An adaptive sparsegrid highorder stochastic collocation method for Bayesian inference in groundwater reactive transport modeling
Abstract
Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparsegrid highorder stochastic collocation (aSGhSC) method. Unlike previous works using firstorder hierarchical basis, we utilize a compactly supported higherorder hierar chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogatemore »
 Authors:

 ORNL
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC)
 OSTI Identifier:
 1055118
 Report Number(s):
 ORNL/TM2012/499
KJ0401000; ERKJE45
 DOE Contract Number:
 DEAC0500OR22725
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
Citation Formats
Zhang, Guannan, Webster, Clayton G, and Gunzburger, Max D. An adaptive sparsegrid highorder stochastic collocation method for Bayesian inference in groundwater reactive transport modeling. United States: N. p., 2012.
Web. doi:10.2172/1055118.
Zhang, Guannan, Webster, Clayton G, & Gunzburger, Max D. An adaptive sparsegrid highorder stochastic collocation method for Bayesian inference in groundwater reactive transport modeling. United States. doi:10.2172/1055118.
Zhang, Guannan, Webster, Clayton G, and Gunzburger, Max D. Sat .
"An adaptive sparsegrid highorder stochastic collocation method for Bayesian inference in groundwater reactive transport modeling". United States. doi:10.2172/1055118. https://www.osti.gov/servlets/purl/1055118.
@article{osti_1055118,
title = {An adaptive sparsegrid highorder stochastic collocation method for Bayesian inference in groundwater reactive transport modeling},
author = {Zhang, Guannan and Webster, Clayton G and Gunzburger, Max D},
abstractNote = {Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparsegrid highorder stochastic collocation (aSGhSC) method. Unlike previous works using firstorder hierarchical basis, we utilize a compactly supported higherorder hierar chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost. The developed method is evaluated first using a simple analytical density function with multiple modes and then using two synthetic groundwater reactive transport models. The groundwater models represent different levels of complexity; the first example involves coupled linear reactions and the second example simulates nonlinear ura nium surface complexation. The results show that the aSGhSC is an effective and efficient tool for Bayesian inference in groundwater modeling in comparison with conventional MCMC sim ulations. The computational efficiency is expected to be more beneficial to more computational expensive groundwater problems.},
doi = {10.2172/1055118},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2012},
month = {9}
}