### 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 language | English (US) |
---|---|

Pages (from-to) | 12-30 |

Number of pages | 19 |

Journal | Journal of Computational Physics |

Volume | 396 |

DOIs | |

State | Published - Nov 1 2019 |

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### 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.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 396, pp. 12-30. https://doi.org/10.1016/j.jcp.2019.06.032

}

TY - JOUR

T1 - Demonstration of the relationship between sensitivity and identifiability for inverse uncertainty quantification

AU - Wu, Xu

AU - Shirvan, Koroush

AU - Kozlowski, Tomasz

PY - 2019/11/1

Y1 - 2019/11/1

N2 - 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.

AB - 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.

KW - Identifiability

KW - Inverse uncertainty quantification

KW - Modular Bayesian approach

KW - Sensitivity

UR - http://www.scopus.com/inward/record.url?scp=85068137533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068137533&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2019.06.032

DO - 10.1016/j.jcp.2019.06.032

M3 - Article

AN - SCOPUS:85068137533

VL - 396

SP - 12

EP - 30

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -