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


Adaptive Locally Weighted Projection Regression Method for Uncertainty Quantification

Peng Chen 1, Nicholas Zabaras 1*

1 Materials Process Design and Control Laboratory, 101 Frank H. T. Rhodes Hall, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-3801, USA.

Received 6 July 2012; Accepted (in revised version) 28 December 2012
Available online 19 March 2013
doi:10.4208/cicp.060712.281212a

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.

AMS subject classifications: 65C30, 65C05, 60-08, 62J05

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Key words: Locally weighted projection regression, multi-output, adaptivity, uncertainty quantification.

*Corresponding author.
Email: nzabaras@gmail.com (N. Zabaras)
 

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