Quantification of model uncertainty: Calibration, model discrepancy, and identifiability

Paul D. Arendt, Daniel W. Apley, Wei Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

183 Scopus citations


To use predictive models in engineering design of physical systems, one should first quantify the model uncertainty via model updating techniques employing both simulation and experimental data. While calibration is often used to tune unknown calibration parameters of a computer model, the addition of a discrepancy function has been used to capture model discrepancy due to underlying missing physics, numerical approximations, and other inaccuracies of the computer model that would exist even if all calibration parameters are known. One of the main challenges in model updating is the difficulty in distinguishing between the effects of calibration parameters versus model discrepancy. We illustrate this identifiability problem with several examples, explain the mechanisms behind it, and attempt to shed light on when a system may or may not be identifiable. In some instances, identifiability is achievable under mild assumptions, whereas in other instances, it is virtually impossible. In a companion paper, we demonstrate that using multiple responses, each of which depends on a common set of calibration parameters, can substantially enhance identifiability.

Original languageEnglish (US)
Article number100908
JournalJournal of Mechanical Design, Transactions of the ASME
Issue number10
StatePublished - 2012


  • Gaussian processes
  • Kriging
  • calibration
  • identifiability
  • model updating
  • uncertainty quantification

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

Fingerprint Dive into the research topics of 'Quantification of model uncertainty: Calibration, model discrepancy, and identifiability'. Together they form a unique fingerprint.

Cite this