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Applied Math Seminar

Wednesday, 14 November, 2012

SPEAKER: Guannah Zhang, Householder Fellow, ORNL

TITLE: An Adaptive Sparse-grid High-order Stochastic Collocation Method

for Bayesian Inference with Computationally Expensive Simulations

ABSTRACT:  Bayesian inference has become vital to stochastic parameter identification

for complex physical systems, but 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 sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierarchical 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 indicator 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. Several numerical examples demonstrate that the aSG-hSC is an effective and efficient tool for Bayesian inference in parameter identification in comparison with conventional MCMC simulations. The computational efficiency is expected to be more beneficial to more computational expensive physical problems.




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