skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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); 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:
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. https://www.osti.gov/servlets/purl/1430618.
@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 = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 5 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

An Adaptive Exploration-Exploitation Algorithm for Constructing Metamodels in Random Simulation Using a Novel Sequential Experimental Design
journal, October 2013

  • Ajdari, Ali; Mahlooji, Hashem
  • Communications in Statistics - Simulation and Computation, Vol. 43, Issue 5
  • DOI: 10.1080/03610918.2012.720743

Multivariate Adaptive Regression Splines
journal, March 1991


High dimensional Kriging metamodelling utilising gradient information
journal, May 2016

  • Ulaganathan, S.; Couckuyt, I.; Dhaene, T.
  • Applied Mathematical Modelling, Vol. 40, Issue 9-10
  • DOI: 10.1016/j.apm.2015.12.033

Bayesian Calibration and Uncertainty Analysis for Computationally Expensive Models Using Optimization and Radial Basis Function Approximation
journal, June 2008

  • Bliznyuk, Nikolay; Ruppert, David; Shoemaker, Christine
  • Journal of Computational and Graphical Statistics, Vol. 17, Issue 2
  • DOI: 10.1198/106186008X320681

Calculations of Sobol indices for the Gaussian process metamodel
journal, March 2009

  • Marrel, Amandine; Iooss, Bertrand; Laurent, Béatrice
  • Reliability Engineering & System Safety, Vol. 94, Issue 3
  • DOI: 10.1016/j.ress.2008.07.008

Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations
journal, January 2015


Hierarchical adaptive experimental design for Gaussian process emulators
journal, July 2009


A Critical Appraisal of Design of Experiments for Uncertainty Quantification
journal, February 2017


An efficient, high-order perturbation approach for flow in random porous media via Karhunen–Loève and polynomial expansions
journal, March 2004


Surrogate modeling approximation using a mixture of experts based on EM joint estimation
journal, August 2010

  • Bettebghor, Dimitri; Bartoli, Nathalie; Grihon, Stéphane
  • Structural and Multidisciplinary Optimization, Vol. 43, Issue 2
  • DOI: 10.1007/s00158-010-0554-2

A Novel Hybrid Sequential Design Strategy for Global Surrogate Modeling of Computer Experiments
journal, January 2011

  • Crombecq, Karel; Gorissen, Dirk; Deschrijver, Dirk
  • SIAM Journal on Scientific Computing, Vol. 33, Issue 4
  • DOI: 10.1137/090761811

Numerical assessment of metamodelling strategies in computationally intensive optimization
journal, June 2012


Global sensitivity analysis using polynomial chaos expansions
journal, July 2008


Global sensitivity analysis in hydrological modeling: Review of concepts, methods, theoretical framework, and applications
journal, April 2015


Surrogate based sensitivity analysis of process equipment
journal, April 2011

  • Stephens, D. W.; Gorissen, D.; Crombecq, K.
  • Applied Mathematical Modelling, Vol. 35, Issue 4
  • DOI: 10.1016/j.apm.2010.09.044

An adaptive design and interpolation technique for extracting highly nonlinear response surfaces from deterministic models
journal, July 2009


Review of surrogate modeling in water resources: REVIEW
journal, July 2012

  • Razavi, Saman; Tolson, Bryan A.; Burn, Donald H.
  • Water Resources Research, Vol. 48, Issue 7
  • DOI: 10.1029/2011WR011527

Assessment of parametric uncertainty for groundwater reactive transport modeling
journal, May 2014

  • Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.
  • Water Resources Research, Vol. 50, Issue 5
  • DOI: 10.1002/2013WR013755

A Fuzzy Hybrid Sequential Design Strategy for Global Surrogate Modeling of High-Dimensional Computer Experiments
journal, January 2015

  • van der Herten, J.; Couckuyt, I.; Deschrijver, D.
  • SIAM Journal on Scientific Computing, Vol. 37, Issue 2
  • DOI: 10.1137/140962437

Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations
journal, October 2016

  • Conrad, Patrick R.; Marzouk, Youssef M.; Pillai, Natesh S.
  • Journal of the American Statistical Association, Vol. 111, Issue 516
  • DOI: 10.1080/01621459.2015.1096787

Automated Near-Field Scanning Algorithm for the EMC Analysis of Electronic Devices
journal, June 2012

  • Deschrijver, D.; Vanhee, F.; Pissoort, D.
  • IEEE Transactions on Electromagnetic Compatibility, Vol. 54, Issue 3
  • DOI: 10.1109/TEMC.2011.2163821

Adaptive sequential sampling for surrogate model generation with artificial neural networks
journal, September 2014


Variance-based sensitivity analysis of model outputs using surrogate models
journal, June 2011


An efficient integrated approach for global sensitivity analysis of hydrological model parameters
journal, March 2013


Modeling the performance of large-scale CO2 storage systems: A comparison of different sensitivity analysis methods
journal, September 2013

  • Wainwright, Haruko M.; Finsterle, Stefan; Zhou, Quanlin
  • International Journal of Greenhouse Gas Control, Vol. 17
  • DOI: 10.1016/j.ijggc.2013.05.007

