HAL - INRIA :: [hal-00641108, version 2] Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set

hal-00641108, version 2

Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set

Clément Chevalier ( Author to contact preferably ) ¹, Julien Bect (, ) ^2, 3, David Ginsbourger () ¹, Emmanuel Vazquez () ^2, 3, Victor Picheny () ⁴, Yann Richet () ⁵

(2011-11-14)

Abstract: Stepwise Uncertainty Reduction (SUR) strategies aim at constructing a sequence of sampling points for a function f : Rd → R, in such a way that the residual uncertainty about a quantity of interest becomes small. In the context of Gaussian Process-based approximation of computer experiments, these strategies have been shown to be particularly efficient for the problem of estimating the volume of excursion of a function f above a threshold. However, these strategies remain difficult to use in practice because of their high computational complexity, and they only deliver at each iteration a single point to evaluate. In this paper we introduce parallel sampling criteria, which allow selecting several sampling points simultaneously. Such criteria are of particular interest when the function f is expensive to evaluate and many CPUs are available. We also manage to drastically reduce the computational cost of these strategies using closed form expressions. We illustrate their performances in various numerical experiments, including a nuclear safety test case.

1: Institute of Mathematical Statistics and Actuarial Science
University of Bern
2: GdR MASCOT-NUM ((Méthodes d'Analyse Stochastique des Codes et Traitements Numériques))
CNRS : GDR3179
3: Supélec Sciences des Systèmes - EA4454 (E3S)
SUPELEC
4: Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS)
CERFACS
5: Institut de radioprotection et de sûreté nucléaire (IRSN)
Ministère de l'écologie de l'Energie, du Développement durable et de l'Aménagement du territoire – Ministère de l'économie, de l'industrie et de l'emploi – Ministère de l'Enseignement Supérieur et de la Recherche Scientifique – Ministère de la Défense – Ministère de la santé

Collaboration : GDR Mascot-Num, ReDICE Consortium

hal-00641108, version 2
http://hal.archives-ouvertes.fr/hal-00641108
oai:hal.archives-ouvertes.fr:hal-00641108
From: David Ginsbourger <>
Submitted on: Thursday, 19 April 2012 13:09:40
Updated on: Thursday, 19 April 2012 13:41:45

See detailed view

Associated documents

PDF :

Export

Bibtex EndNote TEI RefWorks

%% hal-00641108, version 2
%% http://hal.archives-ouvertes.fr/hal-00641108
@unpublished{CHEVALIER-2011-689134,
    hal_id = {hal-00641108},
    url = {http://hal.archives-ouvertes.fr/hal-00641108},
    title = {{Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set}},
    author = {Chevalier, Cl{\'e}ment and Bect, Julien and Ginsbourger, David and Vazquez, Emmanuel and Picheny, Victor and Richet, Yann},
    abstract = {{Stepwise Uncertainty Reduction (SUR) strategies aim at constructing a sequence of sampling points for a function f : Rd $\rightarrow$ R, in such a way that the residual uncertainty about a quantity of interest becomes small. In the context of Gaussian Process-based approximation of computer experiments, these strategies have been shown to be particularly efficient for the problem of estimating the volume of excursion of a function f above a threshold. However, these strategies remain difficult to use in practice because of their high computational complexity, and they only deliver at each iteration a single point to evaluate. In this paper we introduce parallel sampling criteria, which allow selecting several sampling points simultaneously. Such criteria are of particular interest when the function f is expensive to evaluate and many CPUs are available. We also manage to drastically reduce the computational cost of these strategies using closed form expressions. We illustrate their performances in various numerical experiments, including a nuclear safety test case.}},
    keywords = {Computer experiments; Gaussian processes; Sequential design; Probability of failure estimation; Active learning; Metamodel-based inversion},
    language = {English},
    affiliation = {Institute of Mathematical Statistics and Actuarial Science , GdR MASCOT-NUM - (M{\'e}thodes d'Analyse Stochastique des Codes et Traitements Num{\'e}riques) , Sup{\'e}lec Sciences des Syst{\`e}mes - EA4454 - E3S , Centre Europ{\'e}en de Recherche et de Formation Avanc{\'e}e en Calcul Scientifique - CERFACS , Institut de radioprotection et de s{\^u}ret{\'e} nucl{\'e}aire - IRSN},
    collaboration = {GDR Mascot-Num, ReDICE Consortium },
    year = {2011},
    month = Nov,
    pdf = {http://hal.archives-ouvertes.fr/hal-00641108/PDF/Fast\_parallel\_SUR.pdf},
}

