05 Fakultät Informatik, Elektrotechnik und Informationstechnik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/6
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Item Open Access Data-efficient and safe learning with Gaussian processes(2020) Schreiter, Jens; Toussaint, Marc (Prof. Dr. rer. nat.)Data-based modeling techniques enjoy increasing popularity in many areas of science and technology where traditional approaches are limited regarding accuracy and efficiency. When employing machine learning methods to generate models of dynamic system, it is necessary to consider two important issues. Firstly, the data-sampling process should induce an informative and representative set of points to enable high generalization accuracy of the learned models. Secondly, the algorithmic part for efficient model building is essential for applicability, usability, and the quality of the learned predictive model. This thesis deals with both of these aspects for supervised learning problems, where the interaction between them is exploited to realize an exact and powerful modeling. After introducing the non-parametric Bayesian modeling approach with Gaussian processes and basics for transient modeling tasks in the next chapter, we dedicate ourselves to extensions of this probabilistic technique to relevant practical requirements in the subsequent chapter. This chapter provides an overview on existing sparse Gaussian process approximations and propose some novel work to increase efficiency and model selection on particularly large training data sets. For example, our sparse modeling approach enables real-time capable prediction performance and efficient learning with low memory requirements. A comprehensive comparison on various real-world problems confirms the proposed contributions and shows a variety of modeling tasks, where approximate Gaussian processes can be successfully applied. Further experiments provide more insight about the whole learning process, and thus a profound understanding of the presented work. In the fourth chapter, we focus on active learning schemes for safe and information-optimal generation of meaningful data sets. In addition to the exploration behavior of the active learner, the safety issue is considered in our work, since interacting with real systems should not result in damages or even completely destroy it. Here we propose a new model-based active learning framework to solve both tasks simultaneously. As basis for the data-sampling process we employ the presented Gaussian process techniques. Furthermore, we distinguish between static and transient experimental design strategies. Both problems are separately considered in this chapter. Nevertheless, the requirements for each active learning problem are the same. This subdivision into a static and transient setting allows a more problem-specific perspective on the two cases, and thus enables the creation of specially adapted active learning algorithms. Our novel approaches are then investigated for different applications, where a favorable trade-off between safety and exploration is always realized. Theoretical results maintain these evaluations and provide respectable knowledge about the derived model-based active learning schemes. For example, an upper bound for the probability of failure of the presented active learning methods is derived under reasonable assumptions. Finally, the thesis concludes with a summary of the investigated machine learning problems and motivate some future research directions.Item Open Access The Generalized Minimum Manhattan Network Problem(2015) Schnizler, MichaelIn this thesis we consider the Generalized Minimum Manhattan Network Problem: given a set containing n pairs of points in R2 or Rd, the goal is to find a rectilinear network of minimal length which contains a path of minimal length (a so-called Manhattan path) between the two points of each pair. We restrict our search to a discrete subspace and show that under specific conditions an optimal solution can be found in polynomial time using a dynamic program. The conditions concern the intersection graph of the bounding boxes of the pairs. Its maximum degree as well as the treewidth must be bounded by two constants which are independent of n. Finally, we present a simple greedy algorithm for practical purposes.Item Open Access Circuit complexity of group theoretic problems(2021) Weiß, Armin; Diekert, Volker (Prof. Dr. rer. nat.)In dieser kumulativen Habilitationsschrift werden sechs Arbeiten zum Thema "Schaltkreiskomplexität von Gruppentheoretischen Problemen" zusammengefasst. An vorderster Stelle steht hierbei das Wortproblem: Gegeben ein Wort über den Erzeugern einer Gruppe, ist die Frage, ob das Wort das Einselement der Gruppe darstellt. Daneben werden noch weitere Probleme, wie das Konjugationsproblem, das Power-Wortproblem (wie das Wortproblem, aber die Eingabe wird in komprimierter Form gegeben) und das Lösen von Gleichungen betrachtet. Die meisten der hier zusammengefassten Arbeiten betrachten die genannten Probleme für spezielle Klassen von Gruppen und klassifizieren deren Komplexität mit Methoden der Schaltkreiskomplexität. Eine Ausnahme bildet die letzte Arbeit zum Thema Gleichungen: hier liegt der Zusammenhang zur Schaltkreiskomplexität darin, dass sich das Erfüllbarkeitsproblem für Gleichungen in endlichen auslösbaren Gruppen ähnlich verhält wie das Erfüllbarkeitsproblem für CC^0 Schaltkreise.Item Open Access Load-balancing for scalable simulations with large particle numbers(2021) Hirschmann, Steffen; Pflüger, Dirk (Prof. Dr.)Item Open Access Equation satisfiability in solvable groups(2022) Idziak, Paweł; Kawałek, Piotr; Krzaczkowski, Jacek; Weiß, ArminThe study of the complexity of the equation satisfiability problem in finite groups had been initiated by Goldmann and Russell in (Inf. Comput. 