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  <doc>
    <id>9204</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>3:1</pageFirst>
    <pageLast>3:6</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>115</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization</title>
    <abstract language="eng">The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.</abstract>
    <parentTitle language="eng">23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)</parentTitle>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2023.3</identifier>
    <enrichment key="Series">Open Access Series in Informatics (OASIcs)</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2023-08-27</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-91309</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Martin Weiser</submitter>
    <author>Fabian Danecker</author>
    <author>Martin Weiser</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
    <collection role="projects" number="MathPlus-TrU-4">MathPlus-TrU-4</collection>
  </doc>
  <doc>
    <id>9184</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted>2023</thesisYearAccepted>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>4</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Newton's Method for Global Free Flight Trajectory Optimization</title>
    <abstract language="eng">Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.</abstract>
    <parentTitle language="eng">Operations Research Forum</parentTitle>
    <identifier type="doi">10.1007/s43069-023-00238-z</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-91846</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-89876</enrichment>
    <enrichment key="SourceTitle">Operations Research Forum 4, 63 (2023).</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Fabian Danecker</submitter>
    <author>Fabian Danecker</author>
    <author>Martin Weiser</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
    <collection role="projects" number="MathPlus-TrU-4">MathPlus-TrU-4</collection>
  </doc>
  <doc>
    <id>8331</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>830</pageFirst>
    <pageLast>856</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>198</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization</title>
    <abstract language="eng">Flight planning, the computation of optimal routes in view of flight time and  fuel consumption under given weather conditions, is traditionally done by finding globally shortest paths in a predefined airway network. Free flight trajectories, not restricted to a network, have the potential to reduce the costs significantly, and can be computed using locally convergent continuous optimal control methods.&#13;
&#13;
Hybrid methods that start with a discrete global search and refine with a fast continuous local optimization combine the best properties of both approaches, but rely on a good switchover, which requires error estimates for discrete paths relative to continuous trajectories.&#13;
    &#13;
Based on vertex density and local complete connectivity, we derive localized and a priori bounds for the flight time of discrete paths relative to the optimal continuous trajectory, and illustrate their properties on a set of benchmark problems. It turns out that localization improves the error bound by four orders of magnitude, but still leaves ample opportunities for tighter bounds using a posteriori error estimators.</abstract>
    <parentTitle language="eng">Journal of Optimization Theory and Applications</parentTitle>
    <identifier type="doi">10.1007/s10957-023-02264-7</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2023-06-19</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Martin Weiser</submitter>
    <author>Fabian Danecker</author>
    <author>Martin Weiser</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8331/article.pdf</file>
  </doc>
  <doc>
    <id>8881</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>13</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>106</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization</title>
    <abstract language="eng">We present an efficient algorithm that finds a globally optimal solution to the 2D Free Flight Trajectory Optimization Problem (aka Zermelo Navigation Problem) up to arbitrary precision in finite time. The algorithm combines a discrete and a continuous optimization phase. In the discrete phase, a set of candidate paths that densely covers the trajectory space is created on a directed auxiliary graph. Then Yen’s algorithm provides a promising set of discrete candidate paths which subsequently undergo a locally convergent refinement stage. Provided that the auxiliary graph is sufficiently dense, the method finds a path that lies within the convex domain around the global minimizer. From this starting point, the second stage will converge rapidly to the optimum. The density of the auxiliary graph depends solely on the wind field, and not on the accuracy of the&#13;
solution, such that the method inherits the superior asymptotic convergence properties of the optimal control stage.</abstract>
    <parentTitle language="eng">22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)</parentTitle>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2022.2</identifier>
    <enrichment key="Series">Open Access Series in Informatics (OASIcs)</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2022-08-01</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Martin Weiser</submitter>
    <author>Fabian Danecker</author>
    <author>Martin Weiser</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
  </doc>
  <doc>
    <id>8134</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>2020-12-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Discrete-Continuous Algorithm for Free Flight Planning</title>
    <abstract language="eng">We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="doi">10.3390/a14010004</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-81343</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="SourceTitle">Algorithms</enrichment>
    <enrichment key="AcceptedDate">2020-12-20</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Fabian Danecker</submitter>
    <author>Fabian Danecker</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>20-33</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>shortest path</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>flight planning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>free flight</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discrete-continuous algorithm</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discrete optimization</value>
    </subject>
    <collection role="msc" number="49M37">Methods of nonlinear programming type [See also 90C30, 65Kxx]</collection>
    <collection role="msc" number="65K10">Optimization and variational techniques [See also 49Mxx, 93B40]</collection>
    <collection role="msc" number="65L10">Boundary value problems</collection>
    <collection role="msc" number="90C27">Combinatorial optimization</collection>
    <collection role="msc" number="90C35">Programming involving graphs or networks [See also 90C27]</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="institutes" number="traffic">Mathematics of Transportation and Logistics</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MfLMS">Mathematics for Life and Materials Science</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="Mathematical Algorithmic Intelligence">Mathematical Algorithmic Intelligence</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8134/BorndoerferDaneckerWeiser2020.pdf</file>
  </doc>
  <doc>
    <id>10084</id>
    <completedYear>2026</completedYear>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>225</pageFirst>
    <pageLast>256</pageLast>
    <pageNumber/>
    <edition>Computational Social Science of Social Cohesion and Polarization</edition>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName>Springer, Cham.</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2026-02-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Investigation into the Causal Mechanism of Political Opinion Dynamics: A Model of Hierarchical Coarse-Graining with Community-Bounded Social Influence</title>
    <abstract language="eng">The increasing polarization in democratic societies is an emergent outcome of political opinion dynamics. Yet, the fundamental mechanisms behind the formation of political opinions, from individual beliefs to collective consensus, remain unknown. Understanding that a causal mechanism must account for both bottom-up and top-down influences, we conceptualize political opinion dynamics as hierarchical coarse-graining, where microscale opinions integrate into a macro-scale state variable. Using the CODA (Continuous Opinions Discrete Actions) model, we simulate Bayesian opinion updating, social identity-based information integration, and migration between social identity groups to represent higher-level connectivity. This results in coarse-graining across micro, meso, and macro levels. Our findings show that higher-level connectivity shapes information integration, yielding three regimes: independent (disconnected, local convergence), parallel (fast, global convergence), and iterative (slow, stepwise convergence). In the iterative regime, low connectivity fosters transient diversity, indicating an informed consensus. In all regimes, time-scale separation leads to downward causation, where agents converge on the aggregate majority choice, driving consensus. Critically, any degree of coherent higher-level information integration can overcome misalignment via global downward causation. The results highlight how emergent properties of the causal mechanism, such as downward causation, are essential for consensus and may inform more precise investigations into polarized political discourse.</abstract>
