@article{33481,
abstract = {{While 2D Gibbsian particle systems might exhibit orientational order resulting in a lattice-like structure, these particle systems do not exhibit positional order if the interaction between particles satisfies some weak assumptions. Here we investigate to which extent particles within a box of size may fluctuate from their ideal lattice position. We show that particles near the center of the box typically show a displacement at least of order . Thus we extend recent results on the hard disk model to particle systems with fairly arbitrary particle spins and interaction. Our result applies to models such as rather general continuum Potts type models, e.g. with Widom–Rowlinson or Lenard-Jones-type interaction.}},
author = {{Richthammer, Thomas and Fiedler, Michael}},
journal = {{Stochastic Processes and their Applications}},
pages = {{1--32}},
publisher = {{Elsevier}},
title = {{{A lower bound on the displacement of particles in 2D Gibbsian particle systems}}},
doi = {{https://doi.org/10.1016/j.spa.2020.10.003}},
volume = {{132}},
year = {{2021}},
}
@inproceedings{21572,
author = {{Ridderbusch, Steffen and Offen, Christian and Ober-Blöbaum, Sina and Goulart, Paul}},
booktitle = {{2021 60th IEEE Conference on Decision and Control (CDC)}},
location = {{Austin, TX, USA}},
pages = {{2896}},
publisher = {{IEEE}},
title = {{{Learning ODE Models with Qualitative Structure Using Gaussian Processes }}},
doi = {{10.1109/CDC45484.2021.9683426}},
year = {{2021}},
}
@inproceedings{29868,
author = {{Jiménez, F. and Ober-Blöbaum, Sina}},
booktitle = {{Nichtlineare Sci}},
title = {{{Fractional Damping Through Restricted Calculus of Variations}}},
volume = {{31}},
year = {{2021}},
}
@phdthesis{32057,
abstract = {{Ein zentraler Aspekt bei der Untersuchung dynamischer Systeme ist die Analyse ihrer invarianten Mengen wie des globalen Attraktors und (in)stabiler Mannigfaltigkeiten. Insbesondere wenn das zugrunde liegende System von einem Parameter abhängt, ist es entscheidend, sie im Bezug auf diesen Parameter effizient zu verfolgen. Für die Berechnung invarianter Mengen stützen wir uns für ihre Approximation auf numerische Algorithmen. Typischerweise können diese Methoden jedoch nur auf endlich-dimensionale dynamische Systeme angewendet werden. In dieser Arbeit präsentieren wir daher einen numerischen Rahmen für die globale dynamische Analyse unendlich-dimensionaler Systeme. Wir werden Einbettungstechniken verwenden, um das core dynamical system (CDS) zu definieren, welches ein dynamisch äquivalentes endlich-dimensionales System ist.Das CDS wird dann verwendet, um eingebettete invariante Mengen, also eins-zu-eins Bilder, mittels Mengen-orientierten numerischen Methoden zu approximieren. Bei der Konstruktion des CDS ist es entscheidend, eine geeignete Beobachtungsabbildung auszuwählen und die geeignete inverse Abbildung zu entwerfen. Dazu werden wir geeignete numerische Implementierungen des CDS für DDEs und PDEs vorstellen. Für eine nachfolgende geometrische Analyse der eingebetteten invarianten Menge betrachten wir eine Lerntechnik namens diffusion maps, die ihre intrinsische Geometrie enthüllt sowie ihre Dimension schätzt. Schließlich wenden wir unsere entwickelten numerischen Methoden an einigen bekannten unendlich-dimensionale dynamischen Systeme an, wie die Mackey-Glass-Gleichung, die Kuramoto-Sivashinsky-Gleichung und die Navier-Stokes-Gleichung.}},
author = {{Gerlach, Raphael}},
title = {{{The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems}}},
doi = {{10.17619/UNIPB/1-1278}},
year = {{2021}},
}
@article{32016,
author = {{Delarue, Benjamin and Ramacher, Pablo}},
journal = {{Journal of Symplectic Geometry}},
number = {{6}},
pages = {{1281 -- 1337}},
title = {{{Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions}}},
doi = {{10.4310/JSG.2021.v19.n6.a1}},
volume = {{19}},
year = {{2021}},
}
@article{34042,
author = {{Li, Jiaao and Ma, Yulai and Miao, Zhengke and Shi, Yongtang and Wang, Weifan and Zhang, Cun-Quan}},
issn = {{0095-8956}},
journal = {{Journal of Combinatorial Theory, Series B}},
keywords = {{Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Theoretical Computer Science}},
pages = {{61--80}},
publisher = {{Elsevier BV}},
title = {{{Nowhere-zero 3-flows in toroidal graphs}}},
doi = {{10.1016/j.jctb.2021.11.001}},
volume = {{153}},
year = {{2021}},
}
@inproceedings{31583,
author = {{Hattermann, M. and Häsel-Weide, Uta and Wallner, Melina}},
booktitle = {{Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education }},
editor = {{Inprasitha, M. and Changsri, N. and Boonsena, N.}},
pages = {{9--15}},
title = {{{Conceptualiziation processes of 6th graders for rotational symmetry}}},
volume = {{3}},
year = {{2021}},
}
@inbook{34161,
author = {{Häsel-Weide, Uta and Rezat, Sebastian and Schacht, F.}},
booktitle = {{Mathematics Education in the Digital Age. Learning, Practice and Theory}},
editor = {{Clark-Wilson, A. and Donevska-Todorova, A. and Faggiano, E. and Trgalová , J. and Weigang, H.-G.}},
pages = {{168--184}},
publisher = {{Routledge}},
title = {{{Challenges of making sense of tasks and automated feedback in digital mathematics textbooks}}},
year = {{2021}},
}
@article{19938,
abstract = {{We show that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not. We provide a universal description of the breaking of umbilic bifurcations by nonysmplectic integrators. We discover extra structure induced from certain types of boundary value problems, including classical Dirichlet problems, that is useful to locate bifurcations. Geodesics connecting two points are an example of a Hamiltonian boundary value problem, and we introduce the jet-RATTLE method, a symplectic integrator that easily computes geodesics and their bifurcations. Finally, we study the periodic pitchfork bifurcation, a codimension-1 bifurcation arising in integrable Hamiltonian systems. It is not preserved by either symplectic on nonsymplectic integrators, but in some circumstances symplecticity greatly reduces the error. }},
author = {{McLachlan, Robert I and Offen, Christian}},
journal = {{Foundations of Computational Mathematics}},
number = {{6}},
pages = {{1363--1400}},
title = {{{Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation}}},
doi = {{10.1007/s10208-020-09454-z}},
volume = {{20}},
year = {{2020}},
}
@article{19939,
author = {{Kreusser, Lisa Maria and McLachlan, Robert I and Offen, Christian}},
issn = {{0951-7715}},
journal = {{Nonlinearity}},
number = {{5}},
pages = {{2335--2363}},
title = {{{Detection of high codimensional bifurcations in variational PDEs}}},
doi = {{10.1088/1361-6544/ab7293}},
volume = {{33}},
year = {{2020}},
}
@inbook{17411,
abstract = {{Many dynamical systems possess symmetries, e.g. rotational and translational invariances of mechanical systems. These can be beneficially exploited in the design of numerical optimal control methods. We present a model predictive control scheme which is based on a library of precomputed motion primitives. The primitives are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim primitives as relative equilibria w.r.t. this symmetry, play a crucial role in the algorithm. The approach is illustrated using an academic mobile robot example.}},
