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    Discrete least squares polynomial approximation with random evaluations - application to PDEs with Random parameters

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    Type
    Presentation
    Authors
    Nobile, Fabio
    Date
    2015-01-07
    Permanent link to this record
    http://hdl.handle.net/10754/624117
    
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    Abstract
    We consider a general problem F(u, y) = 0 where u is the unknown solution, possibly Hilbert space valued, and y a set of uncertain parameters. We specifically address the situation in which the parameterto-solution map u(y) is smooth, however y could be very high (or even infinite) dimensional. In particular, we are interested in cases in which F is a differential operator, u a Hilbert space valued function and y a distributed, space and/or time varying, random field. We aim at reconstructing the parameter-to-solution map u(y) from random noise-free or noisy observations in random points by discrete least squares on polynomial spaces. The noise-free case is relevant whenever the technique is used to construct metamodels, based on polynomial expansions, for the output of computer experiments. In the case of PDEs with random parameters, the metamodel is then used to approximate statistics of the output quantity. We discuss the stability of discrete least squares on random points show convergence estimates both in expectation and probability. We also present possible strategies to select, either a-priori or by adaptive algorithms, sequences of approximating polynomial spaces that allow to reduce, and in some cases break, the curse of dimensionality
    Conference/Event name
    Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
    Additional Links
    http://mediasite.kaust.edu.sa/Mediasite/Play/6e425ffc82e646dfa703ba13f65a02b21d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52
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    Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

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