Local and Dimension Adaptive Stochastic Collocation for Uncertainty Quantification

  • John D. Jakeman
  • Stephen G. Roberts
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 88)


In this paper we present a stochastic collocation method for quantifying uncertainty in models with large numbers of uncertain inputs and non-smooth input-output maps. The proposed algorithm combines the strengths of dimension adaptivity and hierarchical surplus guided local adaptivity to facilitate computationally efficient approximation of models with bifurcations/discontinuties in high-dimensional input spaces. A comparison is made against two existing stochastic collocation methods and found, in the cases tested, to significantly reduce the number of model evaluations needed to construct an accurate surrogate model. The proposed method is then used to quantify uncertainty in a model of flow through porous media with an unknown permeability field. A Karhunen–Loève expansion is used to parameterize the uncertainty and the resulting mean and variance in the speed of the fluid and the time dependent saturation front are computed.


Sparse Grid Error Indicator Permeability Field Stochastic Collocation Grid Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank Jaideep Ray of Sandia National Laboratories, Livermore, CA, USA for providing us with the model discussed in Sect. 6.1.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia

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