### Current state of the art of polynomial chaos metamodel construction

**Ko, J ***(Uncertainty Quantification specialist, Areva, Paris)*

Monday 25 March 2013, 10:30-11:00

Seminar Room 1, Newton Institute

#### Abstract

Polynomial chaos expansion is being increasingly used in the uncertainty quantification of industrial applications. Proposed by Weiner to represent random solution response with respect to input stochastic process with Gaussian random variable using a Hermite polynomial, polynomial chaos expansion (PCE) metamodel mimics the response of the solution over the random input parameter space and can be used in quantile estimation, reliability analysis and solution optimization, in addition to quantifying statistical moments. PCE is useful in the industrial context because analysis on a polynomial metamodel is essentially free in comparison to the time- and CPU-intensive evaluation of the complete numerical model. One of its main appeal lies in its non-intrusive approach: the PCE metamodel can be constructed from samples of the complete numerical model: a black-box. This talk will compare the current state of the art in PCE methodologies, namely the stochastic spectral projection, algebraic quadrature and least-squares, using examples.