author = {{Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Peitz, Sebastian}},
booktitle = {{Advances in Dynamics, Optimization and Computation}},
editor = {{Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}},
isbn = {{9783030512637}},
issn = {{2198-4182}},
publisher = {{Springer}},
title = {{{Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach}}},
doi = {{10.1007/978-3-030-51264-4_9}},
year = {{2020}},
}
@article{21819,
abstract = {{Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We propose a kernel-based method for the approximation of differential operators in reproducing kernel Hilbert spaces and show how eigenfunctions can be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms are applied to molecular dynamics and quantum chemistry examples. Furthermore, we exploit that, under certain conditions, the Schrödinger operator can be transformed into a Kolmogorov backward operator corresponding to a drift-diffusion process and vice versa. This allows us to apply methods developed for the analysis of high-dimensional stochastic differential equations to quantum mechanical systems.}},
author = {{Klus, Stefan and Nüske, Feliks and Hamzi, Boumediene}},
issn = {{1099-4300}},
journal = {{Entropy}},
title = {{{Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator}}},
doi = {{10.3390/e22070722}},
year = {{2020}},
}
@article{16961,
author = {{Liebendörfer, Michael and Göller, Robin and Biehler, Rolf and Hochmuth, Reinhard and Kortemeyer, Jörg and Ostsieker, Laura and Rode, Jana and Schaper, Niclas}},
issn = {{0173-5322}},
journal = {{Journal für Mathematik-Didaktik}},
title = {{{LimSt – Ein Fragebogen zur Erhebung von Lernstrategien im mathematikhaltigen Studium}}},
doi = {{10.1007/s13138-020-00167-y}},
year = {{2020}},
}
@inbook{16963,
author = {{Kuklinski, Christiane and Leis, Elena and Liebendörfer, Michael and Hochmuth, Reinhard}},
booktitle = {{Beiträge zum {Mathematikunterricht} 2019 53. {Jahrestagung} der {Gesellschaft} für {Didaktik} der {Mathematik}.}},
editor = {{Frank, Andreas and Krauss, Stefan and Binder, Karin}},
publisher = {{WTM-Verlag}},
title = {{{Erklärung von Mathematikleistung im Ingenieursstudium}}},
year = {{2020}},
}
@article{16964,
author = {{Hochmuth, Reinhard and Liebendörfer, Michael and Biehler, Rolf and Eichler, Andreas}},
journal = {{Neues Handbuch Hochschullehre}},
pages = {{117--138}},
title = {{{Das Kompetenzzentrum Hochschuldidaktik Mathematik (khdm)}}},
volume = {{95}},
year = {{2020}},
}
@article{16965,
author = {{Schürmann, Mirko and Schaper, Niclas and Liebendörfer, Michael and Biehler, Rolf and Lankeit, Elisa and Hochmuth, Reinhard and Ruge, Johanna and Kuklinski, Christiane}},
journal = {{dghd-Newsletter}},
pages = {{25--29}},
title = {{{Ein Kurzbericht aus dem Forschungsprojekt WiGeMath-Lernzentren als Unterstützungsmaßnahme für mathematikbezogenes Lernen in der Studieneingangsphase}}},
volume = {{01/2020}},
year = {{2020}},
}
@article{10596,
abstract = {{Multi-objective optimization is an active field of research that has many applications. Owing to its success and because decision-making processes are becoming more and more complex, there is a recent trend for incorporating many objectives into such problems. The challenge with such problems, however, is that the dimensions of the solution sets—the so-called Pareto sets and fronts—grow with the number of objectives. It is thus no longer possible to compute or to approximate the entire solution set of a given problem that contains many (e.g. more than three) objectives. On the other hand, the computation of single solutions (e.g. via scalarization methods) leads to unsatisfying results in many cases, even if user preferences are incorporated. In this article, the Pareto Explorer tool is presented—a global/local exploration tool for the treatment of many-objective optimization problems (MaOPs). In the first step, a solution of the problem is computed via a global search algorithm that ideally already includes user preferences. In the second step, a local search along the Pareto set/front of the given MaOP is performed in user specified directions. For this, several continuation-like procedures are proposed that can incorporate preferences defined in decision, objective, or in weight space. The applicability and usefulness of Pareto Explorer is demonstrated on benchmark problems as well as on an application from industrial laundry design.}},
author = {{Schütze, Oliver and Cuate, Oliver and Martín, Adanay and Peitz, Sebastian and Dellnitz, Michael}},
issn = {{0305-215X}},
journal = {{Engineering Optimization}},
number = {{5}},
pages = {{832--855}},
title = {{{Pareto Explorer: a global/local exploration tool for many-objective optimization problems}}},
doi = {{10.1080/0305215x.2019.1617286}},
volume = {{52}},
year = {{2020}},
}
@article{16288,
abstract = {{We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions, and modes of the generator and for system identification. In addition to learning the governing equations of deterministic systems, which then reduces to SINDy (sparse identification of nonlinear dynamics), it is possible to identify the drift and diffusion terms of stochastic differential equations from data. Moreover, we apply gEDMD to derive coarse-grained models of high-dimensional systems, and also to determine efficient model predictive control strategies. We highlight relationships with other methods and demonstrate the efficacy of the proposed methods using several guiding examples and prototypical molecular dynamics problems.}},
author = {{Klus, Stefan and Nüske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi, Cecilia and Schütte, Christof}},
issn = {{0167-2789}},
journal = {{Physica D: Nonlinear Phenomena}},
title = {{{Data-driven approximation of the Koopman generator: Model reduction, system identification, and control}}},
doi = {{10.1016/j.physd.2020.132416}},
volume = {{406}},
year = {{2020}},
}
@inbook{16289,
abstract = {{In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, proper orthogonal decomposition (POD) has been most widely used in the past in order to derive such models. Due to the huge advances concerning both theory as well as the numerical approximation, a very promising alternative based on the Koopman operator has recently emerged. In this chapter, we present two control strategies for model predictive control of nonlinear PDEs using data-efficient approximations of the Koopman operator. In the first one, the dynamic control system is replaced by a small number of autonomous systems with different yet constant inputs. The control problem is consequently transformed into a switching problem. In the second approach, a bilinear surrogate model is obtained via a convex combination of these autonomous systems. Using a recent convergence result for extended dynamic mode decomposition (EDMD), convergence of the reduced objective function can be shown. We study the properties of these two strategies with respect to solution quality, data requirements, and complexity of the resulting optimization problem using the 1-dimensional Burgers equation and the 2-dimensional Navier–Stokes equations as examples. Finally, an extension for online adaptivity is presented.}},
