@article{19937, abstract = {{Symplectic integrators can be excellent for Hamiltonian initial value problems. Reasons for this include their preservation of invariant sets like tori, good energy behaviour, nonexistence of attractors, and good behaviour of statistical properties. These all refer to {\em long-time} behaviour. They are directly connected to the dynamical behaviour of symplectic maps φ:M→M' on the phase space under iteration. Boundary value problems, in contrast, are posed for fixed (and often quite short) times. Symplecticity manifests as a symplectic map φ:M→M' which is not iterated. Is there any point, therefore, for a symplectic integrator to be used on a Hamiltonian boundary value problem? In this paper we announce results that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not.}}, author = {{McLachlan, Robert I and Offen, Christian}}, issn = {{1017-1398}}, journal = {{Numerical Algorithms}}, pages = {{1219--1233}}, title = {{{Symplectic integration of boundary value problems}}}, doi = {{10.1007/s11075-018-0599-7}}, year = {{2018}}, } @unpublished{21634, abstract = {{Predictive control of power electronic systems always requires a suitable model of the plant. Using typical physics-based white box models, a trade-off between model complexity (i.e. accuracy) and computational burden has to be made. This is a challenging task with a lot of constraints, since the model order is directly linked to the number of system states. Even though white-box models show suitable performance in most cases, parasitic real-world effects often cannot be modeled satisfactorily with an expedient computational load. Hence, a Koopman operator-based model reduction technique is presented which directly links the control action to the system's outputs in a black-box fashion. The Koopman operator is a linear but infinite-dimensional operator describing the dynamics of observables of nonlinear autonomous dynamical systems which can be nicely applied to the switching principle of power electronic devices. Following this data-driven approach, the model order and the number of system states are decoupled which allows us to consider more complex systems. Extensive experimental tests with an automotive-type permanent magnet synchronous motor fed by an IGBT 2-level inverter prove the feasibility of the proposed modeling technique in a finite-set model predictive control application.}}, author = {{Hanke, Sören and Peitz, Sebastian and Wallscheid, Oliver and Klus, Stefan and Böcker, Joachim and Dellnitz, Michael}}, booktitle = {{arXiv:1804.00854}}, title = {{{Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives}}}, year = {{2018}}, } @article{21940, author = {{Litzinger, Florian and Boninsegna, Lorenzo and Wu, Hao and Nüske, Feliks and Patel, Raajen and Baraniuk, Richard and Noé, Frank and Clementi, Cecilia}}, issn = {{1549-9618}}, journal = {{Journal of Chemical Theory and Computation}}, pages = {{2771--2783}}, title = {{{Rapid Calculation of Molecular Kinetics Using Compressed Sensing}}}, doi = {{10.1021/acs.jctc.8b00089}}, year = {{2018}}, } @article{21941, author = {{Klus, Stefan and Nüske, Feliks and Koltai, Péter and Wu, Hao and Kevrekidis, Ioannis and Schütte, Christof and Noé, Frank}}, issn = {{0938-8974}}, journal = {{Journal of Nonlinear Science}}, pages = {{985--1010}}, title = {{{Data-Driven Model Reduction and Transfer Operator Approximation}}}, doi = {{10.1007/s00332-017-9437-7}}, year = {{2018}}, } @article{21942, author = {{Boninsegna, Lorenzo and Nüske, Feliks and Clementi, Cecilia}}, issn = {{0021-9606}}, journal = {{The Journal of Chemical Physics}}, title = {{{Sparse learning of stochastic dynamical equations}}}, doi = {{10.1063/1.5018409}}, year = {{2018}}, } @article{21943, author = {{Hruska, Eugen and Abella, Jayvee R. and Nüske, Feliks and Kavraki, Lydia E. and Clementi, Cecilia}}, issn = {{0021-9606}}, journal = {{The Journal of Chemical Physics}}, title = {{{Quantitative comparison of adaptive sampling methods for protein dynamics}}}, doi = {{10.1063/1.5053582}}, year = {{2018}}, } @inproceedings{7766, author = {{Schumacher, Jan}}, booktitle = {{Beiträge zum Mathematikunterricht 2018}}, publisher = {{WTM-Verlag}}, title = {{{Semiotische Analyse von Sinnkonstruktionsprozessen bei einem innermathematischen Zugang zum Erlernen negativer Zahlen}}}, year = {{2018}}, } @inbook{8573, author = {{Liebendörfer, Michael}}, booktitle = {{Beiträge zum Mathematikunterricht 2018}}, editor = {{Didaktik der Mathematik der Universität Paderborn, Fachgruppe}}, pages = {{1171--1174}}, publisher = {{WTM-Verlag}}, title = {{{Psychologische Grundbedürfnisse im frühen Mathematikstudium}}}, year = {{2018}}, } @inbook{8574, author = {{Liebendörfer, Michael and Kuklinski, Christiane and Hochmuth, Reinhard}}, booktitle = {{Beiträge zum Mathematikunterricht 2018}}, editor = {{Didaktik der Mathematik der Universität Paderborn, Fachgruppe}}, pages = {{1175--1178}}, publisher = {{WTM-Verlag}}, title = {{{Auswirkungen von innovativen Vorlesungen für Lehramtsstudierende in der Studieneingangsphase}}}, year = {{2018}}, } @book{8576, author = {{Liebendörfer, Michael}}, isbn = {{978-3-658-22506-3 978-3-658-22507-0}}, publisher = {{Springer Fachmedien Wiesbaden}}, title = {{{Motivationsentwicklung im Mathematikstudium}}}, doi = {{10.1007/978-3-658-22507-0}}, year = {{2018}}, } @inproceedings{8750, abstract = {{In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example.}}, author = {{Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}}, booktitle = {{Numerical and Evolutionary Optimization – NEO 2017}}, isbn = {{9783319961033}}, issn = {{1860-949X}}, title = {{{A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems}}}, doi = {{10.1007/978-3-319-96104-0_2}}, year = {{2018}}, } @article{8751, abstract = {{Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.