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    Bayesian Optimal Experimental Design Using Multilevel Monte Carlo

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    Type
    Thesis
    Authors
    Ben Issaid, Chaouki cc
    Advisors
    Tempone, Raul cc
    Committee members
    Bisetti, Fabrizio cc
    Sun, Ying cc
    Long, Quan cc
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2015-05-12
    Embargo End Date
    2016-05-12
    Permanent link to this record
    http://hdl.handle.net/10754/552705
    
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    Access Restrictions
    At the time of archiving, the student author of this thesis opted to temporarily restrict access to it. The full text of this thesis became available to the public after the expiration of the embargo on 2016-05-12.
    Abstract
    Experimental design can be vital when experiments are resource-exhaustive and time-consuming. In this work, we carry out experimental design in the Bayesian framework. To measure the amount of information that can be extracted from the data in an experiment, we use the expected information gain as the utility function, which specifically is the expected logarithmic ratio between the posterior and prior distributions. Optimizing this utility function enables us to design experiments that yield the most informative data about the model parameters. One of the major difficulties in evaluating the expected information gain is that it naturally involves nested integration over a possibly high dimensional domain. We use the Multilevel Monte Carlo (MLMC) method to accelerate the computation of the nested high dimensional integral. The advantages are twofold. First, MLMC can significantly reduce the cost of the nested integral for a given tolerance, by using an optimal sample distribution among different sample averages of the inner integrals. Second, the MLMC method imposes fewer assumptions, such as the asymptotic concentration of posterior measures, required for instance by the Laplace approximation (LA). We test the MLMC method using two numerical examples. The first example is the design of sensor deployment for a Darcy flow problem governed by a one-dimensional Poisson equation. We place the sensors in the locations where the pressure is measured, and we model the conductivity field as a piecewise constant random vector with two parameters. The second one is chemical Enhanced Oil Recovery (EOR) core flooding experiment assuming homogeneous permeability. We measure the cumulative oil recovery, from a horizontal core flooded by water, surfactant and polymer, for different injection rates. The model parameters consist of the endpoint relative permeabilities, the residual saturations and the relative permeability exponents for the three phases: water, oil and microemulsions. We also compare the performance of the MLMC to the LA and the direct Double Loop Monte Carlo (DLMC). In fact, we show that, in the case of the aforementioned examples, MLMC combined with LA turns to be the best method in terms of computational cost.
    Citation
    Ben Issaid, C. (2015). Bayesian Optimal Experimental Design Using Multilevel Monte Carlo. KAUST Research Repository. https://doi.org/10.25781/KAUST-U2H82
    DOI
    10.25781/KAUST-U2H82
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-U2H82
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; MS Theses; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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