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    Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions

    Source: Journal of Mechanical Design:;2019:;volume( 141 ):;issue: 010::page 101404
    Author:
    Pandita, Piyush
    ,
    Bilionis, Ilias
    ,
    Panchal, Jitesh
    DOI: 10.1115/1.4043930
    Publisher: American Society of Mechanical Engineers (ASME)
    Abstract: Bayesian optimal design of experiments (BODEs) have been successful in acquiring information about a quantity of interest (QoI) which depends on a black-box function. BODE is characterized by sequentially querying the function at specific designs selected by an infill-sampling criterion. However, most current BODE methods operate in specific contexts like optimization, or learning a universal representation of the black-box function. The objective of this paper is to design a BODE for estimating the statistical expectation of a physical response surface. This QoI is omnipresent in uncertainty propagation and design under uncertainty problems. Our hypothesis is that an optimal BODE should be maximizing the expected information gain in the QoI. We represent the information gain from a hypothetical experiment as the Kullback–Liebler (KL) divergence between the prior and the posterior probability distributions of the QoI. The prior distribution of the QoI is conditioned on the observed data, and the posterior distribution of the QoI is conditioned on the observed data and a hypothetical experiment. The main contribution of this paper is the derivation of a semi-analytic mathematical formula for the expected information gain about the statistical expectation of a physical response. The developed BODE is validated on synthetic functions with varying number of input-dimensions. We demonstrate the performance of the methodology on a steel wire manufacturing problem.
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      Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions

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    contributor authorPandita, Piyush
    contributor authorBilionis, Ilias
    contributor authorPanchal, Jitesh
    date accessioned2019-09-18T09:02:41Z
    date available2019-09-18T09:02:41Z
    date copyright7/10/2019 12:00:00 AM
    date issued2019
    identifier issn1050-0472
    identifier othermd_141_10_101404
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4258204
    description abstractBayesian optimal design of experiments (BODEs) have been successful in acquiring information about a quantity of interest (QoI) which depends on a black-box function. BODE is characterized by sequentially querying the function at specific designs selected by an infill-sampling criterion. However, most current BODE methods operate in specific contexts like optimization, or learning a universal representation of the black-box function. The objective of this paper is to design a BODE for estimating the statistical expectation of a physical response surface. This QoI is omnipresent in uncertainty propagation and design under uncertainty problems. Our hypothesis is that an optimal BODE should be maximizing the expected information gain in the QoI. We represent the information gain from a hypothetical experiment as the Kullback–Liebler (KL) divergence between the prior and the posterior probability distributions of the QoI. The prior distribution of the QoI is conditioned on the observed data, and the posterior distribution of the QoI is conditioned on the observed data and a hypothetical experiment. The main contribution of this paper is the derivation of a semi-analytic mathematical formula for the expected information gain about the statistical expectation of a physical response. The developed BODE is validated on synthetic functions with varying number of input-dimensions. We demonstrate the performance of the methodology on a steel wire manufacturing problem.
    publisherAmerican Society of Mechanical Engineers (ASME)
    titleBayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions
    typeJournal Paper
    journal volume141
    journal issue10
    journal titleJournal of Mechanical Design
    identifier doi10.1115/1.4043930
    journal fristpage101404
    journal lastpage101404-11
    treeJournal of Mechanical Design:;2019:;volume( 141 ):;issue: 010
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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