    <parentTitle language="deu">Computational Social Science of Social Cohesion and Polarization</parentTitle>
    <identifier type="arxiv">2504.00877</identifier>
    <identifier type="doi">10.1007/978-3-032-01373-6_10</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SourceTitle">Computational Social Science of Social Cohesion and Polarization</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Valeria Widler</author>
    <submitter>Ekaterina Engel</submitter>
    <author>Barbara Kaminska</author>
    <author>Andre C. R. Martins</author>
    <author>Ivan Puga-Gonzalez</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="MathPlusEF45-1">MathPlusEF45-1</collection>
    <collection role="persons" number="widler">Widler, Valeria</collection>
  </doc>
  <doc>
    <id>10225</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>40</pageFirst>
    <pageLast>53</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2025-11-05</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">MaRDMO: Future Gateway to FAIR Mathematical Data</title>
    <abstract language="eng">Mathematical research data plays a crucial role across scientific disciplines, yet its documentation and dissemination remain challenging due to the lack of standardized research data management practices. The MaRDMO Plugin addresses these challenges by integrating mathematical models, algorithms, and interdisciplinary workflows into the established framework of the Research Data Management Organiser (RDMO). Built on FAIR principles, MaRDMO enables structured documentation and retrieval of mathematical research data through guided questionnaires. It connects to multiple knowledge graphs, including MathModDB, MathAlgoDB, and the MaRDI Portal. Users can document and search for models, algorithms, and workflows via dynamic selection interfaces that also leverage other sources such as Wikidata. The plugin facilitates the export to the individual MaRDI services, ensuring data quality through automated validation. By embedding mathematical research data management into the widely adopted RDMO platform, MaRDMO represents a significant step toward making mathematical research data more findable, accessible, and reusable.</abstract>
    <parentTitle language="eng">E-Science-Tage 2025: Research Data Management: Challenges in a Changing World</parentTitle>
    <identifier type="doi">10.11588/heibooks.1652.c23913</identifier>
    <enrichment key="AcceptedDate">2025/05/08</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Reidelbach Marco</author>
    <submitter>Marco Reidelbach</submitter>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="reidelbach">Reidelbach, Marco</collection>
    <collection role="projects" number="MaRDI-TA4">MaRDI-TA4</collection>
  </doc>
  <doc>
    <id>9990</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>470</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2025-04-15</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise</title>
    <abstract language="eng">Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the potential to transform data-rich fields where well-established dynamical models remain unknown. This work contributes to the recent trend in data-driven sparse identification of nonlinear dynamics of finding the best sparse fit to observational data in a large library of potential nonlinear models. We propose an efficient first-order Conditional Gradient algorithm for solving the underlying optimization problem. In comparison to the most prominent alternative framework, the new framework shows significantly improved performance on several essential issues like sparsity-induction, structure-preservation, noise robustness, and sample efficiency. We demonstrate these advantages on several dynamics from the field of synchronization, particle dynamics, and enzyme chemistry.</abstract>
    <parentTitle language="eng">Journal of Computational and Applied Mathematics</parentTitle>
    <identifier type="doi">10.1016/j.cam.2025.116675</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2025-03-28</enrichment>
    <author>Alejandro Carderera</author>
    <submitter>Christoph Spiegel</submitter>
    <author>Sebastian Pokutta</author>
    <author>Christof Schütte</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="persons" number="pokutta">Pokutta, Sebastian</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
  </doc>
  <doc>
    <id>10227</id>
    <completedYear/>
    <publishedYear>2025</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">FAIR Representation of Mathematical Research Data: MathModDB and MathAlgoDB as Knowledge Graphs for Mathematical Models and Numerical Algorithms</title>
    <parentTitle language="eng">2nd Conference on Research Data Infrastructure (CoRDI)</parentTitle>
    <identifier type="doi">10.5281/zenodo.16735911</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Björn Schembera</author>
    <submitter>Marco Reidelbach</submitter>
    <author>Frank Wübbeling</author>
    <author>Aurela Shehu</author>
    <author>Christine Biedinger</author>
    <author>Jochen Fiedler</author>
    <author>Marco Reidelbach</author>
    <author>Burkhard Schmidt</author>
    <author>Eloi Ferrer</author>
    <author>Thomas Koprucki</author>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="reidelbach">Reidelbach, Marco</collection>
    <collection role="persons" number="ferrer">Ferrer, Eloi</collection>
    <collection role="projects" number="MaRDI-TA4">MaRDI-TA4</collection>
  </doc>
  <doc>
    <id>10280</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>59</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>masterthesis</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>2025-05-20</thesisDateAccepted>
    <title language="eng">Regression Techniques for Surrogate Modelling in Bayesian Inverse Problems</title>
    <abstract language="eng">For many real-world applications, a system of interest can be represented via a mathematical model which depends on a set of parameters. In order to identify the parameters, a set of observations is available and an Inverse Problem is formulated. Identifying the parameters from the observations is often a challenging task, especially when the model is expensive to evaluate. This is the case for Partial Differential Equations models, where numerical simulations which are both inexact and computationally expensive are required to obtain the model output. To ease the computational costs, surrogate models can be used to approximate the forward model. In this work, we present two different regression techniques, Gaussian Process Regression and Lipschitz Regression. After reformulating the Inverse Problem to account for the surrogate model, we develope an adaptive training strategy to train the surrogate model. The proposed training strategy aims at optimizing not only the training points’ positions but also their evaluation accuracies. Moreover, interleaved sampling of the posterior distribution of the unknown parameters is performed while the surrogate model is trained, providing a solution for the Inverse Problem. The quality of the surrogating techniques as well as the effectiveness of the adaptive training strategy are tested through different numerical experiments.</abstract>
    <enrichment key="opus.source">publish</enrichment>
    <advisor>Martin Weiser</advisor>
    <author>Paolo Villani</author>
    <submitter>Martin Weiser</submitter>
    <advisor>Tobias Breiten</advisor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="villani">Villani, Paolo</collection>
    <collection role="projects" number="DigitalTwins">DigitalTwins</collection>
    <thesisGrantor>Technische Universität Berlin</thesisGrantor>
  </doc>
  <doc>
    <id>9957</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>5116</pageFirst>
    <pageLast>5121</pageLast>
    <pageNumber/>
    <edition/>
    <issue>10</issue>
    <volume>129</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2025-02-27</completedDate>
    <publishedDate>--</publishedDate>
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    <title language="eng">Chiral Plasmonic Crystals Self-Assembled by DNA Origami</title>
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    <title language="eng">Reliable approximation of long relaxation timescales in molecular dynamics</title>