%F hal-00641108, version 2
%0 Unpublished Work
%U http://hal.archives-ouvertes.fr/hal-00641108
%2 INFO:INFO_MO;MATH:MATH_ST;STAT:TH;MATH:MATH_OC;STAT:OT;STAT:ML;STAT:CO;STAT:ME
%T Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set
%A Chevalier, Clément
%A Bect, Julien
%A Ginsbourger, David
%A Vazquez, Emmanuel
%A Picheny, Victor
%A Richet, Yann
%+ Institute of Mathematical Statistics and Actuarial Science , GdR MASCOT-NUM - (Méthodes d'Analyse Stochastique des Codes et Traitements Numériques) , Supélec Sciences des Systèmes - EA4454 - E3S , Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique - CERFACS , Institut de radioprotection et de sûreté nucléaire - IRSN
%Z SSE - Département Signaux et Systèmes Electroniques
%X Stepwise Uncertainty Reduction (SUR) strategies aim at constructing a sequence of sampling points for a function f : Rd → R, in such a way that the residual uncertainty about a quantity of interest becomes small. In the context of Gaussian Process-based approximation of computer experiments, these strategies have been shown to be particularly efficient for the problem of estimating the volume of excursion of a function f above a threshold. However, these strategies remain difficult to use in practice because of their high computational complexity, and they only deliver at each iteration a single point to evaluate. In this paper we introduce parallel sampling criteria, which allow selecting several sampling points simultaneously. Such criteria are of particular interest when the function f is expensive to evaluate and many CPUs are available. We also manage to drastically reduce the computational cost of these strategies using closed form expressions. We illustrate their performances in various numerical experiments, including a nuclear safety test case.
%G English
%2 2011-11-14
%K Computer experiments; Gaussian processes; Sequential design; Probability of failure estimation; Active learning; Metamodel-based inversion
%Z GDR Mascot-Num, ReDICE Consortium

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="article"><head>Documents without publication reference</head>
<biblStruct type="article" xml:id="hal-00641108"><analytic>
<author><persName><forename>Clément</forename><surname>Chevalier</surname></persName>
<affiliation>
<orgName type="team">Institute of Mathematical Statistics and Actuarial Science</orgName>
<country>CH</country>
<orgName type="institution">University of Bern</orgName>
</affiliation>
</author>
<author><persName><forename>Julien</forename><surname>Bect</surname></persName>
<affiliation>
<orgName type="laboratory">(Méthodes d'Analyse Stochastique des Codes et Traitements Numériques)</orgName>
<orgName type="team">GdR MASCOT-NUM</orgName>
<country>FR</country>
<orgName type="institution">CNRS : GDR3179</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">E3S</orgName>
<orgName type="team">Supélec Sciences des Systèmes - EA4454</orgName>
<country>FR</country>
<orgName type="institution">SUPELEC</orgName>
</affiliation>
</author>
<author><persName><forename>David</forename><surname>Ginsbourger</surname></persName>
<affiliation>
<orgName type="team">Institute of Mathematical Statistics and Actuarial Science</orgName>
<country>CH</country>
<orgName type="institution">University of Bern</orgName>
</affiliation>
</author>
<author><persName><forename>Emmanuel</forename><surname>Vazquez</surname></persName>
<affiliation>
<orgName type="laboratory">(Méthodes d'Analyse Stochastique des Codes et Traitements Numériques)</orgName>
<orgName type="team">GdR MASCOT-NUM</orgName>
<country>FR</country>
<orgName type="institution">CNRS : GDR3179</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">E3S</orgName>
<orgName type="team">Supélec Sciences des Systèmes - EA4454</orgName>
<country>FR</country>
<orgName type="institution">SUPELEC</orgName>
</affiliation>
</author>
<author><persName><forename>Victor</forename><surname>Picheny</surname></persName>
<affiliation>
<orgName type="laboratory">CERFACS</orgName>
<orgName type="team">Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique</orgName>
<country>FR</country>
<orgName type="institution">CERFACS</orgName>
</affiliation>
</author>
<author><persName><forename>Yann</forename><surname>Richet</surname></persName>
<affiliation>
<orgName type="laboratory">IRSN</orgName>
<orgName type="team">Institut de radioprotection et de sûreté nucléaire</orgName>
<country>FR</country>
<orgName type="institution">Ministère de l'écologie de l'Energie, du Développement durable et de l'Aménagement du territoire</orgName>
<orgName type="institution">Ministère de l'économie, de l'industrie et de l'emploi</orgName>
<orgName type="institution">Ministère de l'Enseignement Supérieur et de la Recherche Scientifique</orgName>
<orgName type="institution">Ministère de la Défense</orgName>
<orgName type="institution">Ministère de la santé</orgName>
</affiliation>
</author>
<title type="main" level="a">Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set</title></analytic><monogr><imprint/></monogr><idno type="HALid">http://hal.archives-ouvertes.fr/hal-00641108</idno><idno type="HALFile">http://hal.archives-ouvertes.fr/hal-00641108/PDF/Fast_parallel_SUR.pdf</idno></biblStruct>
</listBibl>
</listBibl>