Reduced Basis Methods for Uncertainty Quantification

Peng Chen; Alfio Quarteroni; Gianluigi Rozza

doi:10.1137/151004550

Reduced Basis Methods for Uncertainty Quantification

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/151004550 ◽

2017 ◽

Vol 5 (1) ◽

pp. 813-869 ◽

Cited By ~ 17

Author(s):

Peng Chen ◽

Alfio Quarteroni ◽

Gianluigi Rozza

Keyword(s):

Uncertainty Quantification ◽

Reduced Basis ◽

Reduced Basis Methods

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A new algorithm for high-dimensional uncertainty quantification based on dimension-adaptive sparse grid approximation and reduced basis methods

Journal of Computational Physics ◽

10.1016/j.jcp.2015.06.006 ◽

2015 ◽

Vol 298 ◽

pp. 176-193 ◽

Cited By ~ 24

Author(s):

Peng Chen ◽

Alfio Quarteroni

Keyword(s):

Uncertainty Quantification ◽

Sparse Grid ◽

High Dimensional ◽

Reduced Basis ◽

Grid Approximation ◽

Reduced Basis Methods

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Accurate Solution of Bayesian Inverse Uncertainty Quantification Problems Combining Reduced Basis Methods and Reduction Error Models

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/140995817 ◽

2016 ◽

Vol 4 (1) ◽

pp. 380-412 ◽

Cited By ~ 17

Author(s):

A. Manzoni ◽

S. Pagani ◽

T. Lassila

Keyword(s):

Uncertainty Quantification ◽

Accurate Solution ◽

Reduced Basis ◽

Error Models ◽

Reduced Basis Methods ◽

Reduction Error

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4 Reduced basis methods

Snapshot-Based Methods and Algorithms ◽

10.1515/9783110671490-004 ◽

2020 ◽

pp. 139-180

Keyword(s):

Reduced Basis ◽

Reduced Basis Methods

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Stabilized Weighted Reduced Basis Methods for Parametrized Advection Dominated Problems with Random Inputs

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/17m1163517 ◽

2018 ◽

Vol 6 (4) ◽

pp. 1475-1502 ◽

Cited By ~ 9

Author(s):

Davide Torlo ◽

Francesco Ballarin ◽

Gianluigi Rozza

Keyword(s):

Reduced Basis ◽

Random Inputs ◽

Reduced Basis Methods

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Stochastic Reduced Basis Methods

AIAA Journal ◽

10.2514/2.1837 ◽

2002 ◽

Vol 40 (8) ◽

pp. 1653-1664 ◽

Cited By ~ 94

Author(s):

Prasanth B. Nair ◽

Andrew J. Keane

Keyword(s):

Reduced Basis ◽

Reduced Basis Methods

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Comparison of advanced reduced-basis methods for transient structural analysis

AIAA Journal ◽

10.2514/3.11834 ◽

1993 ◽

Vol 31 (9) ◽

pp. 1712-1719 ◽

Cited By ~ 6

Author(s):

David M. McGowan ◽

Susan W. Bostic

Keyword(s):

Structural Analysis ◽

Reduced Basis ◽

Reduced Basis Methods

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Non-intrusive Uncertainty Quantification by Combination of Reduced Basis Method and Regression-based Polynomial Chaos Expansion

Uncertainty Management for Robust Industrial Design in Aeronautics - Notes on Numerical Fluid Mechanics and Multidisciplinary Design ◽

10.1007/978-3-319-77767-2_10 ◽

2018 ◽

pp. 169-184

Author(s):

Mehrdad Raisee ◽

Dinesh Kumar ◽

Chris Lacor

Keyword(s):

Uncertainty Quantification ◽

Polynomial Chaos ◽

Polynomial Chaos Expansion ◽

Reduced Basis Method ◽

Chaos Expansion ◽

Reduced Basis ◽

Basis Method

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Reduced Basis Methods for Fractional Laplace Equations via Extension

SIAM Journal on Scientific Computing ◽

10.1137/18m1204802 ◽

2019 ◽

Vol 41 (6) ◽

pp. A3552-A3575 ◽

Cited By ~ 1

Author(s):

Harbir Antil ◽

Yanlai Chen ◽

Akil Narayan

Keyword(s):

Reduced Basis ◽

Laplace Equations ◽

Reduced Basis Methods

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Certified Reduced Basis Methods for Parametrized Partial Differential Equations

10.1007/978-3-319-22470-1 ◽

2016 ◽

Cited By ~ 135

Author(s):

Jan S Hesthaven ◽

Gianluigi Rozza ◽

Benjamin Stamm

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Reduced Basis ◽

Partial Differential ◽

Reduced Basis Methods ◽

Parametrized Partial Differential Equations

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Electromagnetic wave scattering by random surfaces: Shape holomorphy

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202517500439 ◽

2017 ◽

Vol 27 (12) ◽

pp. 2229-2259 ◽

Cited By ~ 10

Author(s):

Carlos Jerez-Hanckes ◽

Christoph Schwab ◽

Jakob Zech

Keyword(s):

Uncertainty Quantification ◽

Electromagnetic Waves ◽

Convergence Rates ◽

Order Reduction ◽

Reduced Basis ◽

Approximation Techniques ◽

Field Patterns ◽

Time Harmonic ◽

First Order Second Moment ◽

Domain Perturbations

For time-harmonic electromagnetic waves scattered by either perfectly conducting or dielectric bounded obstacles, we show that the fields depend holomorphically on the shape of the scatterer. In the presence of random geometrical perturbations, our results imply strong measurability of the fields, in weighted spaces in the exterior of the scatterer. These findings are key to prove dimension-independent convergence rates of sparse approximation techniques of polynomial chaos type for forward and inverse computational uncertainty quantification. Also, our shape-holomorphy results imply parsimonious approximate representations of the corresponding parametric solution families, which are produced, for example, by greedy strategies such as model order reduction or reduced basis approximations. Finally, the presently proved shape holomorphy results imply convergence of shape Taylor expansions of far-field patterns for fixed amplitude domain perturbations in a vicinity of the nominal domain, thereby extending the widely used asymptotic linearizations employed in first-order, second moment domain uncertainty quantification.

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