    <abstract language="eng">Many interesting rare events in molecular systems like ligand association, protein folding or con- formational changes happen on timescales that often are not accessible by direct numerical simulation. Therefore rare event approximation approaches like interface sampling, Markov state model building or advanced reaction coordinate based free energy estimation have attracted huge attention recently. In this article we analyze the reliability of such approaches: How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics. By doing so they also allow for understanding deep connections between the different approaches.</abstract>
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    <identifier type="urn">urn:nbn:de:0297-zib-63718</identifier>
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    <abstract language="eng">Classrooms are becoming increasingly heterogeneous, comprising learners with diverse performance and motivation levels, language proficiencies, and learning differences such as dyslexia and ADHD. While teachers recognize the need for differentiated instruction, growing workloads create substantial barriers, making differentiated instruction an ideal that is often unrealized in practice. Current AI educational tools, which promise differentiated materials, are predominantly student-facing and performance-centric, ignoring other aspects that shape learning outcomes. We introduce FACET, a teacher-facing multi-agent framework designed to address these gaps by supporting differentiation that accounts for motivation, performance, and learning differences. Developed with educational stakeholders from the outset, the framework coordinates four specialized agents, including learner simulation, diagnostic assessment, material generation, and evaluation within a teacher-in-the-loop design. School principals (N = 30) shaped system requirements through participatory workshops, while in-service K-12 teachers (N = 70) evaluated material quality. Mixed-methods evaluation demonstrates strong perceived value for inclusive differentiation. Practitioners emphasized both the urgent need arising from classroom heterogeneity and the importance of maintaining pedagogical autonomy as a prerequisite for adoption. We discuss implications for future school deployment and outline partnerships for longitudinal classroom implementation.</abstract>
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    <title language="eng">Embedded Model Form Uncertainty Quantification with Measurement Noise for Bayesian Model Calibration</title>
    <abstract language="eng">A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian methods provide a robust framework for quantifying and propagating these uncertainties to model predictions. Nevertheless, Bayesian methods paired with inexact models usually produce predictions unable to represent the observed datapoints. Additionally, the quantified uncertainties of these overconfident models cannot be propagated to other Quantities of Interest (QoIs) reliably. A promising solution involves embedding a model inadequacy term in the inference parameters, allowing the quantified model form uncertainty to influence non-observed QoIs.&#13;
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Moreover, we evaluate the performance of this inadequacy-embedding approach in the presence of discrepancies between measurements and model predictions, including noise and outliers. Particular attention is given to how the uncertainty associated with the model inadequacy term propagates to the QoIs, enabling a more comprehensive statistical analysis of prediction’s reliability. Finally, the proposed approach is applied to estimate the uncertainty&#13;
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    <title language="eng">Improving Perovskite/CIGS Tandem Solar Cells for Higher Power Conversion Efficiency through Light Management and Bandgap Engineering</title>
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Solar\nSpectral Irradiance: ASTM G-173. 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    <author>Guillermo Farias-Basulto</author>
    <submitter>Sven Burger</submitter>
    <author>Thede Mehlhop</author>
    <author>Nicolas J. Otto</author>
    <author>Tobias Bertram</author>
    <author>Klaus Jäger</author>
    <author>Stefan Gall</author>
    <author>Nikolaus Weinberger</author>
    <author>Rutger Schlatmann</author>
    <author>Iver Lauermann</author>
    <author>Reiner Klenk</author>
    <author>Emil List-Kratochvil</author>
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    <title language="eng">Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates</title>
    <abstract language="eng">Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Lelièvre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The approximation error of the effective dynamics when it is used to approximate the behavior of the original dynamics has been considered in recent years. As a continuation of the previous work [F. Legoll, T. Lelièvre, and S. Olla, Stoch. Process. Appl, 2017], in this paper we obtain pathwise estimates for effective dynamics when the reaction coordinate function is either nonlinear or vector-valued.</abstract>
    <parentTitle language="eng">Multiscale Modeling and Simulation</parentTitle>
    <identifier type="arxiv">1805.01928</identifier>
    <identifier type="doi">10.1137/18M1186034</identifier>
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    <enrichment key="AcceptedDate">12.06.2019</enrichment>
    <author>Tony Lelièvre</author>
    <submitter>Wei Zhang</submitter>
    <author>Wei Zhang</author>
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    <title language="eng">Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms</title>
    <abstract language="eng">In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality.</abstract>
    <parentTitle language="eng">Journal of Statistical Physics</parentTitle>
    <identifier type="arxiv">1803.09347</identifier>
    <identifier type="doi">10.1007/s10955-019-02286-4</identifier>
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    <enrichment key="AcceptedDate">2019-04-04</enrichment>
    <author>Carsten Hartmann</author>
    <submitter>Paulina Bressel</submitter>
    <author>Christof Schütte</author>
    <author>Wei Zhang</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
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    <volume>62</volume>
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    <completedDate>2021-04-16</completedDate>
    <publishedDate>2021-04-16</publishedDate>
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    <title language="eng">Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes</title>
    <abstract language="eng">This paper studies time-inhomogeneous nonequilibrium diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy production of the time-inhomogeneous process with respect to the transient invariant probability measures. We also study the time reversal of the reverse process in Crooks' fluctuation theorem. We show that the time reversal of the reverse process coincides with the optimally controlled forward process that leads to zero variance importance sampling estimator based on Jarzynski's equality.</abstract>
    <parentTitle language="eng">Journal of Mathematical Physics</parentTitle>
    <identifier type="arxiv">2006.11212</identifier>
    <identifier type="doi">10.1063/5.0038740</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2021-03-29</enrichment>
    <author>Wei Zhang</author>
    <submitter>Wei Zhang</submitter>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
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    <id>7816</id>
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    <publishedYear>2022</publishedYear>
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    <completedDate>2022-03-17</completedDate>
    <publishedDate>2022-03-17</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Multiple projection MCMC algorithms on submanifolds</title>
    <abstract language="eng">We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for this generalization is that the numerical solvers used to project proposed moves to the submanifold of interest may find several solutions. We show that the new algorithms indeed sample the target probability measure correctly, thanks to some carefully enforced reversibility property. We demonstrate the interest of the new MCMC algorithms on illustrative numerical examples.</abstract>
    <parentTitle language="eng">IMA Journal of Numerical Analysis</parentTitle>
    <identifier type="arxiv">2003.09402</identifier>
    <identifier type="doi">10.1093/imanum/drac006</identifier>
    <enrichment key="AcceptedDate">2022/01/29</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Tony Lelievre</author>
    <submitter>Wei Zhang</submitter>
    <author>Gabriel Stoltz</author>
    <author>Wei Zhang</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
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    <volume>465</volume>
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    <completedDate>2022-06-08</completedDate>
