Abstract
Global sensitivity analysis (GSA) and uncertainty quantification (UQ) for groundwater modeling are challenging because of the model complexity and significant computational requirements. To reduce the massive computational cost, a cheap-to-evaluate surrogate model is usually constructed to approximate and replace the expensive groundwater models in the GSA and UQ. Constructing an accurate surrogate requires actual model simulations on a number of parameter samples. Thus, a robust experimental design strategy is desired to locate informative samples so as to reduce the computational cost in surrogate construction and consequently to improve the efficiency in the GSA and UQ. In this study, we develop a Taylor expansion-based adaptive design (TEAD) that aims to build an accurate global surrogate model with a small training sample size. TEAD defines a novel hybrid score function to search informative samples, and a robust stopping criterion to terminate the sample search that guarantees the resulted approximation errors satisfy the desired accuracy. The good performance of TEAD in building global surrogate models is demonstrated in seven analytical functions with different dimensionality and complexity in comparison to two widely used experimental design methods. The application of the TEAD-based surrogate method in two groundwater models shows that the TEAD design can effectively improve the computational efficiency of GSA and UQ for groundwater modeling.
Original language | English |
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Pages (from-to) | 10802-10823 |
Number of pages | 22 |
Journal | Water Resources Research |
Volume | 53 |
Issue number | 12 |
DOIs | |
State | Published - Dec 2017 |
Funding
The MATLAB codes of TEAD are available at https://github.com/ njujinchun/Codes-of-TEAD. We are grateful to the High Performance Computing Center of Nanjing University for providing the computing facility. This study is supported by the National Natural Science Foundation of China grants U1503282 and 41672229. The fourth author is supported by the U.S. Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under contract ERKJ259. The fifth author is supported by DOE Early Career Award DE-SC0008272 and National Science Foundation-Division of Earth Science Grant 1552329. The authors would also like to thank four anonymous reviewers, the Associate Editor Alberto Guadagnini, and the Editor-in-Chief Xavier Sanchez-Vila for their helpful comments.
Keywords
- experimental design
- global sensitivity analysis
- global surrogate model
- groundwater modeling
- uncertainty quantification