State-of-the-Art and Comparative Review of Adaptive Sampling Methods for Kriging

authored by: Jan N. Fuhg, Amélie Fau, Udo Nackenhorst
Abstract: Metamodels aim to approximate characteristics of functions or systems from the knowledge extracted on only a finite number of samples. In recent years kriging has emerged as a widely applied metamodeling technique for resource-intensive computational experiments. However its prediction quality is highly dependent on the size and distribution of the given training points. Hence, in order to build proficient kriging models with as few samples as possible adaptive sampling strategies have gained considerable attention. These techniques aim to find pertinent points in an iterative manner based on information extracted from the current metamodel. A review of adaptive schemes for kriging proposed in the literature is presented in this article. The objective is to provide the reader with an overview of the main principles of adaptive techniques, and insightful details to pertinently employ available tools depending on the application at hand. In this context commonly applied strategies are compared with regards to their characteristics and approximation capabilities. In light of these experiments, it is found that the success of a scheme depends on the features of a specific problem and the goal of the analysis. In order to facilitate the entry into adaptive sampling a guide is provided. All experiments described herein are replicable using a provided open source toolbox.
Organisation(s): Institute of Continuum Mechanics
Institute of Mechanics and Computational Mechanics
External Organisation(s): Université Paris-Saclay
Type: Article
Journal: Archives of Computational Methods in Engineering
Volume: 28
Pages: 2689-2747
No. of pages: 59
ISSN: 1134-3060
Publication date: 06.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computer Science Applications, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s11831-020-09474-6 (Access: Open)
https://doi.org/10.15488/10721 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{bc010e7d0696467fb3e98ec30a249cb8,
title = "State-of-the-Art and Comparative Review of Adaptive Sampling Methods for Kriging",
abstract = "Metamodels aim to approximate characteristics of functions or systems from the knowledge extracted on only a finite number of samples. In recent years kriging has emerged as a widely applied metamodeling technique for resource-intensive computational experiments. However its prediction quality is highly dependent on the size and distribution of the given training points. Hence, in order to build proficient kriging models with as few samples as possible adaptive sampling strategies have gained considerable attention. These techniques aim to find pertinent points in an iterative manner based on information extracted from the current metamodel. A review of adaptive schemes for kriging proposed in the literature is presented in this article. The objective is to provide the reader with an overview of the main principles of adaptive techniques, and insightful details to pertinently employ available tools depending on the application at hand. In this context commonly applied strategies are compared with regards to their characteristics and approximation capabilities. In light of these experiments, it is found that the success of a scheme depends on the features of a specific problem and the goal of the analysis. In order to facilitate the entry into adaptive sampling a guide is provided. All experiments described herein are replicable using a provided open source toolbox.",
author = "Fuhg, {Jan N.} and Am{\'e}lie Fau and Udo Nackenhorst",
note = "Funding Information: The first author acknowledges the financial support from the Deutsche Forschungsgemeinschaft under Germanys{\textquoteright} Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). Open Access funding provided by Projekt DEAL. Acknowledgements ",
year = "2021",
month = jun,
doi = "10.1007/s11831-020-09474-6",
language = "English",
volume = "28",
pages = "2689--2747",
journal = "Archives of Computational Methods in Engineering",
issn = "1134-3060",
publisher = "Springer Netherlands",
number = "4",
}