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    <title language="eng">Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks</title>
    <abstract language="eng">In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artificial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The algorithm is useful in understanding the dynamical behaviors of metastable processes on large timescales. We demonstrate the capability of our algorithm on a high-dimensional model problem, and on the simple molecular system alanine dipeptide.</abstract>
    <parentTitle language="deu">Journal of Computational Physics</parentTitle>
    <identifier type="arxiv">2110.14523</identifier>
    <identifier type="doi">10.1016/j.jcp.2022.111377</identifier>
    <enrichment key="AcceptedDate">2022-06-07</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Wei Zhang</author>
    <submitter>Wei Zhang</submitter>
    <author>Tiejun Li</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
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    <title language="eng">Learning chemical reaction networks from trajectory data</title>
    <abstract language="eng">We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed,our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l^1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit.</abstract>
    <parentTitle language="eng">SIAM Journal on Applied Dynamical Systems (SIADS)</parentTitle>
    <identifier type="arxiv">1902.04920</identifier>
    <identifier type="doi">10.1137/19M1265880</identifier>
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    <author>Wei Zhang</author>
    <submitter>Wei Zhang</submitter>
    <author>Stefan Klus</author>
    <author>Tim Conrad</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
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    <collection role="persons" number="schuette">Schütte, Christof</collection>
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    <edition/>
    <issue>7</issue>
    <volume>11</volume>
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    <completedDate>2024-02-20</completedDate>
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    <title language="eng">EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation</title>
    <abstract language="eng">We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state (NESS) systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness, and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an 8D limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.</abstract>
    <parentTitle language="eng">National Science Review</parentTitle>
    <identifier type="doi">10.1093/nsr/nwae052</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2024-01-29</enrichment>
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    <author>Yue Zhao</author>
    <submitter>Wei Zhang</submitter>
    <author>Wei Zhang</author>
    <author>Tiejun Li</author>
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    <collection role="persons" number="zhang">Zhang, Wei</collection>
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    <title language="eng">Generative modeling of conditional probability distributions on the   level-sets of collective variables</title>
    <abstract language="eng">Given a probability distribution $\mu$ in $\mathbb{R}^d$ represented by data, we study in this paper the generative modeling of its conditional probability distributions on the level-sets of a collective variable $\xi: \mathbb{R}^d \rightarrow \mathbb{R}^k$, where $1 \le k&lt;d$. We propose a general and efficient learning approach that is able to learn generative models on different level-sets of $\xi$ simultaneously. To improve the learning quality on level-sets in low-probability regions, we also propose a strategy for data enrichment by utilizing data from enhanced sampling techniques. We demonstrate the effectiveness of our proposed learning approach through concrete numerical examples. The proposed approach is potentially useful for the generative modeling of molecular systems in biophysics, for instance.</abstract>
    <identifier type="arxiv">2512.17374</identifier>
    <enrichment key="SubmissionStatus">under review</enrichment>
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    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Fatima-Zahrae Akhyar</author>
    <submitter>Wei Zhang</submitter>
    <author>Wei Zhang</author>
    <author>Gabriel Stoltz</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
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    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
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    <completedDate>2026-01-05</completedDate>
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    <title language="eng">How nanotextured interfaces influence the electronics in perovskite solar cells</title>
    <parentTitle language="eng">EES Sol.</parentTitle>
    <identifier type="doi">10.1039/D5EL00208G</identifier>
    <identifier type="arxiv">2506.10691</identifier>
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    <enrichment key="AcceptedDate">2025-12-28</enrichment>
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    <author>Dilara Abdel</author>
    <submitter>Sven Burger</submitter>
    <author>Jacob Relle</author>
    <author>Thomas Kirchartz</author>
    <author>Patrick Jaap</author>
    <author>Jürgen Fuhrmann</author>
    <author>Sven Burger</author>
    <author>Christiane Becker</author>
    <author>Klaus Jäger</author>
    <author>Patricio Farrell</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
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    <collection role="persons" number="burger">Burger, Sven</collection>
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    <language>eng</language>
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    <issue>2</issue>
    <volume>23</volume>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2025-05-30</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On finding optimal collective variables for complex systems by minimizing the deviation between effective and full dynamics</title>
    <abstract language="eng">This paper is concerned with collective variables, or reaction coordinates, that map a discrete-in-time Markov process X_n in R^d to a (much) smaller dimension k≪d. We define the effective dynamics under a given collective variable map ξ as the best Markovian representation of X_n under ξ. The novelty of the paper is that it gives strict criteria for selecting optimal collective variables via the properties of the effective dynamics. In particular, we show that the transition density of the effective dynamics of the optimal collective variable solves a relative entropy minimization problem from certain family of densities to the transition density of X_n. We also show that many transfer operator-based data-driven numerical approaches essentially learn quantities of the effective dynamics. Furthermore, we obtain various error estimates for the effective dynamics in approximating dominant timescales / eigenvalues and transition rates of the original process X_n and how optimal collective variables minimize these errors. Our results contribute to the development of theoretical tools for the understanding of complex dynamical systems, e.g. molecular kinetics, on large timescales. These results shed light on the relations among existing data-driven numerical approaches for identifying good collective variables, and they also motivate the development of new methods.</abstract>
    <parentTitle language="eng">Multiscale Modeling and Simulation</parentTitle>
    <identifier type="arxiv">2405.02001</identifier>
    <identifier type="doi">10.1137/24M1658917</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2025-02-19</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Wei Zhang</author>
    <submitter>Wei Zhang</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="no-project">no-project</collection>
    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>10192</id>
    <completedYear>2025</completedYear>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularity</title>
    <abstract language="eng">Euclidean diffusion models have achieved remarkable success in generative modeling across diverse domains, and they have been extended to manifold case in recent advances. Instead of explicitly utilizing the structure of special manifolds as studied in previous works, we investigate direct sampling of the Euclidean diffusion models for general manifold-constrained data in this paper. We reveal the multiscale singularity of the score function in the embedded space of manifold, which hinders the accuracy of diffusion-generated samples. We then present an elaborate theoretical analysis of the singularity structure of the score function by separating it along the tangential and normal directions of the manifold. To mitigate the singularity and improve the sampling accuracy, we propose two novel methods: (1) Niso-DM, which introduces non-isotropic noise along the normal direction to reduce scale discrepancies, and (2) Tango-DM, which trains only the tangential component of the score function using a tangential-only loss function. Numerical experiments demonstrate that our methods achieve superior performance on distributions over various manifolds with complex geometries.</abstract>
