Non-intrusive low-rank separated approximation of high-dimensional stochastic models

Alireza Doostan; AbdoulAhad Validi; Gianluca Iaccarino

doi:10.1016/j.cma.2013.04.003

Non-intrusive low-rank separated approximation of high-dimensional stochastic models

Alireza Doostan, AbdoulAhad Validi, Gianluca Iaccarino

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Abstract

This work proposes a sampling-based (non-intrusive) approach within the context of low-. rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with high-dimensional random inputs. Under some conditions discussed in details, the number of random realizations of the solution, required for a successful approximation, grows linearly with respect to the number of random inputs. The construction of the separated representation is achieved via a regularized alternating least-squares regression, together with an error indicator to estimate model parameters. The computational complexity of such a construction is quadratic in the number of random inputs. The performance of the method is investigated through its application to three numerical examples including two ODE problems with high-dimensional random inputs. © 2013 Elsevier B.V.

Original language	English (US)
Pages (from-to)	42-55
Number of pages	14
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	263
DOIs	https://doi.org/10.1016/j.cma.2013.04.003
State	Published - Aug 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): AEA 48803
Acknowledgements: The work of AD and AV was partially supported by the Department of Energy under Advanced Scientific Computing Research Early Career Research Award DE-SC0006402, the National Science Foundation grant DMS-1228359, and the Predictive Science Academic Alliance Program (PSAAP) at Stanford University. GI gratefully acknowledges financial support from KAUST under award AEA 48803.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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title = "Non-intrusive low-rank separated approximation of high-dimensional stochastic models",

abstract = "This work proposes a sampling-based (non-intrusive) approach within the context of low-. rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with high-dimensional random inputs. Under some conditions discussed in details, the number of random realizations of the solution, required for a successful approximation, grows linearly with respect to the number of random inputs. The construction of the separated representation is achieved via a regularized alternating least-squares regression, together with an error indicator to estimate model parameters. The computational complexity of such a construction is quadratic in the number of random inputs. The performance of the method is investigated through its application to three numerical examples including two ODE problems with high-dimensional random inputs. {\textcopyright} 2013 Elsevier B.V.",

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note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): AEA 48803 Acknowledgements: The work of AD and AV was partially supported by the Department of Energy under Advanced Scientific Computing Research Early Career Research Award DE-SC0006402, the National Science Foundation grant DMS-1228359, and the Predictive Science Academic Alliance Program (PSAAP) at Stanford University. GI gratefully acknowledges financial support from KAUST under award AEA 48803. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1016/j.cma.2013.04.003",

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AU - Validi, AbdoulAhad

AU - Iaccarino, Gianluca

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): AEA 48803 Acknowledgements: The work of AD and AV was partially supported by the Department of Energy under Advanced Scientific Computing Research Early Career Research Award DE-SC0006402, the National Science Foundation grant DMS-1228359, and the Predictive Science Academic Alliance Program (PSAAP) at Stanford University. GI gratefully acknowledges financial support from KAUST under award AEA 48803. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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N2 - This work proposes a sampling-based (non-intrusive) approach within the context of low-. rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with high-dimensional random inputs. Under some conditions discussed in details, the number of random realizations of the solution, required for a successful approximation, grows linearly with respect to the number of random inputs. The construction of the separated representation is achieved via a regularized alternating least-squares regression, together with an error indicator to estimate model parameters. The computational complexity of such a construction is quadratic in the number of random inputs. The performance of the method is investigated through its application to three numerical examples including two ODE problems with high-dimensional random inputs. © 2013 Elsevier B.V.

AB - This work proposes a sampling-based (non-intrusive) approach within the context of low-. rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with high-dimensional random inputs. Under some conditions discussed in details, the number of random realizations of the solution, required for a successful approximation, grows linearly with respect to the number of random inputs. The construction of the separated representation is achieved via a regularized alternating least-squares regression, together with an error indicator to estimate model parameters. The computational complexity of such a construction is quadratic in the number of random inputs. The performance of the method is investigated through its application to three numerical examples including two ODE problems with high-dimensional random inputs. © 2013 Elsevier B.V.

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JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

Non-intrusive low-rank separated approximation of high-dimensional stochastic models

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