. Optimal RCs are minimizers of a certain loss function, and reduced models based on them guarantee a good approximation of the statistical long-term properties of the original high-dimensional process. We show that for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. Remarkably, for reversible systems, the numerical effort required to evaluate the loss function scales only with the variability of the underlying, low-dimensional mechanism, and not with that of the full system. The theory provided lays the foundation for an efficient and data-sparse computation of RCs via modern machine learning techniques.</abstract>
    <parentTitle language="eng">Multiscale Modelling &amp; Simulation</parentTitle>
    <identifier type="arxiv">2107.10158</identifier>
    <identifier type="doi">10.1137/21M1448367</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">30.10.2022</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Ekaterina Engel</submitter>
    <author>Mattes Mollenhauer</author>
    <author>Péter Koltai</author>
    <author>Christof Schütte</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>8437</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>34</pageLast>
    <pageNumber/>
    <edition/>
    <issue>327</issue>
    <volume>23</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Kernel Autocovariance Operators of Stationary Processes: Estimation and Convergence</title>
    <abstract language="eng">We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and obtain several asymptotic results as well as finite sample error bounds. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition.</abstract>
    <parentTitle language="eng">Journal of Machine Learning Research</parentTitle>
    <identifier type="arxiv">2004.00891</identifier>
    <identifier type="url">https://jmlr.org/papers/v23/20-442.html</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Mattes Mollenhauer</author>
    <submitter>Ekaterina Engel</submitter>
    <author>Stefan Klus</author>
    <author>Christof Schütte</author>
    <author>Péter Koltai</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <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>8166</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>3249</pageFirst>
    <pageLast>3271</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>230</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-06-18</completedDate>
    <publishedDate>2021-06-18</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Statistical analysis of tipping pathways in agent-based models</title>
    <abstract language="eng">Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach.</abstract>
    <parentTitle language="eng">Eur. Phys. J. Spec. Top.</parentTitle>
    <identifier type="arxiv">2103.02883</identifier>
    <identifier type="doi">10.1140/epjs/s11734-021-00191-0</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Luzie Helfmann</author>
    <submitter>Luzie Helfmann</submitter>
    <author>Jobst Heitzig</author>
    <author>Péter Koltai</author>
    <author>Jürgen Kurths</author>
    <author>Christof Schütte</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="tipping">Stability and Tipping in Social Systems</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>
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