國立虎尾科技大學 |

Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs/ by Dinh Dung ... [et al.].
other author:	Dung, Dinh.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xv, 207 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Differential equations, Partial. -
Online resource:	https://doi.org/10.1007/978-3-031-38384-7
ISBN:	9783031383847

Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs
Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs[electronic resource] /by Dinh Dung ... [et al.]. - Cham :Springer International Publishing :2023. - xv, 207 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23341617-9692 ;. - Lecture notes in mathematics ;1943..

The present book develops the mathematical and numerical analysis of linear, elliptic and parabolic partial differential equations (PDEs) with coefficients whose logarithms are modelled as Gaussian random fields (GRFs), in polygonal and polyhedral physical domains. Both, forward and Bayesian inverse PDE problems subject to GRF priors are considered. Adopting a pathwise, affine-parametric representation of the GRFs, turns the random PDEs into equivalent, countably-parametric, deterministic PDEs, with nonuniform ellipticity constants. A detailed sparsity analysis of Wiener-Hermite polynomial chaos expansions of the corresponding parametric PDE solution families by analytic continuation into the complex domain is developed, in corner- and edge-weighted function spaces on the physical domain. The presented Algorithms and results are relevant for the mathematical analysis of many approximation methods for PDEs with GRF inputs, such as model order reduction, neural network and tensor-formatted surrogates of parametric solution families. They are expected to impact computational uncertainty quantification subject to GRF models of uncertainty in PDEs, and are of interest for researchers and graduate students in both, applied and computational mathematics, as well as in computational science and engineering.

ISBN: 9783031383847

Standard No.: 10.1007/978-3-031-38384-7doiSubjects--Topical Terms:

527784
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs
LDR:02392nam a2200325 a 4500 001 1117844
003 DE-He213
005 20231013010627.0
006 m d
007 cr nn 008maaau
008 240126s2023 sz s 0 eng d
020 $a 9783031383847 $q (electronic bk.)
020 $a 9783031383830 $q (paper)
024 7 $a 10.1007/978-3-031-38384-7 $2 doi
035 $a 978-3-031-38384-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377
072 7 $a PBKJ $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.353 $2 23
090 $a QA377 $b .A532 2023
245 0 0 $a Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs $h [electronic resource] / $c by Dinh Dung ... [et al.].
260 $a Cham : $c 2023. $b Springer International Publishing : $b Imprint: Springer,
300 $a xv, 207 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2334
520 $a The present book develops the mathematical and numerical analysis of linear, elliptic and parabolic partial differential equations (PDEs) with coefficients whose logarithms are modelled as Gaussian random fields (GRFs), in polygonal and polyhedral physical domains. Both, forward and Bayesian inverse PDE problems subject to GRF priors are considered. Adopting a pathwise, affine-parametric representation of the GRFs, turns the random PDEs into equivalent, countably-parametric, deterministic PDEs, with nonuniform ellipticity constants. A detailed sparsity analysis of Wiener-Hermite polynomial chaos expansions of the corresponding parametric PDE solution families by analytic continuation into the complex domain is developed, in corner- and edge-weighted function spaces on the physical domain. The presented Algorithms and results are relevant for the mathematical analysis of many approximation methods for PDEs with GRF inputs, such as model order reduction, neural network and tensor-formatted surrogates of parametric solution families. They are expected to impact computational uncertainty quantification subject to GRF models of uncertainty in PDEs, and are of interest for researchers and graduate students in both, applied and computational mathematics, as well as in computational science and engineering.
650 0 $a Differential equations, Partial. $3 527784
650 0 $a Gaussian processes. $3 672507
650 0 $a Mathematical analysis. $3 527926
650 0 $a Random fields. $3 788061
650 1 4 $a Differential Equations. $3 681826
650 2 4 $a Probability Theory. $3 1366244
650 2 4 $a Numerical Analysis. $3 671433
650 2 4 $a Functional Analysis. $3 672166
700 1 $a Dung, Dinh. $3 1210557
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v 1943. $3 882220
856 4 0 $u https://doi.org/10.1007/978-3-031-38384-7
950 $a Mathematics and Statistics (SpringerNature-11649)