E-Dissertationen: Browsing E-Dissertationen by Author "Garcke, Jochen"
Now showing items 1-14 of 14
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Algebraic Multigrid for Eigenproblems in Industrial Applications of Big Data and Engineering
Gries, Silvia (2023-12-18)More and more data are generated and gathered by computational simulations, network evaluations, and sensor usage in industrial applications and many other methods. To make the most out of the collected data, these should ... -
Algebraic Multigrid for Meshfree Methods
Nick, Fabian Pascal (2020-02-11)This thesis deals with the development of a new Algebraic Multigrid method (AMG) for the solution of linear systems arising from Generalized Finite Difference Methods (GFDM). In particular, we consider the Finite Pointset ... -
The ANOVA decomposition and generalized sparse grid methods for the high-dimensional backward Kolmogorov equation
Hullmann, Alexander (2015-03-12)In this thesis, we discuss numerical methods for the solution of the high-dimensional backward Kolmogorov equation, which arises in the pricing of options on multi-dimensional jump-diffusion processes.
First, we apply ... -
Error analysis of regularized and unregularized least-squares regression on discretized function spaces
Bohn, Bastian (2017-01-04)In this thesis, we analyze a variant of the least-squares regression method which operates on subsets of finite-dimensional vector spaces.
In the first part, we focus on a regression problem which is constrained to ... -
Geometrical Methods for the Analysis of Simulation Bundles
Iza Teran, Victor Rodrigo (2017-03-29)Efficiently analyzing large amounts of high dimensional data derived from the simulation of industrial products is a challenge that is confronted in this thesis. For this purpose, simulations are considered as abstract ... -
Informed Machine Learning: Integrating Prior Knowledge into Data-Driven Learning Systems
von Rüden, Laura (2023-11-14)Machine Learning is an important method in Artificial Intelligence (AI). It has shown great success in building models for tasks like prediction or image recognition by learning from patterns in large amounts of data. ... -
Interpretable deep learning for studying the Earth system: Soil-moisture-precipitation coupling across Europe
Tesch, Jan Tobias (2023-11-23)The Earth system is a highly complex dynamical system. While considerable process understanding has been achieved in past research, many processes and relations in the Earth system remain poorly understood due to this ... -
Intrinsic Dimension Estimation using Simplex Volumes
Wissel, Daniel Rainer (2018-01-18)In this thesis, we introduce a novel approach for the estimation of the intrinsic dimension of high-dimensional datasets. For this purpose, the volumes of high-dimensional simplices, with vertex points sampled from local ... -
Low-dimensional Representations for Diverse Collections of 3D Surface Meshes
Hahner, Sara Vera (2024-02-29)The surfaces of 3D shapes are discretized by surface meshes that represent them in a processable way. This enables simulations of deforming components in CAE, animations for movies, or representations of human organs to ... -
Maschinelles Lernen durch Funktionsrekonstruktion mit verallgemeinerten dünnen Gittern
Garcke, Jochen (2004)Diese Arbeit beschäftigt sich mit einem neuen Ansatz für das Klassifikationsproblem beim Maschinellen Lernen durch Funktionsrekonstruktion. Es basiert auf dem Zugang des Regularisierungsnetzwerks, aber im Gegensatz zu ... -
Numerical Methods for Uncertainty Quantification in Gas Network Simulation
Fuchs, Barbara (2018-09-26)When modeling the gas flow through a network, some elements such as pressure control valves can cause kinks in the solution. In this thesis we modify the method of simplex stochastic collocation such that it is applicable ... -
The Signature Transform in Numerics and Machine Learning
Paparella, Biagio (2024-04-23)In this work we study the signature transform from the viewpoint of applied and numerical mathematics.
The theoretical background is established in the first part, where the signature is defined as a map ... -
Simulation of Ion Migration with Particle Dynamics and the Heat-Poisson-Nernst-Planck System
Neuen, Christian P. T. (2016-12-22)In this thesis we study the numerical simulation of ion migration and its coupled thermal effects. Many of the existing mathematical models in this area of research implicitly rely on thermal equilibrium conditions, despite ... -
Social-aware Robot Navigation based on Deep Reinforcement Learning
Zhou, Yanying (2024-04-24)With the increase of applications involving autonomous mobile robots, there is a growing need for them to navigate safely and effectively in environments shared with humans. In recent years, social-aware robot navigation ...