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  <doc>
    <id>7317</id>
    <completedYear/>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>6</issue>
    <volume>14</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-04-08</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Multidimensional Approximation of Nonlinear Dynamical Systems</title>
    <abstract language="eng">A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.</abstract>
    <parentTitle language="eng">Journal of Computational and Nonlinear Dynamics</parentTitle>
    <identifier type="doi">10.1115/1.4043148</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Patrick Gelß</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Stefan Klus</author>
    <author>Jens Eisert</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>6260</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>7</issue>
    <volume>31</volume>
    <type>article</type>
    <publisherName>IOP Publishing Ltd &amp; London Mathematical Society</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2018-06-04</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Tensor-based dynamic mode decomposition</title>
    <parentTitle language="eng">Nonlinearity</parentTitle>
    <identifier type="doi">10.1088/1361-6544/aabc8f</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2018-04-09</enrichment>
    <author>Stefan Klus</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Patrick Gelß</author>
    <author>Sebastian Peitz</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-CH2">ECMATH-CH2</collection>
    <collection role="projects" number="SFB-1114-B3">SFB-1114-B3</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
  </doc>
  <doc>
    <id>10097</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>14</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Continuous optimization methods for the graph isomorphism problem</title>
    <parentTitle language="eng">Information and Inference: A Journal of the IMA</parentTitle>
    <identifier type="doi">10.1093/imaiai/iaaf011</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Stefan Klus</author>
    <submitter>Christoph Spiegel</submitter>
    <author>Patrick Gelß</author>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <collection role="persons" number="gelß">Gelß, Patrick</collection>
    <collection role="projects" number="QOPT">QOPT</collection>
  </doc>
  <doc>
    <id>9758</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>39</issue>
    <volume>57</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Existence and uniqueness of solutions of the Koopman--von Neumann equation on bounded domains</title>
    <parentTitle language="eng">Journal of Physics A: Mathematical and Theoretical</parentTitle>
    <identifier type="doi">10.1088/1751-8121/ad6f7d</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Steven-Marian Stengl</author>
    <submitter>Christoph Spiegel</submitter>
    <author>Patrick Gelß</author>
    <author>Stefan Klus</author>
    <author>Sebastian Pokutta</author>
    <collection role="persons" number="pokutta">Pokutta, Sebastian</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <collection role="persons" number="gelß">Gelß, Patrick</collection>
    <collection role="persons" number="stengl">Stengl, Steven-Marian</collection>
    <collection role="projects" number="QOPT">QOPT</collection>
  </doc>
  <doc>
    <id>8950</id>
    <completedYear/>
    <publishedYear>2022</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">Low-Rank Tensor Decompositions of Quantum Circuits</title>
    <abstract language="eng">Quantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation, optimization, and physical realization of quantum circuits is of utmost importance for designing novel algorithms. We show&#13;
how matrix product states (MPSs) and matrix product operators (MPOs) can be used to express certain quantum states, quantum gates, and entire quantum circuits as low-rank tensors. This enables the analysis and simulation of complex quantum circuits on classical computers and to gain insight into the underlying structure of the system. We present different examples to demonstrate the advantages of MPO formulations and show that they are more efficient than conventional techniques if the bond dimensions of the wave function representation can be kept small throughout the simulation.</abstract>
    <parentTitle language="eng">Journal of Computational Physics</parentTitle>
    <identifier type="arxiv">2205.09882</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">true</enrichment>
    <author>Patrick Gelß</author>
    <submitter>Patrick Gelß</submitter>
    <author>Stefan Klus</author>
    <author>Sebastian Knebel</author>
    <author>Zarin Shakibaei</author>
    <author>Sebastian Pokutta</author>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="persons" number="pokutta">Pokutta, Sebastian</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <collection role="persons" number="gelß">Gelß, Patrick</collection>
    <collection role="persons" number="knebel">Knebel, Sebastian</collection>
    <collection role="persons" number="shakibaei">Shakibaei, Zarin</collection>
  </doc>
</export-example>
