Adaptive surrogate models for parametric studies

TL;DR

This paper investigates and compares various adaptive sampling techniques for Kriging-based surrogate models, including multifidelity and reduced hyperparameter models, to improve efficiency in parametric studies.

Contribution

It provides the first comprehensive comparison of adaptive sampling methods for Kriging, introduces new techniques for multifidelity and partial least squares Kriging, and presents an innovative adaptive scheme for binary classification.

Findings

Adaptive sampling techniques significantly reduce sample requirements.

Multifidelity Kriging enhances model accuracy with fewer evaluations.

New adaptive scheme effectively identifies chaotic oscillator behavior.

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.