author = {{Peitz, Sebastian and Klus, Stefan}},
booktitle = {{Lecture Notes in Control and Information Sciences}},
isbn = {{9783030357122}},
issn = {{0170-8643}},
pages = {{257--282}},
publisher = {{Springer}},
title = {{{Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator}}},
doi = {{10.1007/978-3-030-35713-9_10}},
volume = {{484}},
year = {{2020}},
}
@article{16290,
abstract = {{The control of complex systems is of critical importance in many branches of science, engineering, and industry, many of which are governed by nonlinear partial differential equations. Controlling an unsteady fluid flow is particularly important, as flow control is a key enabler for technologies in energy (e.g., wind, tidal, and combustion), transportation (e.g., planes, trains, and automobiles), security (e.g., tracking airborne contamination), and health (e.g., artificial hearts and artificial respiration). However, the high-dimensional, nonlinear, and multi-scale dynamics make real-time feedback control infeasible. Fortunately, these high- dimensional systems exhibit dominant, low-dimensional patterns of activity that can be exploited for effective control in the sense that knowledge of the entire state of a system is not required. Advances in machine learning have the potential to revolutionize flow control given its ability to extract principled, low-rank feature spaces characterizing such complex systems.We present a novel deep learning modelpredictive control framework that exploits low-rank features of the flow in order to achieve considerable improvements to control performance. Instead of predicting the entire fluid state, we use a recurrent neural network (RNN) to accurately predict the control relevant quantities of the system, which are then embedded into an MPC framework to construct a feedback loop. In order to lower the data requirements and to improve the prediction accuracy and thus the control performance, incoming sensor data are used to update the RNN online. The results are validated using varying fluid flow examples of increasing complexity.}},
author = {{Bieker, Katharina and Peitz, Sebastian and Brunton, Steven L. and Kutz, J. Nathan and Dellnitz, Michael}},
issn = {{0935-4964}},
journal = {{Theoretical and Computational Fluid Dynamics}},
pages = {{577–591}},
title = {{{Deep model predictive flow control with limited sensor data and online learning}}},
doi = {{10.1007/s00162-020-00520-4}},
volume = {{34}},
year = {{2020}},
}
@article{16309,
abstract = {{In recent years, the success of the Koopman operator in dynamical systems
analysis has also fueled the development of Koopman operator-based control
frameworks. In order to preserve the relatively low data requirements for an
approximation via Dynamic Mode Decomposition, a quantization approach was
recently proposed in [Peitz & Klus, Automatica 106, 2019]. This way, control
of nonlinear dynamical systems can be realized by means of switched systems
techniques, using only a finite set of autonomous Koopman operator-based
reduced models. These individual systems can be approximated very efficiently
from data. The main idea is to transform a control system into a set of
autonomous systems for which the optimal switching sequence has to be computed.
In this article, we extend these results to continuous control inputs using
relaxation. This way, we combine the advantages of the data efficiency of
approximating a finite set of autonomous systems with continuous controls. We
show that when using the Koopman generator, this relaxation --- realized by
linear interpolation between two operators --- does not introduce any error for
control affine systems. This allows us to control high-dimensional nonlinear
systems using bilinear, low-dimensional surrogate models. The efficiency of the
proposed approach is demonstrated using several examples with increasing
complexity, from the Duffing oscillator to the chaotic fluidic pinball.}},
author = {{Peitz, Sebastian and Otto, Samuel E. and Rowley, Clarence W.}},
journal = {{SIAM Journal on Applied Dynamical Systems}},
number = {{3}},
pages = {{2162--2193}},
title = {{{Data-Driven Model Predictive Control using Interpolated Koopman Generators}}},
doi = {{10.1137/20M1325678}},
volume = {{19}},
year = {{2020}},
}
@inbook{13108,
abstract = {{Diagrammatisches Schlie{\ss}en wird im Zusammenhang mit dem Lernen von Mathmematik und ihrer Symbolsprache als wesentliche Theorie der Wissenskonstruktion diskutiert. Dabei wird h{\"{a}}ufig davon ausgegangen, dass die Wissenskonstruktion im Sinne diagrammatischen Schlie{\ss}ens erfolgt. Deskriptive Rekonstruktionen diagrammatischen Schlie{\ss}ens bei Lernenden stellen jedoch ein Desiderat der mathematikdidaktischen Forschung dar. Der vorliegende Beitrag befasst sich mit der Fragestellung, wie sich diagrammatisches Schlie{\ss}en bei Lernenden rekonstruieren l{\"{a}}sst. Als m{\"{o}}gliche Werkzeuge f{\"{u}}r eine solche Rekonstruktion werden Toulmins Argumentationsschema und Vergnauds Schema-Begriff exemplarisch angewandt, um das diagrammatische Schlie{\ss}en eines Sch{\"{u}}lerpaars beim Einstieg in die Subtraktion negativer Zahlen zu rekonstruieren. Abschlie{\ss}end wird die tats{\"{a}}chliche Eignung der beiden Ans{\"{a}}tze zur Rekonstruktion diagrammatischen Schlie{\ss}ens diskutiert.}},
author = {{Schumacher, Jan and Rezat, Sebastian}},
booktitle = {{Zeichen und Sprache im Mathematikunterricht}},
editor = {{Kadunz, Gert}},
publisher = {{Springer}},
title = {{{Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge}}},
doi = {{10.1007/978-3-662-61194-4_5}},
year = {{2020}},
}
@article{29399,
author = {{Limebeer, D. J. N. and Ober-Blöbaum, Sina and Farshi, F. H.}},
journal = {{IEEE Transactions on Automatic Control}},
pages = {{1381--1396}},
title = {{{Variational integrators for dissipative systems}}},
volume = {{65(4)}},
year = {{2020}},
}
@article{16297,
abstract = {{In real-world problems, uncertainties (e.g., errors in the measurement,
precision errors) often lead to poor performance of numerical algorithms when
not explicitly taken into account. This is also the case for control problems,
where optimal solutions can degrade in quality or even become infeasible. Thus,
there is the need to design methods that can handle uncertainty. In this work,
we consider nonlinear multi-objective optimal control problems with uncertainty
on the initial conditions, and in particular their incorporation into a
feedback loop via model predictive control (MPC). In multi-objective optimal
control, an optimal compromise between multiple conflicting criteria has to be
found. For such problems, not much has been reported in terms of uncertainties.
