Polynomial regression approaches using derivative information for uncertainty quantification

Oleg Roderick, Mihai Anitescu, Paul Fischer

Research output: Contribution to journalArticlepeer-review


In this work we describe a polynomial regression approach that uses derivative information for analyzing the performance of a complex system that is described by a mathematical model depending on several stochastic parameters. We construct a surrogate model as a goal-oriented projection onto an incomplete space of polynomials; find coordinates of the projection by regression; and use derivative information to significantly reduce the number of the sample points required to obtain a good model. The simplified model can be used as a control variate to significantly reduce the sample variance of the estimate of the goal. For our test model, we take a steady-state description of heat distribution in the core of the nuclear reactor core, and as our goal we take the maximum centerline temperature in a fuel pin. For this case, the resulting surrogate model is substantially more computationally efficient than random sampling or approaches that do not use derivative information, and it has greater precision than linear models.

Original languageEnglish (US)
Pages (from-to)122-139
Number of pages18
JournalNuclear Science and Engineering
Issue number2
StatePublished - Feb 2010
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear Energy and Engineering


Dive into the research topics of 'Polynomial regression approaches using derivative information for uncertainty quantification'. Together they form a unique fingerprint.

Cite this