RT Journal Article
ID 1705e44e62934820
A1 Mathelin, Lionel
T1 QUANTIFICATION OF UNCERTAINTY FROM HIGH-DIMENSIONAL SCATTERED DATA VIA POLYNOMIAL APPROXIMATION
JF International Journal for Uncertainty Quantification
JO IJUQ
YR 2014
FD 2014-05-20
VO 4
IS 3
SP 243
OP 271
K1 uncertainty quantification
K1 least angle regression
K1 high-dimensional model reduction
K1 total least squares
K1 alternate least squares
K1 polynomial chaos
AB This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high-dimensional stochastic space in the context of limited amount of information. The proposed approach involves a procedure for the selection of an approximation basis and the evaluation of the associated coefficients. The selection of the approximation basis relies on the a priori choice of the high-dimensional model representation format combined with a modified least angle regression technique. The resulting basis then provides the structure for the actual approximation basis, possibly using different functions, more parsimonious and nonlinear in its coefficients. To evaluate the coefficients, both an alternate least squares and an alternate weighted total least squares methods are employed. Examples are provided for the approximation of a random variable in a high-dimensional space as well as the estimation of a random field. Stochastic dimensions up to 100 are considered, with an amount of information as low as about 3 samples per dimension, and robustness of the approximation is demonstrated with respect to noise in the dataset. The computational cost of the solution method is shown to scale only linearly with the cardinality of the a priori basis and exhibits a (Nq)s, 2 ≤ s ≤ 3, dependence with the number Nq of samples in the dataset. The provided numerical experiments illustrate the ability of the present approach to derive an accurate approximation from scarce scattered data even in the presence of noise.
PB Begell House
LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,348c4184660ca52f,1705e44e62934820.html