To address this problem class, we design an offline/online framework to compute
an approximation of efficient control strategies. This approach is closely
related to explicit MPC for nonlinear systems, where the potentially expensive
optimization problem is solved in an offline phase in order to enable fast
solutions in the online phase. In order to reduce the numerical cost of the
offline phase, we exploit symmetries in the control problems. Furthermore, in
order to ensure optimality of the solutions, we include an additional online
optimization step, which is considerably cheaper than the original
multi-objective optimization problem. We test our framework on a car
maneuvering problem where safety and speed are the objectives. The
multi-objective framework allows for online adaptations of the desired
objective. Alternatively, an automatic scalarizing procedure yields very
efficient feedback controls. Our results show that the method is capable of
designing driving strategies that deal better with uncertainties in the initial
conditions, which translates into potentially safer and faster driving
strategies.}},
author = {{Hernández Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}},
journal = {{International Journal of Robust and Nonlinear Control}},
pages = {{7593--7618}},
title = {{{Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty}}},
doi = {{10.1002/rnc.5197}},
volume = {{30(17)}},
year = {{2020}},
}
@article{29398,
author = {{Hernández Castellanos, C. I. O. and Schütze, G. and Sun, J.-Q. and Ober-Blöbaum, Sina and Morales-Luna, G.}},
journal = {{Mathematics}},
title = {{{Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping}}},
volume = {{8(11):1959}},
year = {{2020}},
}
@inbook{29413,
author = {{Flaßkamp, K. and Ober-Blöbaum, Sina and Peitz, S. and Junge, O. and Schütze, O. and Froyland, G. and Padberg-Gehle, K.}},
booktitle = {{Advances in Dynamics, Optimization and Computation}},
pages = {{209--237}},
publisher = {{Springer International Publishing}},
title = {{{Symmetry in optimal control: A multiobjective model predictive control approach}}},
year = {{2020}},
}
@inproceedings{29422,
author = {{Lishkova, Y. and Ober-Blöbaum, Sina and Cannon, M. and Leyendecker, S.}},
booktitle = {{Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe}},
title = {{{A multirate variational approach to simulation and optimal control for flexible spacecraft}}},
year = {{2020}},
}
@inproceedings{29423,
author = {{Faulwasser, T. and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann, K. }},
booktitle = {{24th International Symposium on Mathematical Theory of Networks and Systems}},
title = {{{A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems}}},
year = {{2020}},
}
@inproceedings{29424,
author = {{Cresson, J. and Jiménez, F. and Ober-Blöbaum, Sina}},
booktitle = {{24th International Symposium on Mathematical Theory of Networks and Systems}},
title = {{{Modelling of the convection-diffusion equation through fractional restricted calculus of variations}}},
year = {{2020}},
}
@article{29545,
author = {{Jean, Frédéric and Maslovskaya, Sofya and Zelenko, Igor}},
issn = {{0046-5755}},
journal = {{Geometriae Dedicata}},
keywords = {{Geometry and Topology}},
number = {{1}},
pages = {{295--314}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry}}},
doi = {{10.1007/s10711-020-00581-z}},
volume = {{213}},
year = {{2020}},
}
@inproceedings{29546,
author = {{Maslovskaya, Sofya and Caillau, Jean-Baptiste and Djema, Walid and Giraldi, Laetitia and Jean-Luc, Jean-Luc and Pomet, Jean-Baptiste}},
title = {{{The turnpike property in maximization of microbial metabolite production}}},
year = {{2020}},
}
@article{31264,
abstract = {{AbstractGiven a closed orientable hyperbolic manifold of dimension $$\ne 3$$
≠
3
we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.
}},
author = {{Küster, Benjamin and Weich, Tobias}},
issn = {{0010-3616}},
journal = {{Communications in Mathematical Physics}},
keywords = {{Mathematical Physics, Statistical and Nonlinear Physics}},
number = {{2}},
pages = {{917--941}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Pollicott-Ruelle Resonant States and Betti Numbers}}},
doi = {{10.1007/s00220-020-03793-2}},
volume = {{378}},
year = {{2020}},
}
@inproceedings{31372,
author = {{Hoffmann, Max}},
booktitle = {{Beiträge zum Mathematikunterricht 2020}},
editor = {{Siller, Hans-Stefan and Weigel, Wolfgang and Wörler, Jan Franz}},
pages = {{1353--1356}},
publisher = {{WTM-Verlag}},
title = {{{Schnittstellenaktivitäten zum Kongruenzsatz WSW}}},
doi = {{10.17877/DE290R-21368}},
year = {{2020}},
}
@article{31376,
author = {{Hoffmann, Max}},
journal = {{Der Mathematikunterricht}},
pages = {{36–47}},
title = {{{Zirkel und Lineal ohne Parallelenaxiom: Ein konstruktiver Zugang zur hyperbolischen Geometrie.}}},
volume = {{66 (6)}},
year = {{2020}},
}
@misc{31386,
author = {{Hoffmann, Max}},
booktitle = {{Mathematische Semesterberichte}},
pages = {{119–121}},
title = {{{Rezension: Andrew Granville und Jenniver Granville: Prime Supects: The Anatomy of Integers and Permutations}}},
doi = {{10.1007/s00591-019-00269-w}},
volume = {{67}},
year = {{2020}},
}
@misc{31384,
author = {{Hoffmann, Max}},
booktitle = {{Mathematische Semesterberichte}},
pages = {{115–116}},
title = {{{Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher über Möbius zu Penrose}}},
doi = {{10.1007/s00591-019-00264-1}},
volume = {{67}},
year = {{2020}},
}
@book{31381,
editor = {{Hoffmann, Max}},
title = {{{Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung – ein Nachwuchsheft}}},
year = {{2020}},
}
@inbook{31551,
author = {{Häsel-Weide, Uta and Nührenbörger, Marcus}},
booktitle = {{Kinder lernen Zukunft – Anforderungen und tragfähige Grundlagen}},
editor = {{Hecker, Ulrich and Lassek, Maresi and Ramseger, Jörg}},
pages = {{108--118}},
publisher = {{Grundschulverband}},
title = {{{Tragfähige Grundlagen}}},
volume = {{Band 150}},
year = {{2020}},
}
@inbook{31552,
author = {{Heckmann, Lara and Häsel-Weide, Uta}},
booktitle = {{Beiträge zum Mathematikunterricht 2020}},
editor = {{Siller, Hans-Stefan and Weigel, Wolfgang and Wörler, Jan Franz}},
isbn = {{978-3-95987-139-6}},
pages = {{393--396}},
publisher = {{WTM Verlag}},
title = {{{Aufgaben für den inklusiven Mathematikunterricht - aus der Sicht von Lehrkräften.}}},
year = {{2020}},
}
@inbook{31549,
author = {{Häsel-Weide, Uta}},
booktitle = {{Didaktik des Unterrichts bei Lernschwierigkeiten: Ein Handbuch für Studium und Praxis}},
editor = {{Heimlich, Ulrich and Wember, Franz B.}},
isbn = {{978-3170355699}},
pages = {{308--318}},
publisher = {{W. Kohlhammer GmbH}},
title = {{{Sachrechnen}}},
year = {{2020}},
}
@article{31553,
author = {{Seitz, Susanne and Häsel-Weide, Uta and Wilke, Yannik and Wallner, Melina}},
journal = {{K:ON Kölner Online-Journal für Lehrer*innenbildung}},
number = {{2}},
title = {{{Expertise von Lehrpersonen für inklusiven Mathematikunterricht der Sekundarstufe - Ausgangspunkte zur Professionalisierungsforschung.}}},
year = {{2020}},
}
@inbook{31550,
author = {{Häsel-Weide, Uta}},
booktitle = {{Handbuch Lehrerinnen- und Lehrerbildung}},
editor = {{Cramer, Colin and König, Johannes and Rothland, Martin and Blömeke, Sigrid}},
isbn = {{978-3-8252-5473-5}},
pages = {{462--469}},
publisher = {{Julius Klinkhardt}},
title = {{{Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule.}}},
year = {{2020}},
}
@misc{33273,
abstract = {{Dieses Lernangebot widmet sich der linearen Algebra als dem Teil der Mathematik, der neben der Optimierung und der Stochastik die Grundlage für praktisch alle Entwicklungen im Bereich Künstliche Intelligenz (KI) darstellt. Das Fach ist jedoch für Anfänger meist ungewohnt abstrakt und wird daher oft als besonders schwierig und unanschaulich empfunden. In diesem Kurs wird das Erlernen mathematischer Kenntnisse in linearer Algebra verknüpft mit dem aktuellen und faszinierenden Anwendungsfeld der künstlichen neuronalen Netze (KNN). Daraus ergeben sich in natürlicher Weise Anwendungsbeispiele, an denen die wesentlichen Konzepte der linearen Algebra erklärt werden können.
