Die Veranstaltung finden zusammen statt mit 03-M-SP-26 !

Die Veranstaltung findet zusammen mit der 03-M-SP-2 statt

The lecture deals with the discretisation of partial differential equations and the estimation of the error between continuous and discrete solution. The connection of theory, numerical analysis and implementation is particularly important. The numerical algorithms are to be implemented in programming tasks under guidance.

Profil: SQ
Schwerpunkt: IMA-SQ, IMA-AI
https://lvb.informatik.uni-bremen.de/imat/03-imat-au.pdf


A key assumption of many powerful optimization methods is that all the data is fully accessible from the beginning.

However, from the point of view of many real-world applications (e.g., in logistics, production or project planning, cloud computing, etc.) this assumption is simply not true. Large data centers allocate resources to tasks without knowledge of exact execution times or energy requirements; transit times in networks are often uncertain; or, parameters such as bandwidth, demands or energy consumption are highly fluctuating. The current trend of data collection and data-driven applications often amplifies this phenomenon. As the amount of available data is increasing tremendously due to internet technology, cloud systems and sharing markets, modern algorithms are expected to be highly adaptive and learn and benefit from the dynamically changing mass of data.

In the above examples, our knowledge of the current data is only partial or based on historical estimates. The class ``Algorithms and Uncertainty'' will teach students about the most common models of such uncertain data and how to design and analyze efficient algorithms in these models.

Specifically, we will cover the theory of online optimization, where the input arrives without any prior information (such as network packets arriving to a router) and also needs to be processed immediately, before the next piece of input arrives. This model is best suited for analyzing critical networking and scheduling systems where devices and algorithms must perform well even in the worst-case scenario.

In the cases where previous history can be used to model the upcoming data, we often employ robust optimization or stochastic optimization. In robust optimization, the aim is to optimize the worst-case of all possible realizations of the input data. Hence, this model is rather conservative.
In stochastic optimization however, the algorithms work with the assumption that data is drawn from some probability distribution known ahead of time and typically the goal is to optimize the expected value.

Nowadays, another source of information is often available: machine learning algorithms can generate predictions which are accurate most of the time. However, there is no guarantee on the quality of the prediction, as the current instance may not be covered by the training set. This statement motivated a very recent research domain that will be covered in this course: how to use error-prone predictions in order to improve guaranteed algorithms.

Organization: The course will be taught in English in two sessions per week (4 SWS) including interactive exercise sessions.

Examination: The examination will be by individual oral exam. As admission to the oral exam it is mandatory to present solutions in the exercise session at least twice during the term.

Prerequisites: Having heard an introductory course to discrete algorithms and their mathematical analysis (e.g. Algorithmentheorie, Algorithmische Diskrete Mathematik) or graph theory is beneficial but not required.

Die Veranstaltung findet zusammen mit 03-M-FTH-10 statt.

Findet zusammen mit der LV 03-M-FTH-9 statt.

The quantitative assessment and the management of (extreme) risks are key tools for policy makers and stakeholders in many areas such as climate and environmental research, economics, or finance and insurance. In this course, we will get familiar with basic mathematical concepts of (quantitative) risk assessment and management.

The finite element method is used for the discretisation of partial differential equations in many different applications. In this course we will deepen existing knowledge in finite element methods with respect to different applications and learn new techniques to increase their computational speed.

This course focusses on two advanced tools in modern mathematical image processing, namely the direct method of variational calculus and the iterated soft thresholding algorithm.

Frequency: The seminar is planned as a block seminar, meaning that all talks will be at up to three days, most likely in the middle of December. We will discuss this in the first meeting. The first (organizational) meeting is planned as follows: Wednesday, October 16, at 14:00 pm in the room MZH 3150.

Learning Outcome:
Students learn how recent advances in algorithm theory can be used to improve state-of-the-art algorithms to obtain faster, better or new types of algorithms. They learn about relevant problems that are important and used in many applications. The main goals are to understand, design, and analyze algorithms for solving such problems.
Furthermore, the students will learn how to read and thoroughly understand original research papers. They learn how to prepare slides for these papers and give an oral presentation to other students who have no prior knowledge about the paper.

Contents: This seminar focuses on recent advances in algorithm theory. Most topics considered include important problems on graphs, typically related to optimization problems. These advances include faster running times of the algorithms, solutions with improved performance guarantees or new concepts in algorithm design, such as algorithms with machine-learned predictions.

This is a seminar with subjects from numerical methods for PDEs, expecially finite element methods, with applications to real world problems.

Homepage zur Veranstaltung: https://www.uni-bremen.de/rtg-pi3/qualification/rtg-seminar

3 SWS Seminar
Die Veranstaltung kann nach BPO'10 als BE-6 angerechnet werden und nach BPO'20 nur in Freie Wahl

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