Volume 14, Issue 4
Adaptive Locally Weighted Projection Regression Method for Uncertainty Quantification

Peng Chen & Nicholas Zabaras

Commun. Comput. Phys., 14 (2013), pp. 851-878.

Published online: 2013-10

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  • Abstract

We develop an efficient, adaptive locally weighted projection regression (ALWPR) framework for uncertainty quantification (UQ)of systems governed by ordinary and partial differentialequations. The algorithm adaptively selects the new input points with the largest predictive variance and decides when and where to add new local models. It effectivelylearns the local featuresand accurately quantifies the uncertainty in the prediction of the statistics. The developed methodology provides predictions andconfidenceintervalsatanyquery input andcandealwithmulti-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.


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@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 = {

We develop an efficient, adaptive locally weighted projection regression (ALWPR) framework for uncertainty quantification (UQ)of systems governed by ordinary and partial differentialequations. The algorithm adaptively selects the new input points with the largest predictive variance and decides when and where to add new local models. It effectivelylearns the local featuresand accurately quantifies the uncertainty in the prediction of the statistics. The developed methodology provides predictions andconfidenceintervalsatanyquery input andcandealwithmulti-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.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.060712.281212a}, url = {http://global-sci.org/intro/article_detail/cicp/7184.html} }
TY - JOUR T1 - Adaptive Locally Weighted Projection Regression Method for Uncertainty Quantification AU - Peng Chen & Nicholas Zabaras JO - Communications in Computational Physics VL - 4 SP - 851 EP - 878 PY - 2013 DA - 2013/10 SN - 14 DO - http://dor.org/10.4208/cicp.060712.281212a UR - https://global-sci.org/intro/cicp/7184.html KW - AB -

We develop an efficient, adaptive locally weighted projection regression (ALWPR) framework for uncertainty quantification (UQ)of systems governed by ordinary and partial differentialequations. The algorithm adaptively selects the new input points with the largest predictive variance and decides when and where to add new local models. It effectivelylearns the local featuresand accurately quantifies the uncertainty in the prediction of the statistics. The developed methodology provides predictions andconfidenceintervalsatanyquery input andcandealwithmulti-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.


Peng Chen & Nicholas Zabaras. (1970). Adaptive Locally Weighted Projection Regression Method for Uncertainty Quantification. Communications in Computational Physics. 14 (4). 851-878. doi:10.4208/cicp.060712.281212a
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