Behandelte Themen sind:
Der Vektorraum der reellen Zahlentupel, reelle Vektorräume allgemein
Lineare Abbildungen
Matrizen
Koordinaten und darstellende Matrizen
Lineare Gleichungssysteme, Gaußalgorithmus
Determinante
Ein Ausblick auf nichtlineare Techniken, die für neuronale Netzwerke relevant sind.}},
author = {{Schramm, Thomas and Gasser, Ingenuin and Schwenker, Sören and Seiler, Ruedi and Lohse, Alexander and Zobel, Kay}},
publisher = {{Hamburg Open Online University}},
title = {{{Linear Algebra driven by Data Science}}},
year = {{2020}},
}
@article{33282,
abstract = {{We derive a criterium for the almost sure finiteness of perpetual integrals of L ́evy
processes for a class of real functions including all continuous functions and for general one-
dimensional L ́evy processes that drifts to plus infinity. This generalizes previous work of D ̈oring
and Kyprianou, who considered L ́evy processes having a local time, leaving the general case as an
open problem. It turns out, that the criterium in the general situation simplifies significantly in
the situation, where the process has a local time, but we also demonstrate that in general our cri-
terium can not be reduced. This answers an open problem posed in D ̈oring, L. and Kyprianou, A.
(2015).}},
author = {{Kolb, Martin and Savov, Mladen}},
journal = {{Bernoulli}},
keywords = {{L ́evy processes, Perpetual integrals, Potential measures}},
number = {{2}},
pages = {{1453--1472}},
publisher = {{Bernoulli Society for Mathematical Statistics and Probability}},
title = {{{A Characterization of the Finiteness of Perpetual Integrals of Levy Processes}}},
doi = {{https://doi.org/10.48550/arXiv.1903.03792}},
volume = {{26}},
year = {{2020}},
}
@article{33330,
abstract = {{Reciprocal relations are binary relations Q with entries Q(i,j)∈[0,1], and such that Q(i,j)+Q(j,i)=1. Relations of this kind occur quite naturally in various domains, such as preference modeling and preference learning. For example, Q(i,j) could be the fraction of voters in a population who prefer candidate i to candidate j. In the literature, various attempts have been made at generalizing the notion of transitivity to reciprocal relations. In this paper, we compare three important frameworks of generalized transitivity: g-stochastic transitivity, T-transitivity, and cycle-transitivity. To this end, we introduce E-transitivity as an even more general notion. We also use this framework to extend an existing hierarchy of different types of transitivity. As an illustration, we study transitivity properties of probabilities of pairwise preferences, which are induced as marginals of an underlying probability distribution on rankings (strict total orders) of a set of alternatives. In particular, we analyze the interesting case of the so-called Babington Smith model, a parametric family of distributions of that kind.}},
author = {{Haddenhorst, Björn and Hüllermeier, Eyke and Kolb, Martin}},
journal = {{International Journal of Approximate Reasoning}},
number = {{2}},
pages = {{373--407}},
publisher = {{Elsevier}},
title = {{{Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model}}},
doi = {{https://doi.org/10.1016/j.ijar.2020.01.007}},
volume = {{119}},
year = {{2020}},
}
@unpublished{32101,
author = {{Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin and Hilgert, Joachim}},
booktitle = {{arxiv:2007.14275v3}},
title = {{{Ruelle-Taylor resonaces of Anosov actions}}},
year = {{2020}},
}
@inproceedings{31873,
author = {{Schumacher, Jan}},
publisher = {{LibreCat University}},
title = {{{Deduktion und Abduktion beim diagrammatischen Schließen – das didaktische Potential der Peirceschen Semiotik}}},
doi = {{10.17877/DE290R-21555}},
year = {{2020}},
}
@article{16710,
abstract = {{In this work we present a set-oriented path following method for the computation of relative global
attractors of parameter-dependent dynamical systems. We start with an initial approximation of the
relative global attractor for a fixed parameter λ0 computed by a set-oriented subdivision method.
By using previously obtained approximations of the parameter-dependent relative global attractor
we can track it with respect to a one-dimensional parameter λ > λ0 without restarting the whole
subdivision procedure. We illustrate the feasibility of the set-oriented path following method by
exploring the dynamics in low-dimensional models for shear flows during the transition to turbulence
and of large-scale atmospheric regime changes .
}},
author = {{Gerlach, Raphael and Ziessler, Adrian and Eckhardt, Bruno and Dellnitz, Michael}},
issn = {{1536-0040}},
journal = {{SIAM Journal on Applied Dynamical Systems}},
pages = {{705--723}},
title = {{{A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors}}},
doi = {{10.1137/19m1247139}},
year = {{2020}},
}
@inbook{17994,
abstract = {{In this work we review the novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems developed in [6] and [36]. By utilizing results on embedding techniques for infinite dimensional systems we extend a classical subdivision scheme [8] as well as a continuation algorithm [7] for the computation of attractors and invariant manifolds of finite dimensional systems to the infinite dimensional case. We show how to implement this approach for the analysis of delay differential equations and partial differential equations and illustrate the feasibility of our implementation by computing the attractor of the Mackey-Glass equation and the unstable manifold of the one-dimensional Kuramoto-Sivashinsky equation.}},
author = {{Gerlach, Raphael and Ziessler, Adrian}},
booktitle = {{Advances in Dynamics, Optimization and Computation}},
editor = {{Junge, Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}},
isbn = {{9783030512637}},
issn = {{2198-4182}},
pages = {{55--85}},
publisher = {{Springer}},
title = {{{The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems}}},
doi = {{10.1007/978-3-030-51264-4_3}},
volume = {{304}},
year = {{2020}},
}
@article{19945,
abstract = {{Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations, …) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The Poisson structure is connected to conservation properties and other geometric features of solutions to the PDE and, therefore, of great interest for numerical integration. For the example of Burgers' equations and related PDEs we use Clebsch variables to lift the original system to a collective Hamiltonian system on a symplectic manifold whose structure is related to the original Lie-Poisson structure. On the collective Hamiltonian system a symplectic integrator can be applied. Our numerical examples show excellent conservation properties and indicate that the disadvantage of an increased phase-space dimension can be outweighed by the advantage of symplectic integration.}},
author = {{McLachlan, Robert I and Offen, Christian and Tapley, Benjamin K}},
issn = {{2158-2505}},
journal = {{Journal of Computational Dynamics}},
number = {{1}},
pages = {{111--130}},
publisher = {{American Institute of Mathematical Sciences (AIMS)}},
title = {{{Symplectic integration of PDEs using Clebsch variables}}},
doi = {{10.3934/jcd.2019005}},
volume = {{6}},
year = {{2019}},
}
@article{21,
abstract = {{We address the general mathematical problem of computing the inverse p-th
root of a given matrix in an efficient way. A new method to construct iteration
functions that allow calculating arbitrary p-th roots and their inverses of
symmetric positive definite matrices is presented. We show that the order of
convergence is at least quadratic and that adaptively adjusting a parameter q
always leads to an even faster convergence. In this way, a better performance
than with previously known iteration schemes is achieved. The efficiency of the
iterative functions is demonstrated for various matrices with different
densities, condition numbers and spectral radii.}},
author = {{Richters, Dorothee and Lass, Michael and Walther, Andrea and Plessl, Christian and Kühne, Thomas}},
journal = {{Communications in Computational Physics}},
number = {{2}},
pages = {{564--585}},
publisher = {{Global Science Press}},