    <parentTitle language="eng">NeurIPS 2025</parentTitle>
    <identifier type="arxiv">2505.09922</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="AcceptedDate">2025-09-18</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Zichen Liu</author>
    <submitter>Wei Zhang</submitter>
    <author>Wei Zhang</author>
    <author>Tiejun Li</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>7199</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>293</pageFirst>
    <pageLast>331</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal control of Markov jump processes: Asymptotic analysis, algorithms and applications to the modeling of chemical reaction systems</title>
    <abstract language="eng">Markov jump processes are widely used to model natural and engineered processes. In the context of biological or chemical applications one typically refers to the chemical master equation (CME), which models the evolution of the probability mass of any copy-number combination of the interacting particles. When many interacting particles (“species”) are considered, the complexity of the CME quickly increases, making direct numerical simulations impossible. This is even more problematic when one aims at controlling the Markov jump processes defined by the CME.&#13;
In this work, we study both open loop and feedback optimal control problems of the Markov jump processes in the case that the controls can only be switched at fixed control stages. Based on Kurtz’s limit theorems, we prove the convergence of the respective control value functions of the underlying Markov decision problem as the copy numbers of the species go to infinity. In the case of the optimal control problem on a finite time-horizon, we propose a hybrid control policy algorithm to overcome the difficulties due to the curse of dimensionality when the copy number of the involved species is large. Two numerical examples demonstrate the suitability of both the analysis and the proposed algorithms.</abstract>
    <parentTitle language="eng">Communications in Mathematical Sciences</parentTitle>
    <identifier type="doi">10.4310/CMS.2018.v16.n2.a1</identifier>
    <enrichment key="AcceptedDate">2017-08-10</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Wei Zhang</author>
    <submitter>Wei Zhang</submitter>
    <author>Carsten Hartmann</author>
    <author>Max von Kleist</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>7993</id>
    <completedYear>2020</completedYear>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>2989</pageFirst>
    <pageLast>3031</pageLast>
    <pageNumber>43</pageNumber>
    <edition/>
    <issue>6</issue>
    <volume>59</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-12-06</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Non-reversible sampling schemes on submanifolds</title>
    <abstract language="eng">Calculating averages with respect to probability measures on submanifolds is often necessary in various application areas such as molecular dynamics, computational statistical mechanics and Bayesian statistics. In recent years, various numerical schemes have been proposed in the literature to study this problem based on appropriate reversible constrained stochastic dynamics. In this paper we present and analyse a non-reversible generalisation of the projection-based scheme developed by one of the authors [ESAIM: M2AN, 54 (2020), pp. 391-430]. This scheme consists of two steps - starting from a state on the submanifold, we first update the state using a non-reversible stochastic differential equation which takes the state away from the submanifold, and in the second step we project the state back onto the manifold using the long-time limit of a ordinary differential equation. We prove the consistency of this numerical scheme and provide quantitative error estimates for estimators based on finite-time running averages. Furthermore, we present theoretical analysis which shows that this scheme outperforms its reversible counterpart in terms of asymptotic variance. We demonstrate our findings on an illustrative test example.</abstract>
    <parentTitle language="eng">SIAM Journal on Numerical Analysis</parentTitle>
    <identifier type="arxiv">2011.02835</identifier>
    <identifier type="doi">10.1137/20M1378752</identifier>
    <enrichment key="AcceptedDate">2021-06-25</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Upanshu Sharma</author>
    <submitter>Wei Zhang</submitter>
    <author>Wei Zhang</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>7210</id>
    <completedYear>2018</completedYear>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-09-24</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Ergodic SDEs on submanifolds and related numerical sampling schemes</title>
    <abstract language="eng">In many applications, it is often necessary to sample the mean value of certain quantity with respect to a probability measure $\mu$ on the level set of a smooth function ξ:R^d→R^k, 1≤k&lt;d. A specially interesting case is the so-called conditional probability measure, which is useful in the study of free energy calculation and model reduction of diffusion processes. By Birkhoff's ergodic theorem, one approach to estimate the mean value is to compute the time average along an infinitely long trajectory of an ergodic diffusion process on the level set whose invariant measure is $\mu$. Motivated by the previous work of Ciccotti, Lelièvre, and Vanden-Eijnden, as well as the work of Lelièvre, Rousset, and Stoltz, in this paper we construct a family of ergodic diffusion processes on the level set of ξ whose invariant measures coincide with the given one. For the conditional measure, in particular, we show that the corresponding SDEs of the constructed ergodic processes have relatively simple forms, and, moreover, we propose a consistent numerical scheme which samples the conditional measure asymptotically. The numerical scheme doesn't require computing the second derivatives of ξ and the error estimates of its long time sampling efficiency are obtained.</abstract>
    <parentTitle language="eng">ESAIM: Mathematical Modelling and Numerical Analysis</parentTitle>
    <identifier type="arxiv">1702.08064</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">24.09.2019</enrichment>
    <author>Wei Zhang</author>
    <submitter>Wei Zhang</submitter>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="vis">Visual Data Analysis</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>
    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>10020</id>
    <completedYear/>
    <publishedYear>2025</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">Riemannian denoising diffusion probabilistic models</title>
    <abstract language="eng">We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing methods for generative modeling on manifolds rely on substantial geometric information such as geodesic curves or eigenfunctions of the Laplace-Beltrami operator and, as a result, they are limited to manifolds where such information is available. In contrast, our method, built on a projection scheme, can be applied to more general manifolds, as it only requires being able to evaluate the value and the first order derivatives of the function that defines the submanifold. We provide a theoretical analysis of our method in the continuous-time limit, which elucidates the connection between our RDDPMs and score-based generative models on manifolds. The capability of our method is demonstrated on datasets from previous studies and on new datasets sampled from two high-dimensional manifolds, i.e. SO(10) and the configuration space of molecular system alanine dipeptide with fixed dihedral angle.</abstract>
    <parentTitle language="eng">Communications in Mathematical Sciences</parentTitle>
    <identifier type="arxiv">2505.04338</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2025-12-31</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <author>Zichen Liu</author>
    <submitter>Wei Zhang</submitter>
    <author>Wei Zhang</author>
    <author>Christof Schütte</author>
    <author>Tiejun Li</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>9246</id>
    <completedYear>2023</completedYear>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>2607</pageFirst>
    <pageLast>2631</pageLast>
    <pageNumber/>
    <edition/>
    <issue>11</issue>
    <volume>128</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Analyzing multimodal probability measures with autoencoders</title>
