Dr. Anna Thünen

Vita

• 10/2021--present Post-Doc TU Clausthal (A.Potschka)
• 01/2022--03/2022 Post-Doc CNR/La Sapienza (E.Cristiani, G.Puppo)
• 10/2020-09/2021 Post-Doc RWTH Aachen (M.Herty)
• 02/2021 Dr.rer.nat. RWTH Aachen (M.Herty, S .Steffensen)
• 04/2017 M.Sc. Uni Magdeburg (S.Sager, S .Leyffer)
• 12/2014 B.Sc. Uni Magdeburg (L.Tobiska)

Research

Analysis and Computation of Solutions of Continuous Optimization with Discrete Structures.

Articles and Preprints:

• Michael Herty, Sonja Steffensen, and Anna Thünen: Multiscale Control of Stackelberg Games (Math. Comput. Simul. 2022)[Preprint]
• Sven Leyffer, Sebastian Sager, and Anna Thünen: State Elimination for Mixed-Integer Optimal Control of PDEs by Semigroup Theory (OCAM 2022)
• Michael Herty, Anna Thünen, Torsten Trimborn, Giuseppe Visconti: Continuous limits of residual neural networks in case of large input data (2021)
• Nina Hartgenbusch, Anna Thünen, and Rik W. De Doncker: Optimized Pulse Patterns for Salient Synchronous Machines (IEEJ Trans. IA 2021)
• Michael Herty, Sonja Steffensen, and Anna Thünen: Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower’s Best Response (OMS 2020)[Preprint]

Proceedings and Book Chapters:

• Jan Becker, Alexandra Schwartz, Sonja Steffensen and Anna Thünen: Extensions of Nash Games in Finite and Infinite Dimensions with Applications (Non-Smooth and Complementarity-Based Distributed Parameter Systems. International Series of Numerical Mathematics, vol 172. Birkhäuser 2022)

• Michael Herty and Anna Thünen: Consistent Control of a Stackelberg Game with Infinitely many Followers (IEEE CDC 2021)
• Nina Hartgenbusch, Rik W. De Doncker, and Anna Thünen: Optimized Pulse Patterns for Salient Synchronous Machines (IEEE ICEMS 2020)
• Sonja Steffensen and Anna Thünen: An Explicit Nash Equilibrium to a Multi‐Leader‐Follower Game (PAMM 2019)

Theses:

• PhD: Analysis and Computation of Equilibria in Multilevel Games with Finitely and Infinitely many Players, RWTH Aachen University, 2021.
• MSc: Solving Mixed-Integer Partial Differential Equation Constrained Optimization, Otto von Guericke University Magdeburg, 2017.

Activities

• I coordinate the equal opportunity activity group within SPP1962. Please contact me in case you are member of SPP1962 and would like to join the activity group.
• Dima Moser, Saskia Dietze, and myself were the spokespersons of the scientific assistants at IGPM until September 2021. (RWTH)
• I co-organized a session on mean field games for 19th International Symposium on Dynamic Games and Applications in Porto June 16-19, 2020. [Canceled]
• I was Vice President of the Student Chapter of SIAM in Aachen until September 2020. Check out our blog.
• I co-organized MESIGA 2019 [Meeting of European SIAM and GAMM Chapters] which took place in Aachen September 9-11, 2019.
• I organized the session Nash Equilibrium Problems and Extensions (hierarchy, dynamics and applications) for ICCOPT in Berlin August 5-8, 2019.
• Referee service for Mathematics of Computation, Mathematics and Computers in Simulation, Applied Mathematics and Computation, Optimization Letters.

Further Collaborations

• Mathematical Multiscale Models with Gabriella Puppo (U Roma 1) and Emiliano Cristiani (CNR)
• Multiscale Control Concepts with Simone Göttlich (U Mannheim)
• I do some consultancy on optimization of highly nonlinear problems arising in electric engines with Nina Hartgenbusch (ISEA)
• I study special structures in multi level games with Anja Schedel (U Augsburg)

Current Projects

• Modern Methods for Optimization Problems with Guignard Constraint Qualification (2021-2023) Most algorithms for nonlinear optimization require MFCQ or LICQ as constraint qualification. However not all problems meet this requirement, especially the large class of bilevel optimization problems. Usually regularisation or smoothing techniques are applied in these cases. The goal of this research project is to investigate modern methods and theory that do not need regularization of the problem itself.
• Mathematical Multiscale Models for Control and Forecasting of Vehicular Traffic (2021-2022) financed by DAAD The multiscale modeling technique allows the description of particle systems using methods of kinetic theory for a wide range of applications, including traffic flow, pedestrian dynamics, and swarming behavior of animals. The model classes studied in this context are: Micro-, meso-, and macroscopic models. The finest models are the microsopic ones which study every particle, e.g. a car, a pedestrian, or a bird, individually. The mesoscopic and macroscopic models zoom out and look at the overall behavior of the crowd by considering averaged quantities such as density. There are close relations between the model classes that are studied in numerous research publications but are not yet fully understood for all models and applications. We deal with a traffic model on networks and aims to match an optimal control problem on the macroscopic level to a corresponding microscopic model in order to model the junctions in the network. Theoretical investigations are accompanied by development of algorithms and numerical experiments. Further, we study a composite of two models to obtain a realistic description of traffic on a highway with both cars and trucks. This model is extended by the use of real time data and mobile sensors to adjust traffic forecasts. Both aim to reduce traffic jams and investigate how to influence traffic flow with means of optimal control and precise forecasting.
• Multiscale Control Concepts for Transport-Dominated Problems (2020-2022) In recent years, the description of controllable (or active) particle systems using methods of kinetic gas theory has been achieved and allows now to tackle a wide range of applications as for example traffic flow. In this research project, the inherent hierarchy exploited extensively in kinetic theory for theoretical and numerical considerations will be investigated in order to develop novel analytical and numerical methods for control problems posed on multiple scales as well as under aspects of non-smoothness in the control. The work program includes the analysis of consistent optimality conditions within the model hierarchies, numerical analysis for control aspects relevant in particular on the highest level of the model hierarchy, as well as the development of numerical methods for time-dynamic non-smooth optimization problems on all levels. In addition to the sensitivity of non-smooth kinetic equations, the multi-scale nature of the equations raises questions for boundary control problems of nonlocal hyperbolic equations and switching systems.

Teaching

• Continuous Game Theory, Lecturer, summer term 2022
• Vertiefung Optimierung, co-Organization and exercise sessions, winter term 2021/22
• Lineare Algebra und Analysis 1, co-Organization and exercise sessions, winter term 2021/22
• Seminar: Optimization C (Continuous Optimization), Organization, summer term 2021
• Mathematik I/II (für Bauing., Umwelting., Wirtschaftsing. FR Bau, Mobilität und Verkehr), co-Organization and exercise sessions , winter term 2017/18 - summer term 2021
• Optimization C (Continuous Optimization), Organization and exercise sessions, winter term 2020/21
• Seminar: Differential Games, Organization, winter term 2018/19