title = {{{A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices}}},
doi = {{10.4208/cicp.OA-2018-0053}},
volume = {{25}},
year = {{2019}},
}
@article{21944,
author = {{Nüske, Feliks and Boninsegna, Lorenzo and Clementi, Cecilia}},
issn = {{0021-9606}},
journal = {{The Journal of Chemical Physics}},
title = {{{Coarse-graining molecular systems by spectral matching}}},
doi = {{10.1063/1.5100131}},
year = {{2019}},
}
@inbook{8577,
author = {{Kuklinski, Christiane and Leis, Elena and Liebendörfer, Michael and Hochmuth, Reinhard}},
booktitle = {{Beiträge zum Mathematikunterricht 2019}},
title = {{{Erklärung von Mathematikleistung im Ingenieursstudium}}},
year = {{2019}},
}
@article{16709,
author = {{Sahai, Tuhin and Ziessler, Adrian and Klus, Stefan and Dellnitz, Michael}},
issn = {{0924-090X}},
journal = {{Nonlinear Dynamics}},
title = {{{Continuous relaxations for the traveling salesman problem}}},
doi = {{10.1007/s11071-019-05092-5}},
year = {{2019}},
}
@inbook{16966,
author = {{Kuklinski, Christiane and Liebendörfer, Michael and Hochmuth, Reinhard and Biehler, Rolf and Schaper, Niclas and Lankeit, Elisa and Leis, Elena and Schürmann, Mirko}},
booktitle = {{Proceedings of {CERME} 11}},
title = {{{Features of innovative lectures that distinguish them from traditional lectures and their evaluation by attending students}}},
year = {{2019}},
}
@article{10593,
abstract = {{We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables. A numerical approximation of the Koopman operator therefore yields a linear system for the observation of an autonomous dynamical system. In our approach, by introducing a finite number of constant controls, the dynamic control system is transformed into a set of autonomous systems and the corresponding optimal control problem into a switching time optimization problem. This allows us to replace each of these systems by a K-ROM which can be solved orders of magnitude faster. By this approach, a nonlinear infinite-dimensional control problem is transformed into a low-dimensional linear problem. Using a recent convergence result for the numerical approximation via Extended Dynamic Mode Decomposition (EDMD), we show that the value of the K-ROM based objective function converges in measure to the value of the full objective function. To illustrate the results, we consider the 1D Burgers equation and the 2D Navier–Stokes equations. The numerical experiments show remarkable performance concerning both solution times and accuracy.}},
author = {{Peitz, Sebastian and Klus, Stefan}},
issn = {{0005-1098}},
journal = {{Automatica}},
pages = {{184--191}},
title = {{{Koopman operator-based model reduction for switched-system control of PDEs}}},
doi = {{10.1016/j.automatica.2019.05.016}},
volume = {{106}},
year = {{2019}},
}
@article{10595,
abstract = {{In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in decision space), then this can be used to efficiently solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set.}},
author = {{Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}},
issn = {{0925-5001}},
journal = {{Journal of Global Optimization}},
number = {{4}},
pages = {{891--913}},
title = {{{On the hierarchical structure of Pareto critical sets}}},
doi = {{10.1007/s10898-019-00737-6}},
volume = {{73}},
year = {{2019}},
}
@inproceedings{10597,
abstract = {{In comparison to classical control approaches in the field of electrical drives like the field-oriented control (FOC), model predictive control (MPC) approaches are able to provide a higher control performance. This refers to shorter settling times, lower overshoots, and a better decoupling of control variables in case of multi-variable controls. However, this can only be achieved if the used prediction model covers the actual behavior of the plant sufficiently well. In case of model deviations, the performance utilizing MPC remains below its potential. This results in effects like increased current ripple or steady state setpoint deviations. In order to achieve a high control performance, it is therefore necessary to adapt the model to the real plant behavior. When using an online system identification, a less accurate model is sufficient for commissioning of the drive system. In this paper, the combination of a finite-control-set MPC (FCS-MPC) with a system identification is proposed. The method does not require high-frequency signal injection, but uses the measured values already required for the FCS-MPC. An evaluation of the least squares-based identification on a laboratory test bench showed that the model accuracy and thus the control performance could be improved by an online update of the prediction models.}},
author = {{Hanke, Soren and Peitz, Sebastian and Wallscheid, Oliver and Böcker, Joachim and Dellnitz, Michael}},
booktitle = {{2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)}},
isbn = {{9781538694145}},
title = {{{Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification}}},
doi = {{10.1109/precede.2019.8753313}},
year = {{2019}},
}
@inproceedings{13106,
author = {{Schumacher, Jan}},
booktitle = {{Beiträge zum Mathematikunterricht 2019}},
location = {{Regensburg}},
title = {{{Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen}}},
year = {{2019}},
}
@inproceedings{13107,
abstract = {{In this paper, we first outline a Hypothetical Learning Trajectory (HLT), which aims at a formal understanding of the rules for manipulating integers. The HLT is based on task formats, which promote algebraic thinking in terms of generalizing rules from the analysis of patterns and should be familiar to students from their mathematics education experiences in elementary school. Second, we analyze two students' actual learning process based on Peircean semiotics. The analysis shows that the actual learning process diverges from the hypothesized learning process in that the students do not relate the different levels of the diagrams in a way that allows them to extrapolate the rule for the subtraction of negative numbers. Based on this finding, we point out consequences for the design of the tasks.}},
author = {{Schumacher, Jan and Rezat, Sebastian}},
booktitle = {{Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019)}},
editor = {{Jankvist, Uffe Thomas and Van den Heuvel-Panhuizen, Marja and Veldhuis, Michiel}},
keywords = {{diagrammatic reasoning, hypothetical learning trajectory, induction extrapolatory method, integers, negative numbers, permanence principle, semiotics}},
location = {{Utrecht}},
publisher = {{Freudenthal Group & Freudenthal Institute, Utrecht University and ERME}},
title = {{{A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers}}},
year = {{2019}},
}
@book{13139,
editor = {{Rezat, Sebastian and Fan, Lianghuo and Hattermann, Mathias and Schumacher, Jan and Wuschke, Holger}},
location = {{Paderborn}},
pages = {{392}},
publisher = {{Universitätsbibliothek Paderborn}},
title = {{{Proceedings of the Third International Conference on Mathematics Textbook Research and Development: 16-19 September 2019 Paderborn, Germany}}},
doi = {{10.17619/UNIPB/1-768}},
year = {{2019}},
}
@article{31265,
author = {{Dyatlov, Semyon and Borthwick, David and Weich, Tobias}},
issn = {{1435-9855}},
journal = {{Journal of the European Mathematical Society}},
keywords = {{Applied Mathematics, General Mathematics}},
number = {{6}},
pages = {{1595--1639}},
publisher = {{European Mathematical Society - EMS - Publishing House GmbH}},
title = {{{Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich}}},
doi = {{10.4171/jems/867}},
volume = {{21}},
year = {{2019}},
}
@misc{31302,
author = {{Schütte, Philipp}},
title = {{{Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces}}},
year = {{2019}},
}
@misc{31383,
author = {{Hoffmann, Max}},
booktitle = {{Mathematische Semesterberichte}},
pages = {{117–118}},
title = {{{Rezension: Klaus Volkert: In höheren Räumen – Der Weg der Geometrie in die vierte Dimension}}},
doi = {{10.1007/s00591-018-00244-x}},
volume = {{66}},
year = {{2019}},
}
@unpublished{31191,
abstract = {{The kinetic Brownian motion on the sphere bundle of a Riemannian manifold $M$
is a stochastic process that models a random perturbation of the geodesic flow.
