Buchumschlag

A hybrid alternating least squares - TT-cross algorithm for parametric PDEs

We consider the approximate solution of parametric PDEs using the low-rank tensor train (TT) decomposition. Such parametric PDEs arise, for example, in uncertainty quantification problems in engineering applications. We propose an algorithm that is a hybrid of the alternating least squares and the T...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Dolgov, Sergey (VerfasserIn) , Scheichl, Robert (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: [2019]
In: SIAM ASA journal on uncertainty quantification
Year: 2019, Jahrgang: 7, Heft: 1, Pages: 260-291
ISSN:2166-2525
DOI:10.1137/17M1138881
Online-Zugang:Verlag, Volltext: https://doi.org/10.1137/17M1138881
Verlag, Volltext: https://epubs.siam.org/doi/10.1137/17M1138881
Volltext
Verfasserangaben:Sergey Dolgov and Robert Scheichl

MARC

LEADER 00000caa a2200000 c 4500
001 1667812343
003 DE-627
005 20220816173713.0
007 cr uuu---uuuuu
008 190624s2019 xx |||||o 00| ||eng c
024 7 |a 10.1137/17M1138881  |2 doi 
035 |a (DE-627)1667812343 
035 |a (DE-599)KXP1667812343 
035 |a (OCoLC)1341229191 
040 |a DE-627  |b ger  |c DE-627  |e rda 
041 |a eng 
084 |a 27  |2 sdnb 
100 1 |a Dolgov, Sergey  |d 1988-  |e VerfasserIn  |0 (DE-588)1056973234  |0 (DE-627)794331092  |0 (DE-576)412951290  |4 aut 
245 1 2 |a A hybrid alternating least squares - TT-cross algorithm for parametric PDEs  |c Sergey Dolgov and Robert Scheichl 
264 1 |c [2019] 
300 |a 32 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
500 |a Gesehen am 24.06.2019 
520 |a We consider the approximate solution of parametric PDEs using the low-rank tensor train (TT) decomposition. Such parametric PDEs arise, for example, in uncertainty quantification problems in engineering applications. We propose an algorithm that is a hybrid of the alternating least squares and the TT-cross methods. It computes a TT approximation of the whole solution, which is beneficial when multiple quantities of interest are sought. This might be needed, for example, for the computation of the probability density function via the maximum entropy method [M. Kavehrad and M. Joseph, IEEE Trans. Comm., 34 (1986), pp. 1183--1189]. The new algorithm exploits and preserves the block-diagonal structure of the discretized operator in stochastic collocation schemes. This disentangles computations of the spatial and parametric degrees of freedom in the TT representation. In particular, it only requires solving independent PDEs at a few parameter values, thus allowing the use of existing high performance PDE solvers. In our numerical experiments, we apply the new algorithm to the stochastic diffusion equation and compare it with preconditioned steepest descent in the TT format, as well as with (multilevel) quasi--Monte Carlo and dimension-adaptive sparse grids methods. For sufficiently smooth random fields the new approach is orders of magnitude faster. 
700 1 |a Scheichl, Robert  |d 1972-  |e VerfasserIn  |0 (DE-588)1173753842  |0 (DE-627)1043602305  |0 (DE-576)515668532  |4 aut 
773 0 8 |i Enthalten in  |a Society for Industrial and Applied Mathematics  |t SIAM ASA journal on uncertainty quantification  |d Philadelphia, Pa. : SIAM, 2013  |g 7(2019), 1, Seite 260-291  |h Online-Ressource  |w (DE-627)729754006  |w (DE-600)2690603-X  |w (DE-576)391400703  |x 2166-2525  |7 nnas 
773 1 8 |g volume:7  |g year:2019  |g number:1  |g pages:260-291  |g extent:32  |a A hybrid alternating least squares - TT-cross algorithm for parametric PDEs 
856 4 0 |u https://doi.org/10.1137/17M1138881  |x Verlag  |x Resolving-System  |3 Volltext 
856 4 0 |u https://epubs.siam.org/doi/10.1137/17M1138881  |x Verlag  |3 Volltext 
951 |a AR 
992 |a 20190624 
993 |a Article 
994 |a 2019 
998 |g 1173753842  |a Scheichl, Robert  |m 1173753842:Scheichl, Robert  |d 110000  |d 110200  |d 110000  |d 110400  |e 110000PS1173753842  |e 110200PS1173753842  |e 110000PS1173753842  |e 110400PS1173753842  |k 0/110000/  |k 1/110000/110200/  |k 0/110000/  |k 1/110000/110400/  |p 2  |y j 
999 |a KXP-PPN1667812343  |e 3489371275 
BIB |a Y 
SER |a journal 
JSO |a {"id":{"eki":["1667812343"],"doi":["10.1137/17M1138881"]},"recId":"1667812343","type":{"bibl":"article-journal","media":"Online-Ressource"},"name":{"displayForm":["Sergey Dolgov and Robert Scheichl"]},"language":["eng"],"physDesc":[{"extent":"32 S."}],"relHost":[{"pubHistory":["1.2013 -"],"id":{"eki":["729754006"],"issn":["2166-2525"],"zdb":["2690603-X"]},"recId":"729754006","name":{"displayForm":["Society for Industrial and Applied Mathematics ; American Statistical Association"]},"physDesc":[{"extent":"Online-Ressource"}],"note":["Gesehen am 21.05.13"],"origin":[{"publisher":"SIAM","dateIssuedDisp":"2013-","dateIssuedKey":"2013","publisherPlace":"Philadelphia, Pa."}],"disp":"Society for Industrial and Applied MathematicsSIAM ASA journal on uncertainty quantification","titleAlt":[{"title":"JUQ"},{"title":"Journal on uncertainty quantification"}],"language":["eng"],"type":{"bibl":"periodical","media":"Online-Ressource"},"title":[{"title_sort":"SIAM ASA journal on uncertainty quantification","title":"SIAM ASA journal on uncertainty quantification"}],"part":{"year":"2019","volume":"7","extent":"32","pages":"260-291","text":"7(2019), 1, Seite 260-291","issue":"1"},"corporate":[{"display":"Society for Industrial and Applied Mathematics","role":"aut"},{"role":"isb","display":"American Statistical Association"}]}],"title":[{"title_sort":"hybrid alternating least squares - TT-cross algorithm for parametric PDEs","title":"A hybrid alternating least squares - TT-cross algorithm for parametric PDEs"}],"person":[{"display":"Dolgov, Sergey","role":"aut","family":"Dolgov","given":"Sergey"},{"given":"Robert","family":"Scheichl","role":"aut","display":"Scheichl, Robert"}],"origin":[{"dateIssuedDisp":"[2019]","dateIssuedKey":"2019"}],"note":["Gesehen am 24.06.2019"]} 
SRT |a DOLGOVSERGHYBRIDALTE2019 

Ähnliche Einträge