@Article{CiCP-14-851,
author = {Peng Chen and Nicholas Zabaras},
title = {Adaptive Locally Weighted Projection Regression Method for Uncertainty Quantification},
journal = {Communications in Computational Physics},
year = {2013},
volume = {14},
number = {4},
pages = {851--878},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.060712.281212a},
url = {http://global-sci.org/intro/article_detail/cicp/7184.html}
}