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Advances in Gaussian random field generation: a review

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Abstract

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.

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Acknowledgments

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.

Funding

This study is supported by the National Natural Science Foundation of China (No. 51874262) and the Research Funding from King Abdullah University of Science and Technology (KAUST) through the grant BAS/1/1351-01-01.

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Authors and Affiliations

  1. Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia

    Yang Liu, Jingfa Li & Shuyu Sun

  2. School of Mechanical Engineering, Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil & Gas Development, Beijing Institute of Petrochemical Technology, Beijing, 102617, China

    Jingfa Li & Bo Yu

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  1. Yang Liu
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Correspondence to Shuyu Sun.

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Appendix: Matlab code corresponding to Section 2

Appendix: Matlab code corresponding to Section 2

Here, we provide the MATLAB code for four random field generation methods presented in Section 2. Interested readers may refer to the link https://github.com/YLiu-5/Random_Field_Generation.

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Liu, Y., Li, J., Sun, S. et al. Advances in Gaussian random field generation: a review. Comput Geosci 23, 1011–1047 (2019). https://doi.org/10.1007/s10596-019-09867-y

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