Karhunen-Loéve decomposition of isotropic Gaussian random fields using a tensor approximation of autocovariance kernel

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F18%3A10239977" target="_blank" >RIV/61989100:27240/18:10239977 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68145535:_____/18:00495896 RIV/61989100:27740/18:10239977

Výsledek na webu

<a href="http://doi.org/10.1007/978-3-319-97136-0_14" target="_blank" >http://doi.org/10.1007/978-3-319-97136-0_14</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-97136-0_14" target="_blank" >10.1007/978-3-319-97136-0_14</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Karhunen-Loéve decomposition of isotropic Gaussian random fields using a tensor approximation of autocovariance kernel

Popis výsledku v původním jazyce

Applications of random fields typically require a generation of random samples or their decomposition. In this contribution, we focus on the decomposition of the isotropic Gaussian random fields on a two or three-dimensional domain. The preferred tool for the decomposition of the random field is the Karhunen-Loéve expansion. The Karhunen-Loéve expansion can be approximated using the Galerkin method, where we encounter two main problems. First, the calculation of each element of the Galerkin matrix is expensive because it requires an accurate evaluation of multi-dimensional integral. The second problem consists of the memory requirements, originating from the density of the matrix. We propose a method that overcomes both problems. We use a tensor-structured approximation of the autocovariance kernel, which allows its separable representation. This leads to the representation of the matrix as a sum of Kronecker products of matrices related to the one-dimensional problem, which significantly reduces the storage requirements. Moreover, this representation dramatically reduces the computation cost, as we only calculate two-dimensional integrals. (C) Springer International Publishing AG, part of Springer Nature 2018.

Název v anglickém jazyce

Karhunen-Loéve decomposition of isotropic Gaussian random fields using a tensor approximation of autocovariance kernel

Popis výsledku anglicky

Applications of random fields typically require a generation of random samples or their decomposition. In this contribution, we focus on the decomposition of the isotropic Gaussian random fields on a two or three-dimensional domain. The preferred tool for the decomposition of the random field is the Karhunen-Loéve expansion. The Karhunen-Loéve expansion can be approximated using the Galerkin method, where we encounter two main problems. First, the calculation of each element of the Galerkin matrix is expensive because it requires an accurate evaluation of multi-dimensional integral. The second problem consists of the memory requirements, originating from the density of the matrix. We propose a method that overcomes both problems. We use a tensor-structured approximation of the autocovariance kernel, which allows its separable representation. This leads to the representation of the matrix as a sum of Kronecker products of matrices related to the one-dimensional problem, which significantly reduces the storage requirements. Moreover, this representation dramatically reduces the computation cost, as we only calculate two-dimensional integrals. (C) Springer International Publishing AG, part of Springer Nature 2018.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Volume 11087

ISBN

978-3-319-97135-3

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

15

Strana od-do

188-202

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Karolinka

Datum konání akce

22. 5. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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