國立高雄大學圖資館 |

Language: English

Back

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

Record Type:	Electronic resources : Monograph/item
Title/Author:	Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputsby 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$q(electronic bk.)

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 ;2035..

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$q(electronic bk.)

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

189753
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:02392nmm a2200325 a 4500 001 652279
003 DE-He213
005 20231013010627.0
006 m d
007 cr nn 008maaau
008 240327s2023 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 : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
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 189753
650 0 $a Gaussian processes. $3 211434
650 0 $a Mathematical analysis. $3 186133
650 0 $a Random fields. $3 186303
650 1 4 $a Differential Equations. $3 285983
650 2 4 $a Probability Theory. $3 913371
650 2 4 $a Numerical Analysis. $3 275681
650 2 4 $a Functional Analysis. $3 274845
700 1 $a Dung, Dinh. $3 824911
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v 2035. $3 557764
856 4 0 $u https://doi.org/10.1007/978-3-031-38384-7
950 $a Mathematics and Statistics (SpringerNature-11649)