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      Adaptive surrogate models for parametric studies

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          Abstract

          The computational effort for the evaluation of numerical simulations based on e.g. the finite-element method is high. Metamodels can be utilized to create a low-cost alternative. However the number of required samples for the creation of a sufficient metamodel should be kept low, which can be achieved by using adaptive sampling techniques. In this Master thesis adaptive sampling techniques are investigated for their use in creating metamodels with the Kriging technique, which interpolates values by a Gaussian process governed by prior covariances. The Kriging framework with extension to multifidelity problems is presented and utilized to compare adaptive sampling techniques found in the literature for benchmark problems as well as applications for contact mechanics. This thesis offers the first comprehensive comparison of a large spectrum of adaptive techniques for the Kriging framework. Furthermore a multitude of adaptive techniques is introduced to multifidelity Kriging as well as well as to a Kriging model with reduced hyperparameter dimension called partial least squares Kriging. In addition, an innovative adaptive scheme for binary classification is presented and tested for identifying chaotic motion of a Duffing's type oscillator.

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          Neural Networks and the Bias/Variance Dilemma

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            Universal Approximation Using Radial-Basis-Function Networks

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              Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory

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                Author and article information

                Journal
                12 May 2019
                Article
                1905.05345
                1002320b-47de-429d-9332-30afb0749a5a

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                225 pages, Master's thesis, Leibniz University of Hannover, Germany (2019)
                stat.ML cs.CE cs.LG stat.AP

                Applications,Applied computer science,Machine learning,Artificial intelligence
                Applications, Applied computer science, Machine learning, Artificial intelligence

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