    <abstract language="eng">Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively used to complement and possibly bypass expert knowledge in order to construct collective variables. Our focus here is on neural network approaches based on autoencoders. We study some relevant mathematical properties of the loss function considered for training autoencoders, and provide physical interpretations based on conditional variances and minimum energy paths. We also consider various extensions in order to better describe physical systems, by incorporating more information on transition states at saddle points, and/or allowing for multiple decoders in order to describe several transition paths. Our results are illustrated on toy two dimensional systems and on alanine dipeptide.</abstract>
    <parentTitle language="eng">J. Phys. Chem. B</parentTitle>
    <identifier type="doi">10.1021/acs.jpcb.3c07075</identifier>
    <enrichment key="FulltextUrl">https://arxiv.org/abs/2310.03492</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2024-02-12</enrichment>
    <author>Tony Lelièvre</author>
    <submitter>Wei Zhang</submitter>
    <author>Thomas Pigeon</author>
    <author>Gabriel Stoltz</author>
    <author>Wei Zhang</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>6264</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>809</pageFirst>
    <pageLast>843</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>170</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Statistical analysis of the first passage path ensemble of jump processes</title>
    <abstract language="eng">The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.</abstract>
    <parentTitle language="eng">Journal of Statistical Physics</parentTitle>
    <identifier type="doi">10.1007/s10955-017-1949-x</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Max von Kleist</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <author>Wei Zhang</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="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>9226</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>23</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2023-09-19</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics</title>
    <abstract language="eng">High-dimensional metastable molecular dynamics (MD) can often be characterised by a few features of the system, that is, collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples.</abstract>
    <parentTitle language="eng">Proceedings in Applied Mathematics and Mechanics</parentTitle>
    <subTitle language="eng">Special Issue: 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)</subTitle>
    <identifier type="doi">10.1002/pamm.202300189</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Wei Zhang</author>
    <submitter>Ekaterina Engel</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="no-project">no-project</collection>
    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>6504</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>2017-10-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Variational characterization of free energy: Theory and algorithms</title>
    <abstract language="eng">The article surveys and extends variational formulations of the thermodynamic free&#13;
energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for  nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the different variational formulations for designing efficient stochastic optimization and nonequilibrium simulation algorithms for computing free energies are discussed and illustrated.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-65045</identifier>
    <author>Carsten Hartmann</author>
    <submitter>Paulina Bressel</submitter>
    <author>Lorenz Richter</author>
    <author>Christof Schütte</author>
    <author>Wei Zhang</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-52</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Importance sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Donsker-Varadhan principle</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>thermodynamic free energy</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonequilibrium molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stochastic approximation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cross-entropy method</value>
    </subject>
    <collection role="msc" number="37A60">Dynamical systems in statistical mechanics [See also 82Cxx]</collection>
    <collection role="msc" number="60J60">Diffusion processes [See also 58J65]</collection>
    <collection role="msc" number="82C05">Classical dynamic and nonequilibrium statistical mechanics (general)</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>
    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6504/ZIB-Report_17-52.pdf</file>
  </doc>
  <doc>
    <id>9452</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>e2356748</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>7-8: Giovanni Ciccotti: A Renaissance Physicist</issue>
    <volume>123</volume>
    <type>article</type>
    <publisherName>Taylor &amp; Francis</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-05-25</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Kramers turnover in terms of a macro-state projection on phase space</title>
    <abstract language="eng">We have investigated how Langevin dynamics is affected by the friction&#13;
coefficient using the novel algorithm ISOKANN, which combines the transfer&#13;
operator approach with modern machine learning techniques. ISOKANN describes&#13;
the dynamics in terms of an invariant subspace projection of the Koopman&#13;
operator defined in the entire state space, avoiding approximations due to&#13;
dimensionality reduction and discretization. Our results are consistent with&#13;
the Kramers turnover and show that in the low and moderate friction regimes,&#13;
metastable macro-states and transition rates are defined in phase space, not&#13;
only in position space.</abstract>
    <parentTitle language="eng">Molecular Physics</parentTitle>
    <identifier type="doi">10.1080/00268976.2024.2356748</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">13 May 2024</enrichment>
    <author>Luca Donati</author>
    <submitter>Luca Donati</submitter>
    <author>Christof Schütte</author>
    <author>Marcus Weber</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB-1114-B3">SFB-1114-B3</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-15">MathPlusAA1-15</collection>
    <collection role="persons" number="donati">Donati, Luca</collection>
  </doc>
  <doc>
    <id>10308</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
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    <completedDate>--</completedDate>
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    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Eikonal Approach for Globally Optimal Free Flight Trajectories</title>
    <abstract language="eng">We present an eikonal-based approach that is capable of finding a continuous globally optimal trajectory for an aircraft in a stationary wind field. This minimizes emissions and fuel consumption. If the destination is close to a cut locus of the associated Hamilton-Jacobi-Bellman equation, small numerical discretization errors can lead to selecting a merely locally optimal trajectory and missing the globally optimal one. Based on finite element error estimates, we construct a trust region around the cut loci in order to guarantee uniqueness of trajectories for destinations sufficiently far from cut loci.</abstract>
    <identifier type="arxiv">2603.11830</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Martin Weiser</submitter>
    <author>Arturas Jocas</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
    <collection role="persons" number="jocas">Jocas, Arturas</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>10291</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>095004</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>37</volume>
    <type>article</type>
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    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Photomask linewidth measurement comparison including an improved model-based through-focus measurement approach</title>
    <parentTitle language="eng">Meas. Sci. Technol.</parentTitle>
    <identifier type="doi">10.1088/1361-6501/ae44bb</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2026-02-11</enrichment>
    <author>Jan Krüger</author>
    <submitter>Sven Burger</submitter>
    <author>Sven Dopslaff</author>
    <author>Phillip Manley</author>
    <author>Detlef Bergmann</author>
    <author>Rainer Köning</author>
    <author>Gaoliang Dai</author>
    <author>Kai Hahm</author>
    <author>Philipp-Immanuel Schneider</author>
    <author>Martin Hammerschmidt</author>
    <author>Lin Zschiedrich</author>
    <author>Harald Bosse</author>
    <author>Bernd Bodermann</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <collection role="persons" number="hammerschmidt">Hammerschmidt, Martin</collection>
    <collection role="persons" number="zschiedrich">Zschiedrich, Lin Werner</collection>
    <collection role="persons" number="schneider">Schneider, Philipp-Immanuel</collection>
    <collection role="persons" number="manley">Manley, Phillip</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="CNO-SEQUME">CNO-SEQUME</collection>
  </doc>
  <doc>
    <id>9835</id>
