Variable fidelity regression using low fidelity function blackbox and sparsification

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1 Citation (Scopus)

Abstract

We consider construction of surrogate models based on variable fidelity samples generated by a high fidelity function (an exact representation of some physical phenomenon) and by a low fidelity function (a coarse approximation of the exact representation). A surrogate model is constructed to replace the computationally expensive high fidelity function. For such tasks Gaussian processes are generally used. However, if the sample size reaches a few thousands points, a direct application of Gaussian process regression becomes impractical due to high computational costs. We propose two approaches to circumvent this difficulty. The first approach uses approximation of sample covariance matrices based on the Nyström method. The second approach relies on the fact that engineers often can evaluate a low fidelity function on the fly at any point using some blackbox; thus each time calculating prediction of a high fidelity function at some point, we can update the surrogate model with the low fidelity function value at this point. So, we avoid issues related to the inversion of large covariance matrices — as we can construct model using only a moderate low fidelity sample size. We applied developed methods to a real problem, dealing with an optimization of the shape of a rotating disk.

Original languageEnglish
Title of host publicationConformal and Probabilistic Prediction with Applications - 5th International Symposium, COPA 2016, Proceedings
EditorsJesus Vega, Alexander Gammerman, Zhiyuan Luo, Vladimir Vovk
PublisherSpringer Verlag
Pages147-164
Number of pages18
ISBN (Print)9783319333946
DOIs
Publication statusPublished - 2016
Externally publishedYes
Event5th International Symposium on Conformal and Probabilistic Prediction with Applications, COPA 2016 - Madrid, Spain
Duration: 20 Apr 201622 Apr 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9653
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Symposium on Conformal and Probabilistic Prediction with Applications, COPA 2016
Country/TerritorySpain
CityMadrid
Period20/04/1622/04/16

Keywords

  • Cokriging
  • Gaussian process
  • Multifidelity data
  • Nonlinear regression
  • Nyström approximation

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