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    <publishedYear>2021</publishedYear>
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    <language>eng</language>
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    <volume>31</volume>
    <type>article</type>
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    <completedDate>2020-12-18</completedDate>
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    <title language="eng">Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds</title>
    <abstract language="eng">We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parameterization of a low-dimensional transition manifold in a certain function space. In this article, we enhance this approach by embedding and learning this transition manifold in a reproducing kernel Hilbert space, exploiting the favorable properties of kernel embeddings. Under mild assumptions on the kernel, the manifold structure is shown to be preserved under the embedding, and distortion bounds can be derived. This leads to a more robust and more efficient algorithm compared to the previous parameterization approaches.</abstract>
    <parentTitle language="eng">Journal of Nonlinear Science</parentTitle>
    <identifier type="doi">10.1007/s00332-020-09668-z</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Stefan Klus</author>
    <author>Boumediene Hamzi</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="MathPlusAA1-1">MathPlusAA1-1</collection>
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  <doc>
    <id>8106</id>
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    <publishedYear>2021</publishedYear>
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    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>5</issue>
    <volume>16</volume>
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    <publishedDate>2021-05-13</publishedDate>
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    <title language="eng">Data-driven model reduction of agent-based systems using the Koopman generator</title>
    <abstract language="eng">The dynamical behavior of social systems can be described by agent-based models. Although single agents follow easily explainable rules, complex time-evolving patterns emerge due to their interaction. The simulation and analysis of such agent-based models, however, is often prohibitively time-consuming if the number of agents is large. In this paper, we show how Koopman operator theory can be used to derive reduced models of agent-based systems using only simulation or real-world data. Our goal is to learn coarse-grained models and to represent the reduced dynamics by ordinary or stochastic differential equations. The new variables are, for instance, aggregated state variables of the agent-based model, modeling the collective behavior of larger groups or the entire population. Using benchmark problems with known coarse-grained models, we demonstrate that the obtained reduced systems are in good agreement with the analytical results, provided that the numbers of agents is sufficiently large.</abstract>
    <parentTitle language="eng">PLOS ONE</parentTitle>
    <identifier type="arxiv">2012.07718</identifier>
    <identifier type="doi">10.1371/journal.pone.0250970</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2021-04-19</enrichment>
    <author>Jan-Hendrik Niemann</author>
    <submitter>Jan-Hendrik Niemann</submitter>
    <author>Stefan Klus</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="MathPlus-EF4-3">MathPlus-EF4-3</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
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  <doc>
    <id>8347</id>
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    <publishedYear>2021</publishedYear>
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    <language>eng</language>
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    <issue>5</issue>
    <volume>16</volume>
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    <title language="eng">Simulation data: Data-driven model reduction of agent-based systems using the Koopman generator</title>
    <parentTitle language="eng">PLOS ONE</parentTitle>
    <identifier type="doi">http://doi.org/10.5281/zenodo.4522119</identifier>
    <note>This repository contains the simulation data for the article "Data-driven model reduction of agent-based systems using the Koopman generator" by Jan-Hendrik Niemann, Stefan Klus and Christof Schütte. The archive complete_voter_model.zip contains the simulation results for the extended voter model on a complete graph for the parameters given in the corresponding txt-files to learn a reduced SDE model. The files are of the form [types, time steps, samples, training points].The archive dependency.zip contains additional simulation results of the form [types, time steps, samples, training points] to learn a reduced SDE model. The parameters used are given in the corresponding txt-files.The archive random_voter_model.zip contains the simulation results to learn a reduced SDE model for the given adjacency matrix within the archive. The file aggregate_state is of the form [training points, types, time steps, samples]. The file full_state is of the form [training points, agents, time steps, samples].The archive predator_prey_model.zip contains the simulation results to learn a reduced SDE model and calculation of the mean value of the agent-based model. The data is of the form [types, time steps, samples, training points] and [samples, time steps, types].The archive two_clustered_voter_model.zip contains the simulation results for the extended voter model on a graph with two clusters for the given adjacency matrices to learn a reduced SDE model. The file aggregate_state is of the form [training points, types, time steps, samples]. The file full_state is of the form [training points, agents, time steps, samples].</note>
    <enrichment key="PeerReviewed">yes</enrichment>
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    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Jan-Hendrik Niemann</author>
    <submitter>Jan-Hendrik Niemann</submitter>
    <author>Christof Schütte</author>
    <author>Stefan Klus</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MathPlus-EF4-3">MathPlus-EF4-3</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
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  <doc>
    <id>8186</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>221</volume>
    <type>article</type>
    <publisherName>Elsevier</publisherName>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
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    <title language="eng">Feature space approximation for kernel-based supervised learning</title>
    <parentTitle language="eng">Knowledge-Based Sytems</parentTitle>
    <identifier type="doi">https://doi.org/10.1016/j.knosys.2021.106935</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Patrick Gelss</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Stefan Klus</author>
    <author>Ingmar Schuster</author>
    <author>Christof Schütte</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="ECMATH-CH2">ECMATH-CH2</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="SFB-1114-B3">SFB-1114-B3</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
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