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Title: A Taylor Expansion-Based Adaptive Design Strategy for Global Surrogate Modeling With Applications in Groundwater Modeling

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 effectivelymore » improve the computational efficiency of GSA and UQ for groundwater modeling.« less

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]; ORCiD logo [3]; ORCiD logo [4]; ORCiD logo [1]; ORCiD logo [1]
  1. Nanjing Univ. (China). Key Lab. of Surficial Geochemistry of Ministry of Education, School of Earth Sciences and Engineering
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computational Sciences and Engineering Division
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
  4. Florida State Univ., Tallahassee, FL (United States). Dept. of Scientific Computing
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); National Natural Science Foundation of China (NNSFC)
OSTI Identifier:
1430618
Alternate Identifier(s):
OSTI ID: 1414960
Grant/Contract Number:
AC05-00OR22725; U1503282; 41672229; SC0008272; 155232
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
Journal Volume: 53; Journal Issue: 12; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES

Citation Formats

Mo, Shaoxing, Lu, Dan, Shi, Xiaoqing, Zhang, Guannan, Ye, Ming, Wu, Jianfeng, and Wu, Jichun. A Taylor Expansion-Based Adaptive Design Strategy for Global Surrogate Modeling With Applications in Groundwater Modeling. United States: N. p., 2017. Web. doi:10.1002/2017WR021622.
Mo, Shaoxing, Lu, Dan, Shi, Xiaoqing, Zhang, Guannan, Ye, Ming, Wu, Jianfeng, & Wu, Jichun. A Taylor Expansion-Based Adaptive Design Strategy for Global Surrogate Modeling With Applications in Groundwater Modeling. United States. doi:10.1002/2017WR021622.
Mo, Shaoxing, Lu, Dan, Shi, Xiaoqing, Zhang, Guannan, Ye, Ming, Wu, Jianfeng, and Wu, Jichun. Wed . "A Taylor Expansion-Based Adaptive Design Strategy for Global Surrogate Modeling With Applications in Groundwater Modeling". United States. doi:10.1002/2017WR021622.
@article{osti_1430618,
title = {A Taylor Expansion-Based Adaptive Design Strategy for Global Surrogate Modeling With Applications in Groundwater Modeling},
author = {Mo, Shaoxing and Lu, Dan and Shi, Xiaoqing and Zhang, Guannan and Ye, Ming and Wu, Jianfeng and Wu, Jichun},
abstractNote = {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.},
doi = {10.1002/2017WR021622},
journal = {Water Resources Research},
number = 12,
volume = 53,
place = {United States},
year = {Wed Dec 27 00:00:00 EST 2017},
month = {Wed Dec 27 00:00:00 EST 2017}
}

Journal Article:
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  • The Polynomial Dimensional Decomposition (PDD) is employed in this work for the global sensitivity analysis and uncertainty quantification (UQ) of stochastic systems subject to a moderate to large number of input random variables. Due to the intimate connection between the PDD and the Analysis of Variance (ANOVA) approaches, PDD is able to provide a simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to the Polynomial Chaos expansion (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of standard methods unaffordable formore » real engineering applications. In order to address the problem of the curse of dimensionality, this work proposes essentially variance-based adaptive strategies aiming to build a cheap meta-model (i.e. surrogate model) by employing the sparse PDD approach with its coefficients computed by regression. Three levels of adaptivity are carried out in this paper: 1) the truncated dimensionality for ANOVA component functions, 2) the active dimension technique especially for second- and higher-order parameter interactions, and 3) the stepwise regression approach designed to retain only the most influential polynomials in the PDD expansion. During this adaptive procedure featuring stepwise regressions, the surrogate model representation keeps containing few terms, so that the cost to resolve repeatedly the linear systems of the least-squares regression problem is negligible. The size of the finally obtained sparse PDD representation is much smaller than the one of the full expansion, since only significant terms are eventually retained. Consequently, a much smaller number of calls to the deterministic model is required to compute the final PDD coefficients.« less
  • Surrogate models are commonly used in Bayesian approaches such as Markov Chain Monte Carlo (MCMC) to avoid repetitive CPU-demanding model evaluations. However, the approximation error of a surrogate may lead to biased estimations of the posterior distribution. This bias can be corrected by constructing a very accurate surrogate or implementing MCMC in a two-stage manner. Since the two-stage MCMC requires extra original model evaluations, the computational cost is still high. If the information of measurement is incorporated, a locally accurate approximation of the original model can be adaptively constructed with low computational cost. Based on this idea, we propose amore » Gaussian process (GP) surrogate-based Bayesian experimental design and parameter estimation approach for groundwater contaminant source identification problems. A major advantage of the GP surrogate is that it provides a convenient estimation of the approximation error, which can be incorporated in the Bayesian formula to avoid over-confident estimation of the posterior distribution. The proposed approach is tested with a numerical case study. Without sacrificing the estimation accuracy, the new approach achieves about 200 times of speed-up compared to our previous work using two-stage MCMC.« less
  • Stream functions and equivalent freshwater heads are used to simulate steady state flow of variable-density groundwater in a regional, cross-sectional flow model through the Palo Duro Basin, Texas, where fluid densities vary between 1.0 and 1.15 g/cm{sup 3}. Centroid-consistent velocities computed from the stream function solution allow a more precise interpretation of local flow patterns in cross-sectional models than those from the head solution. Effects of significant fluid density variation on the regional groundwater flow pattern are studied by comparing simulation results that incorporate spatially varying, time-invarient densities with those that assume uniform density. Modeling shows that the regional groundwatermore » flow pattern in the Palo Duro Basin is not significantly affected by variations in fluid densities, indicating that the topopgraphically driven flow component dominates buoyancy forces associated with dense brines. An exception is near the eastern boundary where high fluid densities cause stronger downward flow. However, simulated equivalent freshwater heads in the variable-density model differ sifnificantly from simulated heads in the freshwater density model, which is important for model calibration. In addition to the well-known problems of hydraulic parameter and boundary condition uncertainties, modeling strategies for regional flow systems require consideration of uncertainties associated with fluid density and evaluation of equivalent freshwater head data.« less