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 Load-balancing for scalable simulations with large particle numbers(2021) Hirschmann, Steffen; Pflüger, Dirk (Prof. Dr.)Item Open Access Stable and mass-conserving high-dimensional simulations with the sparse grid combination technique for full HPC systems and beyond(2024) Pollinger, Theresa; Pflüger, Dirk (Prof. Dr.)In the light of the ongoing climate crisis, mastering controlled plasma fusion has the potential to be one of the pivotal scientific achievements of the 21st century. To understand the turbulent fields in confined fusion devices, simulation has been and continues to be both an asset and a challenge. The main limiting factor to large-scale high-fidelity predictive simulations lies in the Curse of Dimensionality, which dominates all grid-based discretizations of plasmas based on the Vlasov-Poisson and Vlasov-Maxwell equations. In the full formulation, they result in six-dimensional grids and fine scales that need to be resolved, leading to a potentially untractable number of degrees of freedom. Typical approaches to this problem - coordinate transformations such as gyrokinetics, grid adaptation, restricting oneself to limited resolutions - do not directly address the Curse of Dimensionality, but rather work around it. The sparse grid combination technique, which forms the center of this work, is a multiscale approach that alleviates the curse of dimensionality for time-stepping simulations: Multiple regular grid-based simulations are run and update each other’s information throughout the course of simulation time. The present thesis improves upon the former state-of-the-art of the combination technique in three ways: introducing conservation of mass and numerical stability through the use of better-suited multiscale basis functions, optimizing the code for large-scale HPC systems, and extending the combination technique to the widely-distributed setting. Firstly, this thesis analyzes the often-used hierarchical hat function from the viewpoint of biorthogonal wavelets, which allows to replace the hierarchical hat function by other multiscale functions (such as the mass-conserving CDF wavelets) in a straightforward manner. Numerical studies presented in the thesis show that this not only introduces conservation but also increases accuracy and avoids numerical instabilities - which previously were a major roadblock for large-scale Vlasov simulations with the combination technique. Secondly, the open-source framework DisCoTec was extended to scale the combination technique up to the available memory of entire supercomputing systems. DisCoTec is designed to wrap the combination technique around existing grid-based solvers and draws on the inherent parallelism of the combination technique. Among several other contributions, different communication-avoiding multiscale reduction schemes were developed and implemented into DisCoTec as part of this work. The scalability of the approach is asserted by an extensive set of measurements in this thesis: DisCoTec is shown to scale up to the full system size of four German supercomputers, including the three CPU-based Tier-0/Tier-1 systems. Thirdly, the combination technique was further extended to the widely-distributed setting, where two HPC systems synchronously run a joint simulation. This is enabled by file transfer as well as sophisticated algorithms for assigning the different simulation instances to the systems, two of which were developed as part of this work. By the resulting drastic reductions in the communication volume, tolerable transfer times for combination technique simulations on different HPC systems have been achieved for the first time. These three advances - improved numerical properties, scaling efficiently up to full system sizes, and the possibility to extend the simulation beyond a single system - show the sparse grid combination technique to be a promising approach for future high-fidelity simulations of higher-dimensional problems, such as plasma turbulence.Item Open Access Learning structured models for active planning : beyond the Markov paradigm towards adaptable abstractions(2018) Lieck, Robert; Toussaint, Marc (Prof. Dr.)