A projection method for under determined optimal experimental designs

Handle URI:
http://hdl.handle.net/10754/564878
Title:
A projection method for under determined optimal experimental designs
Authors:
Long, Quan ( 0000-0002-0329-9437 ) ; Scavino, Marco ( 0000-0001-5114-853X ) ; Tempone, Raul ( 0000-0003-1967-4446 ) ; Wang, Suojin
Abstract:
A new implementation, based on the Laplace approximation, was developed in (Long, Scavino, Tempone, & Wang 2013) to accelerate the estimation of the post–experimental expected information gains in the model parameters and predictive quantities of interest. A closed–form approximation of the inner integral and the order of the corresponding dominant error term were obtained in the cases where the parameters are determined by the experiment. In this work, we extend that method to the general cases where the model parameters could not be determined completely by the data from the proposed experiments. We carry out the Laplace approximations in the directions orthogonal to the null space of the corresponding Jacobian matrix, so that the information gain (Kullback–Leibler divergence) can be reduced to an integration against the marginal density of the transformed parameters which are not determined by the experiments. Furthermore, the expected information gain can be approximated by an integration over the prior, where the integrand is a function of the projected posterior covariance matrix. To deal with the issue of dimensionality in a complex problem, we use Monte Carlo sampling or sparse quadratures for the integration over the prior probability density function, depending on the regularity of the integrand function. We demonstrate the accuracy, efficiency and robustness of the proposed method via several nonlinear under determined numerical examples.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Stochastic Numerics Research Group
Publisher:
Informa UK Limited
Journal:
Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures
Conference/Event name:
11th International Conference on Structural Safety and Reliability, ICOSSAR 2013
Issue Date:
9-Jan-2014
DOI:
10.1201/b16387-320
Type:
Conference Paper
ISBN:
9781138000865
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLong, Quanen
dc.contributor.authorScavino, Marcoen
dc.contributor.authorTempone, Raulen
dc.contributor.authorWang, Suojinen
dc.date.accessioned2015-08-04T07:23:54Zen
dc.date.available2015-08-04T07:23:54Zen
dc.date.issued2014-01-09en
dc.identifier.isbn9781138000865en
dc.identifier.doi10.1201/b16387-320en
dc.identifier.urihttp://hdl.handle.net/10754/564878en
dc.description.abstractA new implementation, based on the Laplace approximation, was developed in (Long, Scavino, Tempone, & Wang 2013) to accelerate the estimation of the post–experimental expected information gains in the model parameters and predictive quantities of interest. A closed–form approximation of the inner integral and the order of the corresponding dominant error term were obtained in the cases where the parameters are determined by the experiment. In this work, we extend that method to the general cases where the model parameters could not be determined completely by the data from the proposed experiments. We carry out the Laplace approximations in the directions orthogonal to the null space of the corresponding Jacobian matrix, so that the information gain (Kullback–Leibler divergence) can be reduced to an integration against the marginal density of the transformed parameters which are not determined by the experiments. Furthermore, the expected information gain can be approximated by an integration over the prior, where the integrand is a function of the projected posterior covariance matrix. To deal with the issue of dimensionality in a complex problem, we use Monte Carlo sampling or sparse quadratures for the integration over the prior probability density function, depending on the regularity of the integrand function. We demonstrate the accuracy, efficiency and robustness of the proposed method via several nonlinear under determined numerical examples.en
dc.publisherInforma UK Limiteden
dc.titleA projection method for under determined optimal experimental designsen
dc.typeConference Paperen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentStochastic Numerics Research Groupen
dc.identifier.journalSafety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructuresen
dc.conference.date16 June 2013 through 20 June 2013en
dc.conference.name11th International Conference on Structural Safety and Reliability, ICOSSAR 2013en
dc.conference.locationNew York, NYen
dc.contributor.institutionInstitute for Computational Engineering and Sciences, University of Texas, Austin, United Statesen
dc.contributor.institutionDepartment of Statistics, Texas A and M University, United Statesen
kaust.authorLong, Quanen
kaust.authorTempone, Raulen
kaust.authorScavino, Marcoen
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