# Job Opportunities

###
**Transregio-CRC
154 on Mathematical Modelling, Simulation and Optimization Using the
Example of Gas Networks invites applications **
**for the position of a postdoc/manager**

for job advertisement and application procedure click here

for job advertisement and application procedure click here

###
**Transregio-CRC
154 on Mathematical Modelling, Simulation and Optimization Using the
Example of Gas Networks invites applications **
**for
doctoral researchers**

more information and application procedure below

more information and application procedure below

## Information for the application procedure

You are eligible to apply for a position within the CRC 154, if

- you either hold or are about to obtain a M.Sc. degree by the starting date of the doctoral project, in one of the following areas: Mathematics, Computer Science, or in a closely related field
- you are proficient in the English language
- knowledge of the German language is not a must.

Once recruited, we will offer:

- The possibility to perform research with us in mathematical modelling, simulation and optimization in a highly innovative and active research area in applied mathematics.
- Remuneration is at E 13 TV-L (75%), according to the German public service salary scale).
- Apart from the individual research project, your research program will include trans-regional summer and winter schools, regular lectures and block courses given by guest researchers as well as lecture series that at each site are specifically designed for the main research fields of the CRC 154.
- You will be assigned two mentors that are PIs in the CRC 154 who will guide you through your doctoral research project.

- We aim at an equal representation of women and men at all levels. At each of the member sites, gender equality offices are at the CRC's disposal that offer different services for its university members. Furthermore, the CRC 154 has financial resources with which it finances gender mainstreaming, for example courses that increase the
**career chances of young female researchers.**The CRC also finances measures for improving the**compatibility of work and family life,**which includes contingents of child care places, emergency and holiday care for children and care-dependent relatives. Further details can be found at https://trr154.fau.de/index.php/en/gender-mainstreaming.

With a **single** application, you may apply for more than one position within the CRC 154 (maximum 10), in order of preference.

You will need to provide us with the following documents:

a) Application form (see here)

b) Letter of motivation (max. 1 page)

c) Copies of degree and academic transcripts (with grades and rankings)

d) Brief summary of Master's thesis (max. 1 page)

e) Short CV including letter/s of recommendation and publication list (if any)

All the above-mentioned documents **must** be collected in a single pdf file and have to be uploaded on EasyChair on

__https://easychair.org/conferences/?conf=trr1543____ __

after creating an account on easychair.org.

Please include your data for “author 1” and tick the “corresponding author” box.

As title and as abstract, please choose “Application for CRC 154”.

As keywords, please give the same ranking of the CRC 154 subprojects you apply to as you have given in the application form.

We will only consider applications if they are uploaded there.

We will come back to you soon. Shortlisted candidates will be invited for an interview (traveling to each partner's site may not be necessary). Winners will be announced as soon as possible. Applications will be considered till the corresponding positions have been filled.

## Information about the subprojects with open positions

*Falk Hante (HU Berlin)*

The project develops control theoretical methods for dynamical systems coupling partial differential equations and logic-based integer-valued components. In particular, it studies model-predictive control strategies and optimization-based variants thereof for such hybrid systems. In the third phase, a new focus is on distributed control schemes. The challenges concern well-posedness, closed-loop performance properties and algorithms for numerical realizations of such controllers. These will be met by studying variational equilibria in dynamic mixed-integer programming. The newly developed methods will be applied to decentralized control of hydrogen and natural gas pipeline systems being interconnected by mixing.

*Alexander Martin (FAU Erlangen-Nürnberg), Sebastian Pokutta (TU Berlin), position to be filled both at FAU Erlangen-Nürnberg and at TU Berlin*

In this subproject we study domain decomposition approaches for optimal control problems using the example of gas transport networks. Our main goal is to couple the space-time-domain decomposition method from the second phase with machine learning and mixed-integer programming techniques. To this end, we develop an interlinked data-driven and physics informed algorithm called NeTI (Network Tearing and Interconnection) that combines mixed-integer nonlinear programming, learning of surrogate models, and graph decomposition strategies.

*Max Klimm (TU Berlin), Marc Pfetsch (TU Darmstadt), Martin Skutella (TU Berlin), position to be filled at TU Berlin*

The goal of this project is to provide a comprehensive study of the problem of maximizing the welfare in hydrogen or gas network. Welfare is generated by satisfying routing requests where the ability to satisfy requests is limited by the physical capacity of the networks, e.g., in terms of bounds on the maximum pressures at the nodes. These questions are formulated as non-linear packing problems that lead to a coupling of the discrete decision whose requests have to be satisfied and fractional decisions about how the flows are distributed over time and within the network. The project further studies variants of the problem where the requests appear in random order, and/or a mechanism design variant where the welfare of satisfying a request is unknown to the network operator.