    <completedYear>2025</completedYear>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>98</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2026-01-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Field theories and quantum methods for stochastic reaction-diffusion systems</title>
    <abstract language="eng">Complex systems are composed of many particles or agents that move and interact with one another. In most real-world applications, these systems involve a varying number of particles/agents that change due to interactions with the environment or their internal dynamics. The underlying mathematical framework to model these systems must incorporate the spatial transport of particles/agents and their interactions, as well as changes to their copy numbers, all of which can be formulated in terms of stochastic reaction-diffusion processes. However, the standard probabilistic representation of these processes can be overly complex because of the combinatorial aspects arising due to the non-linear interactions and varying particle numbers. In this manuscript, we review the main field theory representations of stochastic reaction-diffusion systems, which handle these issues "under–the–hood’’. First, we focus on bringing techniques familiar to theoretical physicists —such as second quantization, Fock space, path integrals and quantum field theory— back into the classical domain of reaction-diffusion systems. We demonstrate how various field theory representations, which have evolved historically, can all be unified under a single basis-independent representation. We then extend existing quantum-based methods and notation to work directly on the level of the unifying representation, and we illustrate how they can be used to consistently obtain previous known results in a more straightforward manner, such as numerical discretizations and relations between model parameters at multiple scales. Throughout the work, we contextualize how these representations mirror well-known models of chemical physics depending on their spatial resolution, as well as the corresponding macroscopic (large copy number) limits. The framework presented here may find applications in a diverse set of scientific fields, including physical chemistry, theoretical ecology, epidemiology, game theory and socio-economical models of complex systems, specifically in the modeling and multi-scale simulation of complex systems with varying numbers of particles/agents. The presentation is done in a self-contained educational and unifying manner such that it can be followed by researchers across several fields.</abstract>
    <parentTitle language="eng">Rev. Mod. Phys.</parentTitle>
    <identifier type="arxiv">2409.13377</identifier>
    <identifier type="doi">10.1103/9qlw-gyd7</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">09.10.2025</enrichment>
    <author>Mauricio del Razo</author>
    <submitter>Mauricio del Razo</submitter>
    <author>Tommaso Lamma</author>
    <author>Wout Merbis</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="delrazo">del Razo Sarmina, Mauricio</collection>
    <collection role="projects" number="DFG-OpenMultiscaleBiochem">DFG-OpenMultiscaleBiochem</collection>
  </doc>
  <doc>
    <id>9996</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Reconstructing sudden ambient temperature changes for forensic death time estimation using temperatures in two closed compartments: Proof of concept</title>
    <abstract language="eng">Ambient temperature TA has a strong impact on temperature-based time since death estimation (TTDE). Frequently TA is lowered instantaneously at some time t0 from a previous value TA0 to TA1 &lt; TA0 by, e.g., opening a window or a door. We aim at reconstructing TA0 and t0. &#13;
TTDE literature suggests temperature measurements in closed compartments such as cupboards or neighboring rooms, where TA0 could have been ‘preserved’ after t0. We aim to estimate t0 and TA0 from temperature measurements TZ(t) in closed compartments Z at times t &gt; t0. &#13;
We obtain promising results assuming Newtonian cooling for boxes filled with air, heaps of clothes, or books in two different experimental scenarios. Two different parameter estimators, (TA0^, t0^) based on four temperature measurements and (TA0*, t0*) for 4N measurements were tested.&#13;
Our results in a climate chamber were partially appropriate for TTDE input. A decline at time t0 from TA0 = 22.5°C ↓ TA1 = 14°C was reconstructed at t = t0 + 95min with relative deviations ρt0^ = 27% and ρTA0^ = 19% relative to t - t0 and TA0 – TA1 respectively, for N = 1 with span Δt = 50min. For N = 200 in a time interval [t0 + 95min, t0  + 295min] we found ρt0^ = 5% and ρTA0^ = 11% with the same Δt. &#13;
Further research is necessary to guarantee applicability in routine casework, in particular with respect to more elaborate cooling models, estimation algorithms, and evaluation localization.</abstract>
    <parentTitle language="deu">International Journal of Legal Medicine</parentTitle>
    <identifier type="old">bioRXiv https://doi.org/10.1101/2025.11.14.688394</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2026-03-08</enrichment>
    <author>Jayant Shanmugam Subramaniam</author>
    <submitter>Martin Weiser</submitter>
    <author>Michael Hubig</author>
    <author>Sebastian Schenkl</author>
    <author>Holger Muggenthaler</author>
    <author>Steffen Springer</author>
    <author>Martin Weiser</author>
    <author>Jakob Sudau</author>
    <author>Faisal Shah</author>
    <author>Gita Mall</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="UJena-Forensic">UJena-Forensic</collection>
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    <collection role="persons" number="sudau">Sudau, Jakob</collection>
    <collection role="persons" number="shah">Shah, Faisal</collection>
  </doc>
  <doc>
    <id>10311</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
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    <pageLast/>
    <pageNumber/>
    <edition/>
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    <completedDate>--</completedDate>
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    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Gaussian mixture models for model improvement</title>
    <abstract language="eng">Modeling complex physical systems such as they arise in civil engineering applications requires finding a trade-off between physical fidelity and practicality. Consequently, deviations of simulation from measurements are ubiquitous even after model calibration due to the model discrepancy, which may result from deliberate modeling decisions, ignorance, or lack of knowledge.&#13;
&#13;
If the mismatch between simulation and measurements are deemed unacceptable, the model has to be improved. Targeted model improvement is challenging due to a non-local impact of model discrepancies on measurements and the dependence on sensor configurations. Many approaches to model improvement, such as Bayesian calibration with additive mismatch terms, gray-box models, symbolic regression, or stochastic model updating, often lack interpretability, generalizability, physical consistency, or practical applicability.&#13;
    &#13;
This paper introduces a non-intrusive approach to model discrepancy analysis using mixture models. Instead of directly modifying the model structure, the method maps sensor readings to clusters of physically meaningful parameters, automatically assigning sensor readings to parameter vector clusters. This mapping can reveal systematic discrepancies and model biases, guiding targeted, physics-based refinements by the modeler. The approach is formulated within a Bayesian framework, enabling the identification of parameter clusters and their assignments via the Expectation-Maximization (EM) algorithm.&#13;
&#13;
The methodology is demonstrated through numerical experiments, including an illustrative example and a real-world case study of heat transfer in a concrete bridge.</abstract>
    <identifier type="arxiv">2603.15101</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>Paolo Villani</author>
    <submitter>Martin Weiser</submitter>
    <author>Daniel Andrés Arcones</author>
    <author>Jörg F. Unger</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="villani">Villani, Paolo</collection>
    <collection role="projects" number="DigitalTwins">DigitalTwins</collection>
  </doc>
  <doc>
    <id>10267</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>2380</pageFirst>
    <pageLast>2389</pageLast>
    <pageNumber/>
    <edition/>
    <issue>5</issue>
    <volume>22</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2026-02-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Revealing the Atomistic Mechanism of Rare Events in Molecular Dynamics</title>
