Vorträge

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).

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

Zoomlink:
https://tuhh.zoom.us/j/88999585223?pwd=YsLVQkzLogvKJt6NNFN2x6OypSvbc9.1