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Parametrization of random vectors in polynomial chaos expansions via optimal transportation. (English) Zbl 1351.60089

Summary: Polynomial chaos (PC) expansions are used for the propagation of uncertainty through dynamical systems as an alternative to Monte Carlo methods. Model parameters in a given dynamical system are assumed to have known expansions, which correspond to simple standard distributions, and one is usually interested in the polynomial expansion of the system solution. We are concerned with the problem of estimating the PC expansion of a parameter vector when only realizations from its distribution are given. To this end we apply ideas from optimal transportation theory and network optimization.

MSC:

60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
49Q20 Variational problems in a geometric measure-theoretic setting
62G05 Nonparametric estimation
65C50 Other computational problems in probability (MSC2010)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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