Solving the Estimation-Identification Problem in Two-Phase Flow Modeling
journal, April 1995

  • Finsterle, Stefan; Pruess, Karsten
  • Water Resources Research, Vol. 31, Issue 4
  • DOI: 10.1029/94WR03038

Reduced order models for assessing CO2 impacts in shallow unconfined aquifers
journal, March 2016

  • Keating, Elizabeth H.; Harp, Dylan H.; Dai, Zhenxue
  • International Journal of Greenhouse Gas Control, Vol. 46
  • DOI: 10.1016/j.ijggc.2016.01.008

Hierarchical Nonlinear Approximation for Experimental Design and Statistical Data Fitting
journal, January 2007

  • Busby, Daniel; Farmer, Chris L.; Iske, Armin
  • SIAM Journal on Scientific Computing, Vol. 29, Issue 1
  • DOI: 10.1137/050639983

Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media
journal, January 2017


Uncertainty Quantification in CO 2 Sequestration Using Surrogate Models from Polynomial Chaos Expansion
journal, June 2012

  • Zhang, Yan; Sahinidis, Nikolaos V.
  • Industrial & Engineering Chemistry Research, Vol. 52, Issue 9
  • DOI: 10.1021/ie300856p

Adaptive Sampling Algorithm for Macromodeling of Parameterized $S$-Parameter Responses
journal, January 2011

  • Deschrijver, Dirk; Crombecq, Karel; Nguyen, Huu Minh
  • IEEE Transactions on Microwave Theory and Techniques, Vol. 59, Issue 1
  • DOI: 10.1109/TMTT.2010.2090407

Efficiency enhancement of optimized Latin hypercube sampling strategies: Application to Monte Carlo uncertainty analysis and meta-modeling
journal, February 2015


Gaussian process emulators for quantifying uncertainty in CO 2 spreading predictions in heterogeneous media
journal, August 2017


A response surface methodology to address uncertainties in cap rock failure assessment for CO2 geological storage in deep aquifers
journal, March 2010


A review of surrogate models and their application to groundwater modeling: SURROGATES OF GROUNDWATER MODELS
journal, August 2015

  • Asher, M. J.; Croke, B. F. W.; Jakeman, A. J.
  • Water Resources Research, Vol. 51, Issue 8
  • DOI: 10.1002/2015WR016967

Metamodeling of Combined Discrete/Continuous Responses
journal, October 2001

  • Meckesheimer, Martin; Barton, Russell R.; Simpson, Timothy
  • AIAA Journal, Vol. 39, Issue 10
  • DOI: 10.2514/2.1185

Efficient MCMC Schemes for Computationally Expensive Posterior Distributions
journal, February 2011


Comparing sampling strategies for aerodynamic Kriging surrogate models
journal, July 2012

  • Rosenbaum, B.; Schulz, V.
  • ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 92, Issue 11-12
  • DOI: 10.1002/zamm.201100112

On uncertainty quantification in hydrogeology and hydrogeophysics
journal, December 2017


Design and Analysis of Computer Experiments
journal, November 1989

  • Sacks, Jerome; Welch, William J.; Mitchell, Toby J.
  • Statistical Science, Vol. 4, Issue 4
  • DOI: 10.1214/ss/1177012413

A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions
journal, November 2007

  • Regis, Rommel G.; Shoemaker, Christine A.
  • INFORMS Journal on Computing, Vol. 19, Issue 4
  • DOI: 10.1287/ijoc.1060.0182

Minimax and maximin distance designs
journal, October 1990

  • Johnson, M. E.; Moore, L. M.; Ylvisaker, D.
  • Journal of Statistical Planning and Inference, Vol. 26, Issue 2
  • DOI: 10.1016/0378-3758(90)90122-B

Model emulation and moment-independent sensitivity analysis: An application to environmental modelling
journal, June 2012


Development of a surrogate model and sensitivity analysis for spatio-temporal numerical simulators
journal, July 2014

  • Marrel, Amandine; Perot, Nadia; Mottet, Clémentine
  • Stochastic Environmental Research and Risk Assessment, Vol. 29, Issue 3
  • DOI: 10.1007/s00477-014-0927-y

Global sensitivity analysis of large-scale numerical landslide models based on Gaussian-Process meta-modeling
journal, July 2011


Estimation of plume distribution for carbon sequestration using parameter estimation with limited monitoring data: CO
journal, July 2013

  • Espinet, Antoine; Shoemaker, Christine; Doughty, Christine
  • Water Resources Research, Vol. 49, Issue 7
  • DOI: 10.1002/wrcr.20326

Reduced order models for many-query subsurface flow applications
journal, May 2013

  • Pau, George Shu Heng; Zhang, Yingqi; Finsterle, Stefan
  • Computational Geosciences, Vol. 17, Issue 4
  • DOI: 10.1007/s10596-013-9349-z

Sampling efficiency in Monte Carlo based uncertainty propagation strategies: Application in seawater intrusion simulations
journal, May 2014