If $M$ is a orientable compact constant negatively curved surface, we show that
in the limit of infinitely large perturbation the $L^2$-spectrum of the
infinitesimal generator of a time rescaled version of the process converges to
the Laplace spectrum of the base manifold. In addition, we give explicit error
estimates for the convergence to equilibrium. The proofs are based on
noncommutative harmonic analysis of $SL_2(\mathbb{R})$.}},
author = {{Kolb, Martin and Weich, Tobias and Wolf, Lasse Lennart}},
booktitle = {{arXiv:1909.06183}},
title = {{{Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces}}},
year = {{2019}},
}
@misc{8482,
author = {{Jurgelucks, Benjamin and Schulze, Veronika and Feldmann, Nadine and Claes, Leander}},
title = {{{Arbitrary sensitivity for inverse problems in piezoelectricity}}},
year = {{2019}},
}
@article{33331,
abstract = {{Motivated by the recent contribution (Bauer and Bernard in Annales Henri Poincaré 19:653–693, 2018), we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation. Problems of this type appear in the analysis of continuously monitored quantum systems. We extend the results of Bauer and Bernard (Annales Henri Poincaré 19:653–693, 2018) and prove a general result concerning the convergence to a homogeneous Poisson process using only classical probabilistic tools.}},
author = {{Kolb, Martin and Liesenfeld, Matthias}},
journal = {{Annales Henri Poincaré}},
number = {{6}},
pages = {{1753--1783}},
publisher = {{Institute Henri Poincaré}},
title = {{{Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems}}},
doi = {{http://dx.doi.org/10.1007/s00023-019-00772-9}},
volume = {{20}},
year = {{2019}},
}
@article{33333,
author = {{Wang, Andi Q. and Kolb, Martin and Roberts, Gareth O. and Steinsaltz, David}},
journal = {{The Annals of Applied Probability}},
number = {{1}},
title = {{{Theoretical properties of quasi-stationary Monte Carlo methods}}},
doi = {{http://dx.doi.org/10.1214/18-AAP1422}},
volume = {{29}},
year = {{2019}},
}
@article{33334,
abstract = {{In the present work we characterize the existence of quasistationary distributions for diffusions on (0,∞) allowing singular behavior at 0 and ∞. If absorption at 0 is certain, we show that there exists a quasistationary distribution as soon as the spectrum of the generator is strictly positive. This complements results of Collet et al. and Kolb/Steinsaltz for 0 being a regular boundary point and extends results by Collet et al. on singular diffusions. We also study the existence and uniqueness of quasistationary distributions for a class of one-dimensional diffusions with killing that arise from a biological example and which have two inaccessible boundary points (more specifically 0 is natural and ∞ is entrance).}},
author = {{Hening, Alexandru and Kolb, Martin}},
journal = {{Stochastic Processes and their Applications}},
number = {{5}},
pages = {{1659--1696}},
publisher = {{Bernoulli Society for Mathematical Statistics and Probability}},
title = {{{Quasistationary distributions for one-dimensional diffusions with two singular boundary points}}},
doi = {{http://dx.doi.org/10.1016/j.spa.2018.05.012}},
volume = {{129}},
year = {{2019}},
}
@inproceedings{29867,
author = {{Faulwasser, Tim and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann, Karl}},
pages = {{490--495}},
title = {{{Auf dem Weg zur Geschwindigkeit von Turnpikes zur optimalen Steuerung mechanischer Systeme}}},
volume = {{52(16)}},
year = {{2019}},
}
@unpublished{16711,
abstract = {{Embedding techniques allow the approximations of finite dimensional
attractors and manifolds of infinite dimensional dynamical systems via
subdivision and continuation methods. These approximations give a topological
one-to-one image of the original set. In order to additionally reveal their
geometry we use diffusion mapst o find intrinsic coordinates. We illustrate our
results on the unstable manifold of the one-dimensional Kuramoto--Sivashinsky
equation, as well as for the attractor of the Mackey-Glass delay differential
equation.}},
author = {{Gerlach, Raphael and Koltai, Péter and Dellnitz, Michael}},
booktitle = {{arXiv:1902.08824}},
title = {{{Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems}}},
year = {{2019}},
}
@inproceedings{32089,
author = {{Häsel-Weide, Uta and Nührenbörger, M.}},
booktitle = {{Proceedings of the Third International Conference on Mathematics Textbook Research an Development}},
editor = {{Rezat, Sebastian and Fan, L. and Hattermann, M. and Schumacher, J. and Wuschke, H.}},
pages = {{185--190}},
title = {{{Materials für inclusive mathematics education - Design principles an practices.}}},
year = {{2019}},
}
@article{32090,
author = {{Breucker, T. and Freesemann, O. and Häsel-Weide, Uta and Opitz, E. M. and Nührenbörger, M. and Wittich, C.}},
journal = {{Zeitschrift für Heilpädagogik}},
number = {{70}},
pages = {{316--326}},
title = {{{Fördern im inklusiven Mathematikunterricht im Spannungsfeld zwischen gemeinsamen Lernsituationen und gezielter Förderung.}}},
year = {{2019}},
}
@misc{32091,
author = {{Häsel-Weide, Uta and Nührenbörger, M. and Reinold, M.}},
isbn = {{978-3122009946}},
pages = {{80}},
publisher = {{Klett}},
title = {{{Das Zahlenbuch 4. Förderheft}}},
year = {{2019}},
}
@misc{31954,
author = {{Häsel-Weide, Uta and Nührenbörger, M. and Reinold, M.}},
isbn = {{ 978-3-12-200998-4}},
pages = {{144}},
publisher = {{Klett}},
title = {{{Das Zahlenbuch. Förderkommentar Lernen zum 4. Schuljahr}}},
year = {{2019}},
}
@article{16708,
abstract = {{ In this work we extend the novel framework developed by Dellnitz, Hessel-von Molo, and Ziessler to
the computation of finite dimensional unstable manifolds of infinite dimensional dynamical systems.
To this end, we adapt a set-oriented continuation technique developed by Dellnitz and Hohmann for
the computation of such objects of finite dimensional systems with the results obtained in the work
of Dellnitz, Hessel-von Molo, and Ziessler. We show how to implement this approach for the analysis
of partial differential equations and illustrate its feasibility by computing unstable manifolds of the
one-dimensional Kuramoto--Sivashinsky equation as well as for the Mackey--Glass delay differential
equation.
