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Adaptive Locally Weighted Projection Regression Method for Uncertainty Quantification

Published online by Cambridge University Press:  03 June 2015

Peng Chen  and
Nicholas Zabaras
Peng Chen
Affiliation:
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
Nicholas Zabaras*
Affiliation:
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
*
*Corresponding author.Email:nzabaras@gmail.com
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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 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.

Keywords

65C3065C0560-0862J05Locally weighted projection regressionmulti-outputadaptivityuncertainty quantification
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 4 , October 2013 , pp. 851 - 878
Copyright
Copyright © Global Science Press Limited 2013

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