Experiences with nonintrusive polynomial Chaos and stochastic collocation methods for uncertainty analysis and design

By Michael S. Eldred

Sandia National Laboratories, Albuquerque, NM

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Non—intrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) methods are attractive techniques for uncertainty quantification due to their abilities to produce functional representations of stochastic variability and to achieve exponential convergence rates in statistics of interest. Whereas PCE estimates coefficients for known orthogonal polynomial basis functions, SC forms Lagrange interpolants for known coefficients. The latest results in comparing PCE and SC and embedding these methods within design under uncertainty will be presented.

Time permitting, a short overview of DAKOTA will also be provided. DAKOTA is the software delivery vehicle for much of the uncertainty quantification research at the DOE defense laboratories.


Mike Eldred Mike Eldred has been the project leader for the DAKOTA effort since its inception in 1994. The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible, extensible interface between analysis codes and iterative systems analysis methods. His research interests include surrogate—based optimization, uncertainty quantification, optimization under uncertainty, parallel processing, and object—oriented software development. A number of his publications are available on the DAKOTA web site. Mike received his B.S. in Aerospace Engineering from Virginia Tech in 1989, his M.S.E. and Ph.D. in Aerospace Engineering from the University of Michigan in 1990 and 1993, and is currently a Principal Member of the Technical Staff in the Optimization and Uncertainty Quantification Department within the Computation, Computers, Information, and Mathematics Center at Sandia National Laboratories.


Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000. Abstract (SAND2009-1444W)

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Researchers should cite this work as follows:

  • Michael S. Eldred (2009), "Experiences with nonintrusive polynomial Chaos and stochastic collocation methods for uncertainty analysis and design," http://nanohub.org/resources/5910.

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