Vorträge

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

The goal of parallel-in-time methods is to employ parallelism in the time direction in addition to the space direction, in the hope of obtaining further parallel speedups at the limits of what is possible due to spatial parallelism with domain decomposition alone. Recently diagonalisation techniques have emerged as a way of solving the coupled system for the solution of a differential equation at several timesteps simultaneously. One approach, sometimes referred to as “ParaDiag II” involves preconditioning this “all-at-once” system obtained from time discretisation of a linear constant coefficient ODE (perhaps obtained as the space discretisation of a time dependent PDE) with a nearby system that can be diagonalised in time, allowing the solution of independent blocks in parallel. For nonlinear PDEs this approach can form the basis of a preconditioner within a Newton-Krylov method for the all-at-once system after time averaging the (now generally time dependent) Jacobian system. After some preliminary description of the ParaDiag II approach, I will present results from our investigation of ParaDiag II applied to some testcases from the hierarchy of models used in the development of dry dynamical cores for atmosphere models, including performance benchmarks. Using these results I will identify the key challenges in obtaining further speedups and identify some directions to address these.

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

We present a deep learning-based object tracking framework designed to accurately extract particle trajectories in diverse experimental settings. This framework, which leverages the state-of-the-art object detection model YOLO and the Hungarian Algorithm, is particularly effective for scenarios where objects remain within the scene without coalescence. Our simple approach, requiring minimal initial human input, enables efficient, fast, and accurate extraction of observables of interest across various experimental configurations. The result is high-fidelity data ideally suited for data-driven modeling applications..
The framework is applied to walking droplets experiments, where a liquid droplet, known as a walker, propels itself laterally on the free surface of a vibrating bath of the same liquid. Walking droplets are of significant scientific interest as they are the only known example of quantum-like behaviors at a macroscopic scale Our methodology can track individual walker(s) in real-time across a broad spectrum of experimental settings without suffering from identity-switch issues.

Zoomlink:
https://tuhh.zoom.us/j/81621997062?pwd=fjCD4BJ4QUeI1apbqojagLM7L37Rpl.1

In this talk I will present some recent results on polynomial decay rates for C0-semigroups, assuming that the resolvent grows polynomially at infinity in the complex right half-plane. Unlike many of the recent developments in the literature our results do not require the semigroup to be uniformly bounded. The talk is based on joint work with Chenxi Deng and Jan Rozendaal.

Entropy stability is the foundation of numerical methods for hyperbolic conservation laws, thereby ensuring the stability and reliability of the resulting numerical solutions. Summation-by-parts (SBP) operators provide a general framework to systematically develop entropy-stable schemes by mimicking continuous properties on a discrete level. They have proven to be a powerful tool to provide stable and high-order accurate numerical solutions. Classically, they are developed in order to differentiate polynomials up to a certain degree exactly. However, in many cases alternative function spaces are more appropriate to approximate the underlying solution space. Especially in multidimensional problems with potentially complex domains radial basis functions are known to possess very good approximation properties. The theory of radial basis function approximation provides us with stability and convergence results for scattered data approximation in a meshfree setting.
This talk discusses properties and efficient construction algorithms for multidimensional function space SBP (MFSBP) operators based on scattered data. I focus on radial basis function spaces and show some preliminary results for using MFSBP operators to solve conservation laws. I give an outlook on how convergence results of radial basis functions can be used to prove long-time error behavior of SBP discretizations for linear advection problems.

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