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Title: Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction of sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.
 [1] ;  [2] ;  [3]
  1. National Cheng Kung Univ. (Taiwan)
  2. National Taiwan Univ. (Taiwan)
  3. Georgia Inst. of Technology, Atlanta, GA (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 0040-1706; FG02-13ER26159
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Additional Journal Information:
Journal Volume: 59; Journal Issue: 2; Journal ID: ISSN 0040-1706
Taylor & Francis
Research Org:
Georgia Tech Research Corp., Atlanta, GA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; Credible interval; Overcomplete bases surrogates method; Posterior sample; Stochastic search variable selection
OSTI Identifier: