Demonstration of the relationship between sensitivity and identifiability for inverse uncertainty quantification

Xu Wu, Koroush Shirvan, Tomasz Kozlowski

Research output: Contribution to journalArticle

Abstract

Inverse Uncertainty Quantification (UQ), or Bayesian calibration, is the process to quantify the uncertainties of random input parameters based on experimental data. The introduction of model discrepancy term is significant because “over-fitting” can theoretically be avoided. But it also poses challenges in the practical applications. One of the mostly concerned and unresolved problem is the “lack of identifiability” issue. With the presence of model discrepancy, inverse UQ becomes “non-identifiable” in the sense that it is difficult to precisely distinguish between the parameter uncertainties and model discrepancy when estimating the calibration parameters. Previous research to alleviate the non-identifiability issue focused on using informative priors for the calibration parameters and the model discrepancy, which is usually not a viable solution because one rarely has such accurate and informative prior knowledge. In this work, we show that identifiability is largely related to the sensitivity of the calibration parameters with regards to the chosen responses. We adopted an improved modular Bayesian approach for inverse UQ that does not require priors for the model discrepancy term. The relationship between sensitivity and identifiability was demonstrated with a practical example in nuclear engineering. It was shown that, in order for a certain calibration parameter to be statistically identifiable, it should be significant to at least one of the responses whose data are used for inverse UQ. Good identifiability cannot be achieved for a certain calibration parameter if it is not significant to any of the responses. It is also demonstrated that “fake identifiability” is possible if model responses are not appropriately chosen, or if inaccurate but informative prior distributions are specified.

Original languageEnglish (US)
Pages (from-to)12-30
Number of pages19
JournalJournal of Computational Physics
Volume396
DOIs
StatePublished - Nov 1 2019

Fingerprint

Uncertainty Quantification
Identifiability
Calibration
Demonstrations
Discrepancy
sensitivity
Model
Nuclear engineering
Overfitting
Parameter Uncertainty
Term
Inaccurate
Prior distribution
Prior Knowledge
Bayesian Approach
Relationships
Uncertainty
Quantify
Experimental Data
estimating

Keywords

  • Identifiability
  • Inverse uncertainty quantification
  • Modular Bayesian approach
  • Sensitivity

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

Demonstration of the relationship between sensitivity and identifiability for inverse uncertainty quantification. / Wu, Xu; Shirvan, Koroush; Kozlowski, Tomasz.

In: Journal of Computational Physics, Vol. 396, 01.11.2019, p. 12-30.

Research output: Contribution to journalArticle

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