Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs
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...
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| 主要な著者: | , , , |
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| 団体著者: | |
| フォーマット: | 電子媒体 eBook |
| 言語: | 英語 |
| 出版事項: |
Cham :
Springer International Publishing : Imprint: Springer,
2023.
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| 版: | 1st ed. 2023. |
| シリーズ: | Lecture Notes in Mathematics,
2334 |
| 主題: | |
| オンライン･アクセス: | https://doi.org/10.1007/978-3-031-38384-7 |
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| 100 | 1 | |a Dũng, Dinh. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs |h [electronic resource] / |c by Dinh Dũng, Van Kien Nguyen, Christoph Schwab, Jakob Zech. |
| 250 | |a 1st ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online resource (XV, 207 p.). | ||
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| 490 | 1 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |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, suchas 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. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Numerical analysis. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 1 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Probability Theory. |
| 650 | 2 | 4 | |a Numerical Analysis. |
| 650 | 2 | 4 | |a Functional Analysis. |
| 700 | 1 | |a Nguyen, Van Kien. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Schwab, Christoph. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Zech, Jakob. |e author. |0 (orcid)0000-0003-3163-3735 |1 https://orcid.org/0000-0003-3163-3735 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 830 | 0 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2334 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-38384-7 |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||