*Jens Lang (TU Darmstadt)*

The goal of this project is to develop a holistic dynamic multi-scale ansatz for the numerical solution of compressible instationary Euler equations with uncertain data on network structures. We will use these methods for uncertainty quantification and adaptive multi-level probabilistic constrained optimization on flow networks. For this, we combine adaptive stochastic collocation methods with kernel density estimators in an adjoint-based gradient method.

*Caroline Geiersbach, Michael Hintermüller (WIAS Berlin)*

This subproject is concerned with the coupling of an intraday gas market with the physical transport of gas through a network, subject to uncertainty. This problem is modelled as a non-cooperative equilibrium problem where each risk-averse market player makes decisions in such a way as to maximize profit while simultaneously ensuring that their collective decisions are physically feasible along the network. The goal of this project is to characterize and compute equilibria to this problem. For this, we study the existence of solutions and their sensitivity to perturbations in parameters. To develop algorithms to handle the problem computationally, stochastic approximation and feedback-type mechanisms are employed.

Ioannis Giannakopoulos, Alexander Martin (FAU Erlangen-Nürnberg)

In this subproject we model and analyse multiparameter auction problems on graph structures, motivated by the gas network paradigm. Our main goal is to characterize the structure of revenue-optimal auctions in these network-constrained, multidimensional Bayesian settings, as well as to provide rigorous approximation guarantees. To do so we bring together machinery from the fields of optimal mechanism design, algorithmic game theory, mixed-integer programming, and polyhedral combinatorics.

*Veronika Grimm, Julia Grübel, Alexander Martin (FAU Erlangen-Nürnberg)*

The goal of this subproject is to develop mathematical methods to solve mixed-integer and nonlinear multilevel optimization problems for gas markets coupled with markets of other energy sectors such as electricity. Motivated by the two cases of cooperating or non-cooperating network operators of the different sectors, we investigate on the one hand bilevel problems with potentially multiple solutions on the lower level, for which we establish methods to assess pessimistic solutions. On the other hand, we study multi-leader-follower games and develop problem-tailored solution approaches. Finally, based on our mathematical and algorithmic developments, we characterize equilibria in coupled energy systems for different combinations of market designs in the considered sectors.

*Frauke Liers (FAU Erlangen-Nürnberg), Andrea Walther (HU Berlin), position at HU Berlin*

Bilevel optimization is a wide area in mathematical optimization and plays an important role in the TRR 154, where the coupling of producers and consumers represents one prominent application and the robust protection against uncertainties another one. Many of these bilevel problems can be formulated as nonsmooth, piecewise linear optimization problems with constraints. This project aims at the development, analysis and implementation of a structure-exploiting algorithm for bilevel problems of this kind building on the quite recent approach of abs-linearization and the active signature method. This allows also to treat nonsmooth functions in a bilevel optimization.

*Caren Tischendorf (HU Berlin)*

The project aims to develop stable simulations for coupled network DAEs that allow to find feasible and optimal dynamic controls for coupled networks. We concentrate on networks for gas transport. Couplings of interest arise, for example, from the increasing demand to produce and transport hydrogen in the future. A particular focus goes to the treatment of valves and regulators described by piecewise differentiable functions. We aim to provide an optimal dynamic control for coupled gas networks using the approach to first discretize in space, then optimize the resulting DAE system and finally use our least squares collocation approach for time integration of the boundary value optimality DAE.

*Falk Hante (HU Berlin), Enrique Zuazua (FAU Erlangen-Nürnberg), position at FAU Erlangen-Nürnberg*

The goal of this subproject is to reduce the computational cost of solving dynamical optimal control problems of PDEs modelling gas transport on large networks by developing a stochastic gradient descent procedure based on domain decomposition methods. The main idea is to find a descent direction based only on the sensitivity of the dynamics on a randomly determined subgraph and couple this with an analysis of the network topology and with graph clustering methods. To apply this procedure in the context of gas transport, it is planned to significantly expand the optimal control theory and adjoint methodology for doubly nonlinear parabolic equations as a reformulation of the friction dominated isothermal Euler equations.

*Michael Hintermüller (WIAS Berlin)*

The goal of this project is the development of stochastic gradient methods for the treatment of almost sure state constraints. Such constraints arise for example in the nomination validation of gas networks under uncertain demands but also play a role in the transition towards future hydrogen networks. A focus of the project is the consideration of sequences of relaxed problems intertwined with the stochastic gradient method and a rigorous mathematical convergence analysis of the resulting methods.