Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian process, Part 1: Theory

Xu Wu, Tomasz Kozlowski, Hadi Meidani, Koroush Shirvan

Research output: Contribution to journalArticlepeer-review


In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. “Expert opinion” and “user self-evaluation” have been widely used to specify computer model input uncertainties in previous uncertainty, sensitivity and validation studies. Inverse Uncertainty Quantification (UQ) is the process to inversely quantify input uncertainties based on experimental data in order to more precisely quantify such ad-hoc specifications of the input uncertainty information. In this paper, we used Bayesian analysis to establish the inverse UQ formulation, with systematic and rigorously derived metamodels constructed by Gaussian Process (GP). Due to incomplete or inaccurate underlying physics, as well as numerical approximation errors, computer models always have discrepancy/bias in representing the realities, which can cause over-fitting if neglected in the inverse UQ process. The model discrepancy term is accounted for in our formulation through the “model updating equation”. We provided a detailed introduction and comparison of the full and modular Bayesian approaches for inverse UQ, as well as pointed out their limitations when extrapolated to the validation/prediction domain. Finally, we proposed an improved modular Bayesian approach that can avoid extrapolating the model discrepancy that is learnt from the inverse UQ domain to the validation/prediction domain.

Original languageEnglish (US)
Pages (from-to)339-355
Number of pages17
JournalNuclear Engineering and Design
StatePublished - Aug 15 2018


  • Bayesian calibration
  • Gaussian process
  • Inverse uncertainty quantification
  • Model discrepancy
  • Modular Bayesian

ASJC Scopus subject areas

  • Mechanical Engineering
  • Nuclear and High Energy Physics
  • Safety, Risk, Reliability and Quality
  • Waste Management and Disposal
  • General Materials Science
  • Nuclear Energy and Engineering


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