}},
author = {{Ziessler, Adrian and Dellnitz, Michael and Gerlach, Raphael}},
issn = {{1536-0040}},
journal = {{SIAM Journal on Applied Dynamical Systems}},
pages = {{1265--1292}},
title = {{{The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques}}},
doi = {{10.1137/18m1204395}},
year = {{2019}},
}
@article{16712,
abstract = {{We investigate self-adjoint matrices A∈Rn,n with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is equivariant with respect to the action of a group Γ2(A)⊂O(n) which is isomorphic to ⊗nk=1Z2. If the self-adjoint matrix possesses multiple eigenvalues – this may, for instance, be induced by symmetry properties of an underlying dynamical system – then A is even equivariant with respect to the action of a group Γ(A)≃∏ki=1O(mi) where m1,…,mk are the multiplicities of the eigenvalues λ1,…,λk of A. We discuss implications of this result for equivariant bifurcation problems, and we briefly address further applications for the Procrustes problem, graph symmetries and Taylor expansions.}},
author = {{Dellnitz, Michael and Gebken, Bennet and Gerlach, Raphael and Klus, Stefan}},
issn = {{1468-9367}},
journal = {{Dynamical Systems}},
pages = {{1--19}},
title = {{{On the equivariance properties of self-adjoint matrices}}},
doi = {{10.1080/14689367.2019.1661355}},
year = {{2019}},
}
@inbook{32092,
author = {{Häsel-Weide, Uta}},
booktitle = {{Zwischen Persönlichkeitsbildung und Leistungsentwicklung. Fachspezifische Zugänge zu inklusivem Unterricht}},
editor = {{Baumert, B. and Willen, M.}},
isbn = {{ 978-3781523234}},
pages = {{175--181}},
publisher = {{Klinkhardt}},
title = {{{Lernumgebungen für den inklusiven Mathematikunterricht zwischen reichhaltiger Offenheit und fokussierter Förderung}}},
year = {{2019}},
}
@article{19935,
abstract = {{A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples. }},
author = {{McLachlan, Robert I and Offen, Christian}},
issn = {{0951-7715}},
journal = {{Nonlinearity}},
pages = {{2895--2927}},
title = {{{Bifurcation of solutions to Hamiltonian boundary value problems}}},
doi = {{10.1088/1361-6544/aab630}},
year = {{2018}},
}
@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{19940,
abstract = {{Two smooth map germs are right-equivalent if and only if they generate two
Lagrangian submanifolds in a cotangent bundle which have the same contact with
the zero-section. In this paper we provide a reverse direction to this
classical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a
symplectic manifold have the same contact with a third Lagrangian submanifold
if and only if the intersection problems correspond to stably right equivalent
map germs. We, therefore, obtain a correspondence between local Lagrangian
intersection problems and catastrophe theory while the classical version only
captures tangential intersections. The correspondence is defined independently
of any Lagrangian fibration of the ambient symplectic manifold, in contrast to
other classical results. Moreover, we provide an extension of the
correspondence to families of local Lagrangian intersection problems. This
gives rise to a framework which allows a natural transportation of the notions
of catastrophe theory such as stability, unfolding and (uni-)versality to the
geometric setting such that we obtain a classification of families of local
Lagrangian intersection problems. An application is the classification of
Lagrangian boundary value problems for symplectic maps.}},
author = {{Offen, Christian}},
booktitle = {{arXiv:1811.10165}},
title = {{{Local intersections of Lagrangian manifolds correspond to catastrophe theory}}},
year = {{2018}},
}
@article{19943,
abstract = {{In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to prove the existence of obstructions arising from conformal symplectic symmetries on the bifurcation behaviour of solutions to Hamiltonian boundary value problems. Under non-degeneracy conditions, a group action by conformal symplectic symmetries has the effect that the flow map cannot degenerate in a direction which is tangential to the action. This imposes restrictions on which singularities can occur in boundary value problems. Our results generalise classical results about conjugate loci on Riemannian manifolds to a large class of Hamiltonian boundary value problems with, for example, scaling symmetries. }},
author = {{McLachlan, Robert I and Offen, Christian}},
journal = {{New Zealand Journal of Mathematics}},
keywords = {{Hamiltonian boundary value problems, singularities, conformal symplectic geometry, catastrophe theory, conjugate loci}},
pages = {{83--99}},
title = {{{Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci}}},
volume = {{48}},
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{8569,
author = {{Biehler, Rolf and Hochmuth, Reinhard and Schaper, Niclas and Kuklinski, Christiane and Lankeit, Elisa and Leis, Elena and Liebendörfer, Michael and Schürmann, Mirko}},
booktitle = {{3. Auswertungsworkshop der Begleitforschung. Dokumentation der Projektbeiträge.}},
editor = {{Hanft, Anke and Bischoff, Franziska and Kretschmer, Stefanie}},
pages = {{32--41}},
publisher = {{Carl von Ossietzky Universität Oldenburg}},
title = {{{Verbundprojekt WiGeMath: Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase}}},
year = {{2018}},
}
@article{8571,
author = {{Frühbis-Krüger, Anne and Liebendörfer, Michael}},
journal = {{Computeralgebra-Rundbrief}},
number = {{63}},
title = {{{Minisymposium CAS in der Hochschullehre - ein Blick in die Praxis}}},
year = {{2018}},
}
@inbook{8572,
author = {{Frühbis-Krüger, Anne and Kemper, Gregor and Koepf, Wolfram and Liebendörfer, Michael}},
booktitle = {{Beiträge zum Mathematikunterricht 2018}},
pages = {{83--84}},
publisher = {{WTM-Verlag}},
title = {{{CAS in der Hochschullehre - Ein Blick in die Praxis}}},
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}},
}
@inproceedings{8575,
abstract = {{The transition from high school to university mathematics has proven to be difficult for many students but especially for pre-service secondary teachers. To support these students at mastering this transition, various universities have introduced support measures of various kinds. The WiGeMath project developed a taxonomy that makes it possible to describe and compare these measures concerning their goals as well as their frame characteristics. We will exemplify the use of the taxonomy in the description of one specific innovative measure that was part of the WiGeMath evaluations. Moreover, we will present first results concerning the goal-fulfilment of this measure concerning affective characteristics of the student cohort and their predominant beliefs.}},
author = {{Kuklinski, Christiane and Leis, Elena and Liebendörfer, Michael and Hochmuth, Reinhard and Biehler, Rolf and Lankeit, Elisa and Neuhaus, Silke and Schaper, Niclas and Schürmann, Mirko}},
booktitle = {{Proceedings of the Second Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2018, 5-7 April 2018)}},
editor = {{Durand-Guerrier, V. and Hochmuth, R. and Goodchild, S. and Hogstad, N.M.}},
keywords = {{Beliefs., Motivational developments, Novel approaches to teaching, Teacher education, Transition to and across university mathematics}},
pages = {{527--536}},
publisher = {{INDRUM Network, University of Agder}},
title = {{{Evaluating Innovative Measures in University Mathematics – The Case of Affective Outcomes in a Lecture focused on Problem-Solving}}},
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}},
}