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    NeuralPinT
    Parallel-in-time integration (PinT) algorithms, such as Parareal, PFASST, or MGRIT, have demonstrated significant prowess in addressing time-dependent problems. However, the construction of coarse level models for these algorithms is a challenge, demanding expertise numerics, domain science, and a profound understanding of high-performance computing (HPC). The research done in this study is focussing on advancements in leveraging machine learning (ML) techniques, specifically neural operators (NOs), to offer a more generic and efficient approach to the development of effective coarse models. The established PinT algorithms necessitate the creation of coarse level models, introducing complexities that require substantial expertise and time for implementation and tuning. In contrast, the integration of ML techniques, particularly neural operators, presents an adequate way to do this. Neural operators, in their most general form, model the solution operator of partial differential equations (PDEs), mapping a set of inputs (initial conditions, boundary conditions, forcing terms, parameters). NeuralPint formulates the solution operator as a high-dimensional neural network, with parameters learned through a training procedure. The ML-based solution operators enable the iterative construction of solutions to time-dependent problems on extended time scales. By treating the solution obtained in each iteration as the initial condition for the subsequent iteration, the ML-based approach provides a versatile and efficient strategy for solving complex PDEs over extended temporal domains. While ML-based solvers may exhibit limitations in terms of accuracy when considered in isolation, their rapid evaluation times post-training present a compelling advantage. Notably, their computing patterns align seamlessly with GPU architectures, enabling efficient utilization of accelerators. This is in contrast to traditional mesh-based numerical models, which often struggle to exploit the full potential of GPU accelerators. The combination of swift execution times and reasonable accuracy positions ML-based solvers as ideal candidates for constructing effective PinT coarse models. The comonation of ML techniques with PinT algorithms not only simplifies the construction of coarse models but also addresses the computational challenges inherent in high-performance computing environments. The inherent efficiency of ML-based solvers on GPUs aligns well with the demands of PinT coarse models, providing an optimal balance between speed and accuracy. The integration of machine learning, particularly neural operators, into the realm of PinT algorithms represents a transformative approach to constructing efficient coarse models. By capitalizing on the speed and adaptability of ML-based solvers, this methodology offers a generic solution that reduces the dependence on intricate numerical expertise and accelerates the implementation and tuning process.
      44
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    12th International Workshop on Parallel-in-time Integration
    The workshop will be a one-week hybrid event with an emphasis on in-person attendance. That means that participants who give talks will generally be expected to attend in person.1 For colleagues who are uncomfortable being in a crow or are affected by COVID-19, we will livestream all presentations via Zoom. Contingent on the agreement of the presenters, talks will be recorded and be made available either via TUHH’s mediasite platform or a commercial platform like YouTube. Suitable rooms for the workshop have already been reserved at TUHH.2 The core of the workshop will comprise four invited plenary talks of around 45 minutes time, followed by around 15 minutes questions and answers (Q & A), and up to 28 contributed talks of 25 minutes time plus 5 minutes Q & A. We could attract four international and highly qualified plenary speakers from both academica and industry.
      13
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    Positional games and their interconnection with Random Graph Theory
    Positional games are an instance of perfect-information games between two players, and research on such games lies in the intersection of Extremal Combinatorics, Ramsey Theory and Random Graph Theory. Next to ad-hoc and algorithmic arguments, the methods in Positional Games Theory reach from potential function arguments over randomized strategies and derandomization to probabilistic intuition. In particular, research of the last two decades has proven very strong interconnections between extremal results on positional games and random graphs. Questions on games have thus stimulated research in Random Graph Theory, and vice versa. Under this and further aspects, various types of positional games have been studied in the last years with the so-called Maker-Breaker games being the most famous and best studied ones. While recent research gave rise to many intriguing connections between general Maker-Breaker games and properties of random graphs, such as containment or robustness properties, far less is known for other types of positional games. Therefore, one of the central goals in recent research is to examine how far and under which conditions the known interconnections can be carried over to these other game types and how these types are related to each other in general. The goal of our work programme is to expand the general knowledge on various variants of positional games with an emphasis on their relation to Maker-Breaker games and on the general importance of randomness in the study of such games. Amongst others, this will include connections to random graph properties on one the hand and the investigation of randomized strategies on the other hand.
      39
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    TIME parallelisation: for eXascale computing and beyond
    Geldgeber: European High-Performance Computing Joint Undertaking und Bundesministerium für Bildung und Forschung Paving the way for industrial adoption of exascale computing There’s a push towards exascale computing. Imagine a computing system capable of more than one exaflop (about a billion billion calculations per second). Research into exascale computing has shown the potential of parallel-in-time integration as a powerful algorithmic paradigm. In this context, the EU-funded TIME-X project will enable efficient parallel-in-time integration for real-life applications. Bringing together leading scholars from numerical analysis and applied mathematics, computer science and the selected application domains, the project will launch a joint strategic research effort. Its aim is to advance parallel-in-time integration from an academic/mathematical methodology into a widely available technology with a convincing proof of concept.
