Year: 2013
Communications in Computational Physics, Vol. 14 (2013), Iss. 4 : pp. 851–878
Abstract
We develop an efficient, adaptive locally weighted projection regression (ALWPR) framework for uncertainty quantification (UQ) of systems governed by ordinary and partial differential equations. The algorithm adaptively selects the new input points with the largest predictive variance and decides when and where to add new local models. It effectively learns the local features and accurately quantifies the uncertainty in the prediction of the statistics. The developed methodology provides predictions and confidence intervals at any query input and can deal with multi-output cases. Numerical examples are presented to show the accuracy and efficiency of the ALWPR framework including problems with non-smooth local features such as discontinuities in the stochastic space.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.060712.281212a
Communications in Computational Physics, Vol. 14 (2013), Iss. 4 : pp. 851–878
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
-
A nonparametric belief propagation method for uncertainty quantification with applications to flow in random porous media
Chen, Peng | Zabaras, NicholasJournal of Computational Physics, Vol. 250 (2013), Iss. P.616
https://doi.org/10.1016/j.jcp.2013.05.006 [Citations: 3] -
Recent progress of uncertainty quantification in small-scale materials science
Acar, Pınar
Progress in Materials Science, Vol. 117 (2021), Iss. P.100723
https://doi.org/10.1016/j.pmatsci.2020.100723 [Citations: 26]