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Review and comparison of two meta-model-based uncertainty propagation analysis methods in groundwater applications: polynomial chaos expansion and Gaussian process emulation

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Abstract

Gaussian process emulation (GPE) and polynomial chaos expansion (PCE) are tools for meta-model-based uncertainty propagation analysis (UPA) that have gained increasing attention in recent groundwater literature. Previous studies have shown that these two meta-models can provide satisfactorily accurate estimations of the model response in a wide range of groundwater UPA problems. However, PCE and GPE are based on very different mathematical concepts, and a question that arises is which one of these is more suitable for groundwater UPA. The current paper aims to provide an answer to this question by first presenting a theoretical comparison of the two meta-models, then reviewing previous comparisons of the two in other fields of engineering, and subsequently presenting an empirical comparison based on groundwater case studies. For this purpose, both meta-models are applied to two hypothetical test cases corresponding to seawater intrusion in coastal aquifers. The results show that: (1) GPE outperforms PCE in the estimation of the input–output relationships, by providing smaller root mean square errors. (2) In most cases assessed, PCE provides better accuracy in the estimation of mean, standard deviation and the entire shape and the tail of probability distribution functions. (3) Replicates of PCE show less statistical dispersion in the estimation of mean and standard deviations. (4) A trend of increase in the predominance of PCE over GPE can be identified as the probability distributions that are meant to be estimated become noisier and more multi-modal.

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Acknowledgements

The author wishes to thank Editor-in-Chief, Professor George Christakos, Associate Editor and two anonymous reviewers for their valuable comments which helped to improve the final manuscript.

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  1. Civil and Environmental Engineering Faculty, Tarbiat Modares University, P.O. Box 14115-397, Tehran, Iran

    Mohammad Mahdi Rajabi

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Rajabi, M.M. Review and comparison of two meta-model-based uncertainty propagation analysis methods in groundwater applications: polynomial chaos expansion and Gaussian process emulation. Stoch Environ Res Risk Assess 33, 607–631 (2019). https://doi.org/10.1007/s00477-018-1637-7

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