Vorträge

Tail processes and tail measures are important concepts in the theory of regularly varying (heavy tailed) time series. In this talk we will show that these concepts are intimately related to Palm theory of stationary random measures. To motivate the topic, we start with providing some background on regularly varying time series. Then we shall introduce tail fields in an intrinsic way, namely as spectrally decomposable random fields satisfying a certain space shift formula. The index set is allowed to be a general locally compact Hausdorff Abelian group. The field may take its values in an Euclidean space or even in an arbitrary measurable cone, equipped with a pseudo norm. We characterize mass-stationarity of the exceedance random measure in terms of a suitable version of the classical Mecke equation. As a rule, the associated stationary measure is not finite. We shall show that it is homogeneous, that is a tail measure. Finally we will establish a spectral representation of stationary tail measures.

In this talk, we characterize quantitative semi-uniform stability for $C_0$-semigroups
arising from port-Hamiltonian systems, extending and complementing recent results
on exponential and strong stability. Using this characterization, we construct a sim-
ple, universal class of port-Hamiltonian systems that exhibit arbitrary decay rates
slower that $t^{1/2}$. This construction leverages results from the theory of Diophantine
approximation.
This is joint work with Felix Schwenninger (Twente), Ingrid Vukusic (Waterloo),
and Marcus Waurick (Freiberg).

In this talk, I will explore the application of Electrical Impedance Tomography (EIT) in chemical reactors, presenting a theoretical deduction of the underlying mathematical problem from its real-world context. The discussion will focus on the ill-posed nature of the EIT inverse problem and demonstrate how additional modeling assumptions can stabilize the reconstruction process.

The presentation explores ideas for developing an objective framework to evaluate reconstruction performance and seeks input on how to effectively incorporate physical domain information to enhance physics-based reconstruction approaches.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

For the prediction and study of water flows in a river or channel the knowledge of the bottom topography - the bathymetry - is required. Direct measurements of bathymetries are possible, but can be very expensive and time consuming. This motivates the development of methods to reconstruct a bathymetry numerically. In my thesis, an observation of the free surface level is used for this reconstruction. By defining an optimisation problem that is constrained by the one-dimensional shallow water equations it is possible to obtain an approximation on the real bathymetry. In this context, the use of Parallel-in-time methods is investigated in order to accelerate the computations.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

Transformers have been a major breakthrough in Natural Language Processing (NLP) due to their ability to capture long-range dependencies through self-attention. However, the (self-)attention mechanism suffers from massive memory consumption, especially for tasks with large context windows and high resolution data, such as climate data.

In this talk, I will present a transformer model that uses multiple icosahedral grids to enable large (physical) context windows and high resolutions for various climate-related modelling tasks.

As the model is still under development, the presentation will focus on its technical foundations and properties such as resolution independence and multi-scale output in the context of climate data.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

Spectral deferred correction (SDC) is a time-stepping method where fully implicit Runge-Kutta methods (RKM) are solved iteratively. The method is only marginally more complicated to implement than the more ubiquitous diagonally implicit RKM, and it is often simpler for obtaining high-order solutions. We present numerical experiments that show SDC to be a modern and HPC capable method with various advantages over other RKM, including efficient time-parallelisation extensions. To this end, we present adaptive step size selection algorithms for SDC and demonstrate that they boost computational efficiency and resilience against soft faults at the same time. Then, we show that the parallel-in-time algorithm diagonal SDC can be used to extend strong-scaling capabilities beyond the saturation point of space-only scaling. This enables our space-time parallel Python code for the Gray-Scott equation to scale to the entirety of the JUWELS booster machine.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09