Advances in Gaussian random field generation: a review

Yang Liu, Jingfa Li, Shuyu Sun, Bo Yu

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


Gaussian (normal) distribution is a basic continuous probability distribution in statistics, it plays a substantial role in scientific and engineering problems that related to stochastic phenomena. This paper aims to review state-of-the-art of Gaussian random field generation methods, their applications in scientific and engineering issues of interest, and open-source software/packages for Gaussian random field generation. To this end, first, we briefly introduce basic mathematical concepts and theories in the Gaussian random field, then seven commonly used Gaussian random field generation methods are systematically presented. The basic idea, mathematical framework of each generation method are introduced in detail and comparisons of these methods are summarized. Then, representative applications of the Gaussian random field in various areas, especially of engineering interest in recent two decades, are reviewed. For readers’ convenience, four representative example codes are provided, and several relevant up-to-date open-source software and packages that freely available from the Internet are introduced.
Original languageEnglish (US)
Pages (from-to)1011-1047
Number of pages37
JournalComputational Geosciences
Issue number5
StatePublished - Aug 5 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): BAS/1/1351-01-01
Acknowledgements: We gratefully acknowledge the papers that contributing to our work and the figures that we reprinted from these papers, textbooks, and web resources. The authors would like to thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improving the overall quality of the paper


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