To strengthen the support for excellent young researchers and to give them a head start in building their own research profile within the supportive environment of a large center,
ECMath is funding three positions for heads of Junior research Groups in application driven mathematical research. The group leaders are also part of the BMS Postdoctoral Faculty.

Optimization under Uncertainty

PI: Dr. Max Klimm
Technische Universität Berlin
Institute for Mathematics
Straße des 17. Juni 136
D-10623 Berlin, Germany
Phone: +49 (0)30 314 29400
Fax: +49 (0)30 314 25191
email: klimm(at)math.tu-berlin.de

Infrastructure networks, e.g., for traffic, public transport, energy supply and communication, are a key factor for life quality, regional development and economic growth.

The decisions on how to construct and operate these networks have a long-term impact on society and economy and, thus, call for a sound planning.
On the other hand, designing future-proof infrastructures comes with various types of uncertainties.

First, future demand for the service is unknown and can only be estimated. Second, most infrastructure networks are used by several independent parties that optimize their
own well-being rather than the overall network performance. The latter effect becomes apparent in traffic networks where each driver seeks to take a shortest route regardless
of the impact on other drivers. To cope with both the uncertainty in demands and user behavior, we develop new techniques for robust network optimization under user equilibrium constraints.

Numerics and Optimization of Robust Equilibria

PI: Dr. Carlos Rautenberg
Humboldt-Universität zu Berlin
Institute for Mathematics
Unter den Linden 6
D-10099 Berlin, Germany
Phone: +49 (0)30 2093 5497
Fax: +49 (0)30 2093 5859
email: carlos.rautenberg(at)math.hu-berlin.de

In particular, Quasi-variational Inequalities (QVIs) stand out as an specific type of these problems with a profound impact on the formulation of physical and economical phenomena.
They represent a generalization of the usual constrained optimization problem with the addition that the constraint also depends on the variable of interest.
Although some success has been obtained in the theoretical description of solutions, there are still many open questions in analytical aspects and there is a scarcity of numerical methods
that guarantee approximation of solutions due to the highly nonlinear nature of QVIs.

Generally, as controllable variables are available, optimization problems for QVIs arise naturally as certain criteria is required to be minimized or satisfied.
A successful development of solution algorithms, optimization techniques and control approximation schemes would provide tools to solve problems that go from
optimally denoising biomedical images to large scale problems as the prevention of floods in sensitive regions.

As a specific problem, we highlight the optimal placement of sensors for the estimation of the temperature distribution in buildings, which also possesses multi-scale features
and where stochastic perturbations are present. The goal here is to properly locate sensors within certain regions to reliably estimate the temperature distributions in other areas.
A successful resolution to this problem would substantially improve the energy efficiency in the control of the of the temperature in buildings.

Artificial Photosynthesis / Scientific Computing

PI: Dr. Sebastian Matera
Freie Unversität Berlin
Institute for Mathematics
Arnimallee 6 (Raum 013)
D-14195 Berlin, Germany
Phone: +49 (0)30 838 75335
Fax: +49 (0)30 838 75412
email: matera(at)math.fu-berlin.de

On a technical scale, the central interest of chemistry is the macroscopic yield of one or more chemical compounds.
On the other hand, chemical bonding and reaction are best understood on a sub-nanometer scale.

In order to utilize this understanding on a macroscopic scale, we are developing and improving electronic structure based multi-scale modeling strategies.
The focus is on stochastic mesoscopic models of surface reactivity, which link microscopic and macroscopic theories, and their integration into the numerical solution
of the partial differential equations governing macroscopic, reactive flow.

Different numerical techniques are employed and developed/improved like stochastic simulation or high dimensional interpolation/integration.
Special emphasis is put into the development of user-friendly software. With this, we address a number of problems,
e. g. the error propagation during coarse-graining or the identification of those microscopic aspects controlling macroscopic behavior.