178 (1), 253-262, 10 ) where they showed that this problem is in P for nilpotent groups while it is NP -complete for non-solvable groups. Since then, several results have appeared showing that the problem can be solved in polynomial time in certain solvable groups G having a nilpotent normal subgroup H with nilpotent factor G / H . This paper shows that such a normal subgroup must exist in each finite group with equation satisfiability solvable in polynomial time, unless the Exponential Time Hypothesis fails.Item Open Access Quantum support vector machines of high-dimensional data for image classification problems(2023) Vikas Singh, RajputThis thesis presents a comprehensive investigation into the efficient utilization of Quantum Support Vector Machines (QSVMs) for image classification on high-dimensional data. The primary focus is on analyzing the standard MNIST dataset and the high-dimensional dataset provided by TRUMPF SE + Co. KG. To evaluate the performance of QSVMs against classical Support Vector Machines (SVMs) for high-dimensional data, a benchmarking framework is proposed. In the current Noisy Intermediate Scale Quantum (NISQ) era, classical preprocessing of the data is a crucial step to prepare the data for classification tasks using NISQ machines. Various dimensionality reduction techniques, such as principal component analysis (PCA), t-distributed stochastic neighbor embedding (tSNE), and convolutional autoencoders, are explored to preprocess the image datasets. Convolutional autoencoders are found to outperform other methods when calculating quantum kernels on a small dataset. Furthermore, the benchmarking framework systematically analyzes different quantum feature maps by varying hyperparameters, such as the number of qubits, the use of parameterized gates, the number of features encoded per qubit line, and the use of entanglement. Quantum feature maps demonstrate higher accuracy compared to classical feature maps for both TRUMPF and MNIST data. Among the feature maps, one using 𝑅𝑧 and 𝑅𝑦 gates with two features per qubit, without entanglement, achieves the highest accuracy. The study also reveals that increasing the number of qubits leads to improved accuracy for the real-world TRUMPF dataset. Additionally, the choice of the quantum kernel function significantly impacts classification results, with the projected type quantum kernel outperforming the fidelity type quantum kernel. Subsequently, the study examines the Kernel Target Alignment (KTA) optimization method to improve the pipeline. However, for the chosen feature map and dataset, KTA does not provide significant benefits. In summary, the results highlight the potential for achieving quantum advantage by optimizing all components of the quantum classifier framework. Selecting appropriate dimensionality reduction techniques, quantum feature maps, and quantum kernel methods is crucial for enhancing classification accuracy. Further research is needed to address challenges related to kernel optimization and fully leverage the capabilities of quantum computing in machine learning applications.Item Open Access Discontinuous Galerkin methods for two-phase flows in porous media(2010) Grüninger, ChristophIn this work two-phase flows in porous media are simulated numerically with Discontinuous Galerkin methods. The three methods Symmetrical Interior Penalty Galerkin method (SIPG), Non-symmetrical Interior Penalty Galerkin method (NIPG) and the scheme from Oden, Babuška and Baumann (OBB) are considered. The terminology and the examples are taken from soil science. First the Richards equation is solved using these methods. Then a two-phase flows problem in the saturation/pressure formation is solved with OBB and NIPG. The numerical methods are implemented using the software toolkit PDELab. They are tested with examples from other publications. Weighted averages for absolute and relative permeabilities are examined.Item Open Access Learning structured models for active planning : beyond the Markov paradigm towards adaptable abstractions(2018) Lieck, Robert; Toussaint, Marc (Prof. Dr.)Item Open Access Generalizations of the finite element method(2011) Schweitzer, MarcThis paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical method. To this end, we consider meshbased and meshfree generalizations of the finite element method and the use of smooth, discontinuous, singular and numerical enrichment functions.