      358
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    GRK 2583: Modeling, Simulation and Optimization of Fluid Dynamic Applications
    The RTG aims at the holistic education of junior scientists in the mathematical fields of Modeling, Simulation, and Optimization (MSO). The mathematical focus of the RTG is on mathematical modeling, adaptive discretization & approximation algorithms, mathematical data analysis, and shape optimization with PDEs. The RTG's research activities address challenging fluid dynamic problems, where they are inspired by Hamburgspecific applied sciences, such as climate research & meteorology, aerospace & marine engineering, or medicine. Our approach to next generation MSO is based on the leitmotif of the RTG: Mathematics drives applications while being inspired by applications. With this leitmotif the RTG carries forward and improves education and research in MSO by an inherent interdisciplinary approach, i.e., to stimulate fundamental education and research in MSOmathematics by highly complex applications and at the same time transfer tailored MSO-methods developed in mathematics to applied sciences. In this way, the RTG promotes an exchange of research paradigms between the participating disciplines and provides a modern approach to training in fundamental MSO-research for scientfically and socially relevant current problems. The RTG has a clear scientific focus with a well aligned educational profile. The leitmotif is implemented through nine thematically intertwined research topics, which combine aspects of MSOmathematics with an associated fluid dynamic application. Key technologies will jointly be developed and disseminated through lab-activities. Scientific exchange is facilitated and fostered through lecture series, research seminars, colloquia, annual retreats, and summer schools. The international networking of the RTG will benefit from a distinguished guest program involving a variety of world leading experts. The RTG will be hosted by the Lothar Collatz Center for Computing in Science. In particular, the RTG will be embedded in the well-established structures of the Lothar Collatz Graduate School. The academic platform of the RTG is enhanced by joining forces with established activities of the C3S and LCGS, e.g. the Lothar Collatz Seminar, and by contributing to the annual Plön Young Researcher Meeting & Workshop, and by the comprehensive course program of the Hamburg Research Academy (HRA, see Section. The educational program is based on long-standing collaborations of the involved researchers and institutions. The qualification concept is well connected to local and international educational programs that are jointly operated by the UHH and the TUHH. It reects shared experience on best practices and also supports our ambition for a rapid initial advancement as well as leadership skill promotion. Thus, the curriculum involves innovative training modules e.g. research management or entrepreneurship courses supplementary to the scientific education. With this approach the RTG is unique and will perform interdisciplinary research
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    I³-Lab - Business Analytics – Optimierungspotenziale und strategische Risiken für maritime logistische Systeme
    „Business Analytics“ beschreibt die systematische und kontinuierliche Auswertung betrieblich anfallender Daten. Dies umfasst sowohl die Analyse von Daten aus der Vergangenheit als auch die Erstellung von Prognosen sowie die auf diesen Daten basierende, mit mathematischen Methoden optimierte Entscheidungsfindung. Die maritime Logistik beschäftigt sich mit der Planung, Gestaltung und Steuerung von Waren- und Informationsströmen im Zusammenhang mit seegebundenen Transporten, z.B. von Containern. Zu den in diesem Bereich betrachteten maritimen logistischen Systemen zählen zum Beispiel Containerterminals, an denen Schiffe be- und entladen werden, aber auch das Netzwerk der Schiffsrouten. In der maritimen Logistik ergeben sich große Potenziale für die Anwendung von „Business Analytics“, denn dieser Bereich verfügt mittlerweile über sehr große Datenmengen, z.B. bzgl. Schiffsbewegungen und Wetterdaten. Diese umfangreichen Datenmengen können durch innovative Datenanalyse- und Optimierungsmethoden nutzbar gemacht und verwertet werden. So wird die Entwicklung verbesserter Strategien, z.B. im Personal- und Flotteneinsatz, und neuer Lösungen, z.B. im autonom gesteuerten Schiffsverkehr, ermöglicht. Dabei sollten jedoch stets die angewandten Methoden kritisch reflektiert und auf strategische und ethische Risiken hin untersucht werden. Im Rahmen dieses Projektes wird das Ziel verfolgt, für ausgewählte Problemstellungen aus dem Bereich der maritimen Logistik zu untersuchen, welche Chancen der verstärkte Einsatz von „Business Analytics“, also von Methoden der Datenanalyse und Optimierung, bietet und welche operativen und strategischen Risiken für Unternehmen hiermit verbunden sein können. Die Abbildung verdeutlicht zudem den interdisziplinären Charakter des Projektes. In diesem kooperieren vier Institute der Technischen Universität Hamburg, und jedes Institut bringt seine spezielle wissenschaftliche Kompetenz und Expertise in das Projekt ein, um die zu untersuchenden Sachverhalte aus unterschiedlichen Blickwinkeln zu beleuchten. Ein konkreter Forschungsgegenstand im Projekt ist zum Beispiel das Leercontainermanagement. Aufgrund von Marktungleichgewichten müssen häufig Container leer transportiert werden, um anschließend wieder zum Einsatz kommen zu können. Es ist jedoch ökonomisch und ökologisch wünschenswert, die Anzahl dieser Leertransporte gering zu halten. Mit „Business Analytics“ können mithilfe von Vergangenheitsdaten Leercontainerbewegungen in der Vergangenheit analysiert werden. Daraus lassen sich Prognosen über die zukünftigen Bedarfe ableiten, die dann in einem mathematischen Modell zur zukünftigen Steuerung der Leercontainerströme berücksichtigt werden können. Ein weiterer Forschungsbereich, der auch aus strategischer und ethischer Perspektive von großem Interesse ist, ist die Entwicklung von Methoden des sog. Revenue Management. Dabei wird untersucht, wie einerseits Unternehmen ihre Dienstleistungen, z.B. einen Containertransport oder eine Kreuzfahrt, möglichst profitabel verkaufen können, aber dabei gleichzeitig der Anspruch des Kunden an Transparenz und Fairness gewahrt werden kann. Weitere Forschungsthemen im Projekt sind z.B. die Schiffseinsatzplanung und die Entwicklung von Nachfrageprognosen.
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