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Quantification of Uncertainty in Extreme Scale Computations

Debusschere, Bert D.; Jakeman, John D.; Chowdhary, Kamaljit S.; Safta, Cosmin S.; Sargsyan, Khachik S.; Rai, P.R.; Ghanem, R.G.; Knio, O.K.; La Maitre, O.L.; Winokur, J.W.; Li, G.L.; Ghattas, O.G.; Moser, R.M.; Simmons, C.S.; Alexanderian, A.A.; Gattiker, J.G.; Higdon, D.H.; Lawrence, E.L.; Bhat, S.B.; Marzouk, Y.M.; Bigoni, D.B.; Cui, T.C.; Parno, M.P.

Abstract not provided.

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TYPE Conference Poster YEAR 2015
OSTI

Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

SIAM Journal on Scientific Computing

Chen, Yi; Jakeman, John D.; Gittelson, Claude; Xiu, Dongbin

In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. The local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained from the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In this paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.

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TYPE Journal Article YEAR 2015
ScopusOSTIDOI

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis :

Adams, Brian M.; Jakeman, John D.; Swiler, Laura P.; Stephens, John A.; Vigil, Dena V.; Wildey, Timothy M.; Bauman, Lara E.; Bohnhoff, William J.; Dalbey, Keith D.; Eddy, John P.; Ebeida, Mohamed S.; Eldred, Michael S.; Hough, Patricia D.; Hu, Kenneth H.

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

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TYPE SAND Report YEAR 2014
OSTIDOI

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 6.0 theory manual

Adams, Brian M.; Jakeman, John D.; Swiler, Laura P.; Stephens, John A.; Vigil, Dena V.; Wildey, Timothy M.; Bauman, Lara E.; Bohnhoff, William J.; Dalbey, Keith D.; Eddy, John P.; Ebeida, Mohamed S.; Eldred, Michael S.; Hough, Patricia D.; Hu, Kenneth H.

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quanti cation, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

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TYPE SAND Report YEAR 2014
OSTIDOI
Results 101–147 of 147
Results 101–147 of 147