Talks

Iterative parallel-in-time algorithms like Parareal can extend scaling beyond the saturation of purely spatial parallelization when solving initial value problems.
However, they require the user to build coarse models to handle the inevitable serial transport of information in time.
This is a time-consuming and difficult process since there is still limited theoretical insight into what constitutes a good and efficient coarse model.
Novel approaches from machine learning to solve differential equations could provide a more generic way to find coarse-level models for parallel-in-time algorithms.
This talk demonstrates that a physics-informed Fourier Neural Operator (PINO) is an effective coarse model for the parallelization in time of the two-asset Black-Scholes equation using Parareal.
We demonstrate that PINO-Parareal converges as fast as a bespoke numerical coarse model and that, in combination with spatial parallelization by domain decomposition, it provides better overall speedup than both purely spatial parallelization and space-time parallelization with a numerical coarse propagator.

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

Conlon and Gowers in 2016 described a general approach to proving sparse random analogues of extremal results in combinatorics, such as bounding the minimum and maximum number of triangles in any subgraph of G(n,p) with a given number of edges. The general part of this approach is a functional-analytic statement which, given a sparse setting, constructs a dense model. However, there is a condition which must be shown to hold with high probability to apply the dense model theorem. In Conlon and Gowers' work, there is a technical difficulty with the probabilistic part which leads to a rather involved proof, which applies only in a restricted setting (for example, they can handle triangles but not triangles with a pendant edge), and with quite poor bounds on 'high probability'.

We revisit Conlon and Gowers' approach, and show how to avoid their technical problem, giving a simpler proof of their counting result which applies in a general setting and with optimal probability bounds. As a corollary, we prove the 'Counting KLR' theorem of Conlon, Gowers, Samotij and Schacht, but for general hypergraphs and with optimal probability bounds. This is joint work with Julia Boettcher, Joanna Lada and Domenico Mergoni.

Ungefähre Themen des Vortrags:
1. Probleme der Intervallberechnung.
2. Die Beziehung zwischen Intervallanalyse und Wahrscheinlichkeitstheorie.
3. Bayesianisches Modell der kollektiven Entscheidungsfindung und seine Intervallverallgemeinerung.

Machine learning is often explored and developed in isolation from real-world contexts, primarily focusing on abstract tasks or benchmark datasets. However, when integrated into real-world applications, a crucial factor comes into play: human involvement. This talk will introduce human-centric machine learning, a growing field that emphasizes the need to account for human presence at every stage of the ML pipeline. I will present several practical examples illustrating how machine learning can be made more interactive and accessible to non-experts

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

Zoomlink:
https://meeting.rz.tuhh.de/rooms/xvo-f8c-vxq-oz9/join

The availability of real-time phase-resolved wave fields is crucial for the prediction and control of wave-induced motion of marine structures, a key parameter to extend the operational envelope and improve the optimal maneuvering of surface vessels. Using marine radar measurements of the ocean surface, the first step of the prediction problem is to reconstruct the surface dynamics (i.e. to extract the wave-related information from the measurements) in order to get the initial state of a wave model and propagate it in time to obtain the future wave conditions. Although fast and accurate models are available to propagate wave fields, the surface reconstruction — which can be seen as a nonlinear PDE-constrained optimization problem — is a very challenging task to perform in real time. In this talk, the specifics of the problem, which include the cost function to minimize, the wave model (PDE) and the optimization procedure, will be first presented with an emphasis on the use of parallel computation. Then, results will be shown for the simplified case of unidirectional waves. Finally, ideas for the efficient implementation (e.g. parallel in time) of the solver in the case of directional waves will be discussed.