Flexible Research Platform
If there is a current demand, due to certain problem areas and topics arising, additional temporary and short-term groups are set up in a flexible research platform. Currently, the following groups exist (besides the WIAS research groups):
Numerical Methods for Innovative Semiconductor Devices
- Head: Priv.-Doz. Dr. Patricio Farrell
We solve nonlinear systems of partial differential equations, describing charge transport in semiconductors. Typical challenges include boundary layers, nonlinear diffusion and how to correctly preserve the physics. To efficiently solve the PDE system, we develop specialized finite volume methods on anisotropic Voronoi meshes as well as problem-dependent preconditioners. This allows us to simulate innovative semiconductor devices based on perovskites, nanowires and accurate lasers used in self-driving cars.
Probabilistic Methods for Dynamic Communication Networks
- Head: Prof. Dr. Benedikt Jahnel
We perform rigorous applied mathematical research at the interface with data-driven network engineering: Here the main aims are to (i) study connectivity improvements in mobile urban device-to-device augmented networks with the help of dynamic continuum percolation theory, (ii) investigate data routing in device-to-device systems with a focus on bottleneck behavior and thereby advance large-deviations theory for space-time point processes, and (iii) analyze malware propagation in dynamic device-to-device networks by extending the theory of interacting particle systems to random graphs in the continuum.
Data-driven Optimization and Control (Weierstrass group)
- Head: Dr. Jia-Jie Zhu
The research focuses on the mathematical foundations and applications of machine learning and data-driven optimization and control, especially on robustness (distributional robustness, adversarial robustness, generalization, causal intervention, robust optimization), and interfacing dynamical systems and learning.
Multi-species Balance Laws (Weierstrass group)
- Head: Dr. Katharina Hopf
The research is concerned with the mathematical analysis of systems of nonlinear evolutionary partial differential equations arising in the continuum mechanical modelling of diffusive mixtures and multi-component fluids. It aims to contribute to the Cauchy theory for relevant classes of hyperbolic-parabolic-elliptic models, to the qualitative understanding of regimes of instability, to the development of relative entropy/energy methods, and to the derivation of effective models.
Quantitative analysis of stochastic and rough systems (Focus platform)
- Head: Prof. Dr. Peter K. Friz, Dr. Christian Bayer
Stochastics plays an increasingly central role in numerous scientific as well as engineering problems, both as a powerful computational tool and as a model of uncertainties inherent in complex phenomena. The aim of the work is to conduct research at the intersection and forefront of the afore-mentioned fields.
Simulation of Semiconductor Devices for Quantum Technologies (Focus platform)
- The engineering of semiconductor devices for quantum technologies requires powerful device-scale models that bridge the gap between classical electrical engineering, semiconductor physics and open quantum systems. In collaboration with application partners, the focus platform works on components for semiconductor-based quantum computers and quantum photonic devices. By combining the expertise of several research groups, the objective is to advance the mathematical modeling, numerical simulation and optimization of such devices.
An overview of former groups of the flexible research platform may be found here » .