    <abstract language="eng">Interpretable reaction coordinates are essential for understanding rare conformational transitions in molecular dynamics. The Atomistic Mechanism Of Rare Events in Molecular Dynamics (AMORE-MD) framework enhances interpretability of deep-learned reaction coordinates by connecting them to atomistic mechanisms, without requiring any a priori knowledge of collective variables, pathways, or endpoints. Here, AMORE-MD employs the ISOKANN algorithm to learn a neural membership function χ representing the dominant slow process, from which transition pathways are reconstructed as minimum-energy paths aligned with the gradient of χ, and atomic contributions are quantified through gradient-based sensitivity analysis. Iterative enhanced sampling further enriches transition regions and improves coverage of rare events enabling recovery of known mechanisms and chemically interpretable structural rearrangements at atomic resolution for the Müller-Brown potential, alanine dipeptide, and the elastin-derived hexapeptide VGVAPG.</abstract>
    <parentTitle language="eng">Journal of Chemical Theory and Computation</parentTitle>
    <identifier type="arxiv">2511.15514</identifier>
    <identifier type="doi">10.1021/acs.jctc.5c01906</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Jakob Kresse</author>
    <submitter>Alexander Sikorski</submitter>
    <author>Alexander Sikorski</author>
    <author>Surahit Chewle</author>
    <author>Vikram Sunkara</author>
    <author>Marcus Weber</author>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="persons" number="sunkara">Sunkara, Vikram</collection>
    <collection role="persons" number="sikorski">Sikorski, Alexander</collection>
    <collection role="projects" number="SFB-1114-B3">SFB-1114-B3</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="chewle">Chewle, Surahit</collection>
    <collection role="persons" number="kresse">Kresse, Jakob</collection>
  </doc>
  <doc>
    <id>10286</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>173</volume>
    <type>incollection</type>
    <publisherName>Springer Nature</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Identification of Stress in Heterogeneous Contact Models</title>
    <abstract language="eng">We develop a heterogeneous model of the lower limb system to simulate muscle forces and stresses acting on the knee joint. The modelling of the bone dynamics leads to an index-3 DAE, which we discretize by higher order collocation methods. Furthermore, we present an elastomechanical contact knee joint model of the articular cartilage. For the solution of the contact problem we develop an efficient multigrid solver, based on an Augmented-Lagrangian relaxation of the contact constraints. We formulate the identification of joint forces and resulting stresses with respect to different knee joint models as an inverse problem based on&#13;
medical gait data.</abstract>
    <parentTitle language="eng">Non-Smooth and Complementarity-Based Distributed Parameter Systems</parentTitle>
    <subTitle language="deu">Simulation and Hierarchical Optimization, Part II</subTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2024-03-07</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="Series">International Series of Numerical Mathematics</enrichment>
    <author>Felix Baumann</author>
    <submitter>Martin Weiser</submitter>
    <editor>Michael Hintermüller</editor>
    <author>Georg Duda</author>
    <editor>Roland Herzog</editor>
    <author>Anton Schiela</author>
    <editor>Christian Kanzow</editor>
    <author>Martin Weiser</author>
    <editor>Michael Ulbrich</editor>
    <editor>Stefan Ulbrich</editor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="persons" number="felix.baumann">Baumann, Felix</collection>
    <collection role="projects" number="2020-SPP1962">2020-SPP1962</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>10294</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>arXiv:2602.18414</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Pole-Expansion of the T-Matrix Based on a Matrix-Valued AAA-Algorithm</title>
    <parentTitle language="eng">ArXiV</parentTitle>
    <identifier type="doi">10.48550/arXiv.2602.18414</identifier>
    <identifier type="arxiv">2602.18414</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Jan David Fischbach</author>
    <submitter>Sven Burger</submitter>
    <author>Fridtjof Betz</author>
    <author>Lukas Rebholz</author>
    <author>Puneet Garg</author>
    <author>Kristina Frizyuk</author>
    <author>Felix Binkowski</author>
    <author>Sven Burger</author>
    <author>Martin Hammerschmidt</author>
    <author>Carsten Rockstuhl</author>
    <collection role="persons" number="burger">Burger, Sven</collection>
    <collection role="persons" number="hammerschmidt">Hammerschmidt, Martin</collection>
    <collection role="persons" number="binkowski">Binkowski, Felix</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="betz">Betz, Fridtjof</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="CNO-MODAL-NANOLAB">CNO-MODAL-NANOLAB</collection>
    <collection role="projects" number="CNO-MATHPLUS-AA-ENER-1">CNO-MATHPLUS-AA-ENER-1</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>
  <doc>
    <id>10262</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
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    <type>article</type>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Data-driven Reduction of Transfer Operators for Particle Clustering   Dynamics</title>
    <abstract language="eng">We develop an operator-based framework to coarse-grain interacting particle systems that exhibit clustering dynamics. Starting from the particle-based transfer operator, we first construct a sequence of reduced representations: the operator is projected onto concentrations and then further reduced by representing the concentration dynamics on a geometric low-dimensional manifold and an adapted finite-state discretization. The resulting coarse-grained transfer operator is finally estimated from dynamical simulation data by inferring the transition probabilities between the Markov states. Applied to systems with multichromatic and Morse interaction potentials, the reduced model reproduces key features of the clustering process, including transitions between cluster configurations and the emergence of metastable states. Spectral analysis and transition-path analysis of the estimated operator reveal implied time scales and dominant transition pathways, providing an interpretable and efficient description of particle-clustering dynamics.</abstract>
    <identifier type="arxiv">2601.02932</identifier>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Nathalie Wehlitz</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Grigorios Pavliotis</author>
    <author>Christof Schütte</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="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</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="unger">Unger, Nathalie</collection>
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  <doc>
    <id>10314</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
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    <title language="eng">On-the-Fly Lifting of Coarse Reaction-Coordinate Paths to Full-Dimensional Transition Path Ensembles</title>
    <abstract language="eng">Effective dynamics on a low-dimensional collective-variable (CV) or latent space can be simulated far more cheaply than the underlying high-dimensional stochastic system, but exploiting such coarse predictions requires lifting: turning a coarse CV trajectory into dynamically consistent full-dimensional states and path ensembles, without relying on global sampling of invariant or conditional fiber measures. We present a local, on-the-fly lifting strategy based on guided full-system trajectories. First an effective model in CV space is used to obtain a coarse reference trajectory. Then, an ensemble of full-dimensional trajectories is generated from a guided version of the original dynamics, where the guidance steers the trajectory to track the CV reference path. Because guidance biases the path distribution, we correct it via pathwise Girsanov reweighting, yielding a correct-by-construction importance-sampling approximation of the conditional law of the uncontrolled dynamics. We further connect the approach to stochastic optimal control, clarifying how coarse models can inform variance-reducing guidance for rare-event quantities. Numerical experiments demonstrate that inexpensive coarse transition paths can be converted into realistic full-system transition pathways (including barrier crossings and detours) and can accelerate estimation of transition pathways and statistics while providing minimal bias through weighted ensembles.</abstract>
    <identifier type="doi">10.48550/arXiv.2603.23266</identifier>
    <identifier type="arxiv">2603.23266</identifier>
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    <author>Christof Schütte</author>
    <submitter>Alexander Sikorski</submitter>
    <author>Alexander Sikorski</author>
    <author>Jakob Kresse</author>
    <author>Marcus Weber</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="persons" number="sikorski">Sikorski, Alexander</collection>
    <collection role="projects" number="SFB-1114-B3">SFB-1114-B3</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="kresse">Kresse, Jakob</collection>
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