}}, author = {{Peitz, Sebastian and Dellnitz, Michael}}, issn = {{2297-8747}}, journal = {{Mathematical and Computational Applications}}, number = {{2}}, title = {{{A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction}}}, doi = {{10.3390/mca23020030}}, volume = {{23}}, year = {{2018}}, } @inbook{8754, abstract = {{In this chapter, we combine a global, derivative-free subdivision algorithm for multiobjective optimization problems with a posteriori error estimates for reduced-order models based on Proper Orthogonal Decomposition in order to efficiently solve multiobjective optimization problems governed by partial differential equations. An error bound for a semilinear heat equation is developed in such a way that the errors in the conflicting objectives can be estimated individually. The resulting algorithm constructs a library of locally valid reduced-order models online using a Greedy (worst-first) search. Using this approach, the number of evaluations of the full-order model can be reduced by a factor of more than 1000.}}, author = {{Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}}, booktitle = {{Reduced-Order Modeling (ROM) for Simulation and Optimization}}, isbn = {{9783319753188}}, pages = {{47--72}}, title = {{{Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition}}}, doi = {{10.1007/978-3-319-75319-5_3}}, year = {{2018}}, } @article{8755, abstract = {{Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially high-dimensional data sets to compute the corresponding DMD modes and eigenvalues. The goal is to reduce the computational complexity and also the amount of memory required to store the data in order to mitigate the curse of dimensionality. The efficiency of these tensor-based methods will be illustrated with the aid of several different fluid dynamics problems such as the von Kármán vortex street and the simulation of two merging vortices.}}, author = {{Klus, Stefan and Gelß, Patrick and Peitz, Sebastian and Schütte, Christof}}, issn = {{0951-7715}}, journal = {{Nonlinearity}}, number = {{7}}, pages = {{3359--3380}}, title = {{{Tensor-based dynamic mode decomposition}}}, doi = {{10.1088/1361-6544/aabc8f}}, volume = {{31}}, year = {{2018}}, } @inproceedings{8757, abstract = {{A framework for set‐oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed [1]. Following concepts from localized reduced bases methods, error estimators for the reduced cost functionals are utilized to construct a library of locally valid reduced order models. This way, a superset of the Pareto set can efficiently be computed while maintaining a prescribed error bound. In this article, this algorithm is applied to a problem with non‐smooth objective functionals. Using an academic example, we show that the extension to non‐smooth problems can be realized in a straightforward manner. We then discuss the implications on the numerical results.}}, author = {{Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}}, booktitle = {{PAMM}}, issn = {{1617-7061}}, pages = {{51--54}}, title = {{{POD-based multiobjective optimal control of PDEs with non-smooth objectives}}}, doi = {{10.1002/pamm.201710015}}, year = {{2018}}, } @misc{6595, author = {{Feldmann, Nadine and Jurgelucks, Benjamin and Claes, Leander and Henning, Bernd}}, title = {{{Vollständige Charakterisierung von piezoelektrischen Scheiben mit Ringelektroden}}}, year = {{2018}}, } @article{16713, author = {{Gölz, Christian and Voelcker-Rehage, Claudia and Mora, Karin and Reuter, Eva-Maria and Godde, Ben and Dellnitz, Michael and Reinsberger, Claus and Vieluf, Solveig}}, issn = {{1664-042X}}, journal = {{Frontiers in Physiology}}, title = {{{Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics}}}, doi = {{10.3389/fphys.2018.01540}}, year = {{2018}}, } @article{16714, author = {{Vieluf, Solveig and Mora, Karin and Gölz, Christian and Reuter, Eva-Maria and Godde, Ben and Dellnitz, Michael and Reinsberger, Claus and Voelcker-Rehage, Claudia}}, issn = {{0306-4522}}, journal = {{Neuroscience}}, pages = {{203--213}}, title = {{{Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control}}}, doi = {{10.1016/j.neuroscience.2018.07.025}}, year = {{2018}}, } @article{16715, author = {{Bittracher, Andreas and Koltai, Péter and Klus, Stefan and Banisch, Ralf and Dellnitz, Michael and Schütte, Christof}}, issn = {{0938-8974}}, journal = {{Journal of Nonlinear Science}}, pages = {{471--512}}, title = {{{Transition Manifolds of Complex Metastable Systems}}}, doi = {{10.1007/s00332-017-9415-0}}, volume = {{28}}, year = {{2018}}, } @unpublished{16292, abstract = {{In a recent article, we presented a framework to control nonlinear partial differential equations (PDEs) by means of Koopman operator based reduced models and concepts from switched systems. The main idea was to transform a control system into a set of autonomous systems for which the optimal switching sequence has to be computed. These individual systems can be approximated very efficiently by reduced order models obtained from data, and one can guarantee equality of the full and the reduced objective function under certain assumptions. In this article, we extend these results to continuous control inputs using convex combinations of multiple Koopman operators corresponding to constant controls, which results in a bilinear control system. Although equality of the objectives can be carried over when the PDE depends linearly on the control, we show that this approach is also valid in other scenarios using several flow control examples of varying complexity.}}, author = {{Peitz, Sebastian}}, booktitle = {{arXiv:1801.06419}}, title = {{{Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from data}}}, year = {{2018}}, }